Patent Publication Number: US-9847920-B2

Title: Communication control device, communication control method, and computer readable storage medium for specifying an upper limit of a network connection

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2016-033092, filed on Feb. 24, 2016, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to an vacant band specification program, an vacant band specification device, and an vacant band specification method. 
     BACKGROUND 
     In the related art, there is a technology for specifying an upper limit of an vacant band in a network that connects devices. For example, there is a binary search technology of path load for specifying an upper limit of an vacant band in a network based on comparison of a transmission rate with a reception rate in magnitude. 
     For example, as the related art, there is a technology for estimating an available bandwidth of a channel by transmitting a test stream to a reception node, receiving the returned test stream, measuring quality information such as the round-trip time or a packet loss rate, and applying the quality information to a NW analysis model. 
     An example of the related art includes Japanese Laid-open Patent Publication No. 2008-278207. 
     SUMMARY 
     According to an aspect of the invention, a communication control device includes a memory, and a processor coupled to the memory and the processor configured to: transmit packets from the communication control device to a network device at each of a plurality of transmission rates, acquire a plurality of index values respectively indicating amounts of packet loss at the plurality of transmission rates, specify, among the plurality of transmission rates, a first transmission rate on which a corresponding index value among the plurality of index values has a dependence, and specify an upper limit of a vacant band between the communication control device and the network device based on the first transmission rate. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is an explanatory diagram illustrating an example of an vacant band specification method according to an embodiment; 
         FIG. 2  is an explanatory diagram illustrating an example of a communication system according to Embodiment 1; 
         FIG. 3  is a block diagram illustrating a hardware configuration example of a first acceleration device; 
         FIG. 4  is a block diagram illustrating a functional configuration example of the vacant band specification device; 
         FIG. 5  is an explanatory diagram illustrating an example of the stored content of a management table according to Embodiment 1; 
         FIG. 6  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 1 is specified; 
         FIG. 7  is an explanatory diagram illustrating an example in which the transmission rate in a case where the transmission rate and the packet loss rate have the proportion relation is specified; 
         FIG. 8  is an explanatory diagram illustrating another example in which the transmission rate in a case where the transmission rate and the packet loss rate have the proportion relation is specified; 
         FIG. 9  is a (first) explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 1 is more accurately specified; 
         FIG. 10  is a (second) explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 1 is more accurately specified; 
         FIG. 11  is a (first) flowchart illustrating an example of a specification process procedure according to Embodiment 1; 
         FIG. 12  is a (second) flowchart illustrating an example of the specification process procedure according to Embodiment 1; 
         FIG. 13  is a (first) sequence diagram illustrating an operation example of the communication system according to Embodiment 1; 
         FIG. 14  is a (second) sequence diagram illustrating an operation example of the communication system according to Embodiment 1; 
         FIG. 15  is an explanatory diagram illustrating an example of a communication system according to Embodiment 2; 
         FIG. 16  is an explanatory diagram illustrating an example of the stored content of a management table according to Embodiment 2; 
         FIG. 17  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 2 is specified; 
         FIG. 18  is an explanatory diagram illustrating an example in which the transmission rate in a case where the transmission rate and the packet loss rate have the correlation is specified; 
         FIG. 19  is a (first) explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 2 is more accurately specified; 
         FIG. 20  is a (second) explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 2 is more accurately specified; 
         FIG. 21  is a (first) flowchart illustrating an example of a specification process procedure according to Embodiment 2; 
         FIG. 22  is a (second) flowchart illustrating an example of the specification process procedure according to Embodiment 2; 
         FIG. 23  is a (first) sequence diagram illustrating an operation example of the communication system according to Embodiment 2; 
         FIG. 24  is a (second) sequence diagram illustrating an operation example of the communication system according to Embodiment 2; 
         FIG. 25  is an explanatory diagram illustrating an example of a communication system according to Embodiment 3; 
         FIG. 26  is an explanatory diagram illustrating an example of the stored content of a management table according to Embodiment 3; 
         FIG. 27  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 3 is specified; 
         FIG. 28  is a (first) flowchart illustrating an example of a specification process procedure according to Embodiment 3; 
         FIG. 29  is a (second) flowchart illustrating an example of the specification process procedure according to Embodiment 3; 
         FIG. 30  is a (first) sequence diagram illustrating an operation example of the communication system according to Embodiment 3; 
         FIG. 31  is a (second) sequence diagram illustrating an operation example of the communication system according to Embodiment 3; 
         FIG. 32  is an explanatory diagram illustrating an example of a communication system according to Embodiment 4; 
         FIG. 33  is a (first) flowchart illustrating an example of a specification process procedure according to Embodiment 4; 
         FIG. 34  is a (second) flowchart illustrating an example of the specification process procedure according to Embodiment 4; 
         FIG. 35  is a (first) sequence diagram illustrating an operation example of the communication system according to Embodiment 4; and 
         FIG. 36  is a (second) sequence diagram illustrating an operation example of the communication system according to Embodiment 4. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     However, in the aforementioned related art, it is difficult to accurately specify the upper limit of the vacant band in some cases. For example, the reception rate may be decreased by the packet loss, a searching approach to the binary search based on the comparison of the transmission rate with the reception rate in magnitude may be wrong, and a value less than an actual upper limit may be specified as the upper limit of the vacant band. 
     One aspect of the disclosure is to provide an vacant band specification program, an vacant band specification device, and an vacant band specification method capable of accurately specifying an upper limit of an vacant band. 
     Hereinafter, embodiments of an vacant band specification program, an vacant band specification device, and an vacant band specification method will be described in detail with reference to the drawings. 
     Example of Vacant Band Specification Method According to Embodiment 
       FIG. 1  is an explanatory diagram illustrating an example of an vacant band specification method according to an embodiment. In  FIG. 1 , the vacant band specification device  100  is a computer that specifies an upper limit of an vacant band of a network  150  that connects the vacant band specification device and an opposing device. 
     Here, as illustrated in graphs  110  and  120 , if a transmission rate when packets are transmitted in the network  150  increases, a reception rate also tends to increase until the transmission rate reaches the upper limit of the vacant band. Meanwhile, as illustrated in the graphs  110  and  120 , after the transmission rate reaches the upper limit of the vacant band, packets are discarded as many as the transmission rate exceeds the upper limit of the vacant band, and the reception rate tends not to increase. 
     The transmission rate is a value indicating a data amount transmitted for a unit time. A unit of the transmission rate is, for example, bits per second (bps). The reception rate is a value indicating a data amount received for a unit time. A unit of the reception rate is, for example, bps. 
     Thus, for example, a case where an upper limit of an vacant band is searched for by acquiring a reception rate when packets are transmitted at a predetermined transmission rate and determining whether or not the upper limit of the vacant band is greater than the transmission rate through the comparison of the transmission rate with the reception rate in magnitude is considered. 
     Specifically, in a case where the transmission rate is greater than the reception rate, it is determined that the upper limit of the vacant band is less than the transmission rate. In a case where the transmission rate is equal to or less than the reception rate, it is determined that the upper limit of the vacant band is greater than the transmission rate. 
     However, in this case, it is difficult to specify the upper limit of the vacant band of the network  150  with accuracy. Specifically, if packet loss occurs in the network  150 , the reception rate decreases, and thus, it is difficult to determine whether or not the upper limit of the vacant band is greater than a predetermined transmission rate in some cases. The pass loss means that the packet does not reach a destination. 
     In the example of the graph  110 , an increase in the reception rate is suppressed by the packet loss in a range of reference sign  111 , and it is difficult to determine whether or not the upper limit of the vacant band is greater than the transmission rate for the transmission rate included in the range of reference sign  111  in some cases. 
     More specifically, in the network  150  including a radio section, the packet loss may occur due to electromagnetic interference or phasing in the radio section, and thus, it is difficult to determine whether or not the upper limit of the vacant band is greater than a predetermined transmission rate in some cases. As a result, a value less than an actual maximum value is specified as the upper limit of the vacant band, and thus, it is difficult to more efficiently use the network  150 . 
     Thus, in the present embodiment, an vacant band specification method capable of specifying the upper limit of the vacant band of the network  150  with accuracy even though the packet loss occurs and the reception rate becomes low will be described. 
     In the example of  FIG. 1 , a case where the vacant band specification device  100  specifies the upper limit of the vacant band of the network  150  that connects the first device  130  and a second device  140  as the opposing device of the first device  130  will be described. 
     Here, the vacant band specification device  100  may be the first device  130 . An example in which the vacant band specification device  100  is the first device  130  may refer to Embodiment 1, Embodiment 2, or Embodiment 3 to be described below. The vacant band specification device  100  may be the second device  140 . The vacant band specification device  100  may be a third device (not illustrated) different from the first device  130  or the second device  140 . 
     Here, specifically, a case where the vacant band specification device  100  specifies the upper limit of the vacant band of the network  150  that connects the vacant band specification device and the second device  140  as the opposing device by using the example in which the vacant band specification device  100  is the first device  130  will be described. 
     ( 1 - 1 ) The vacant band specification device  100  causes the packets to be transmitted from the first device  130  to the second device  140  at a plurality of transmission rates. For example, the plurality of transmission rates is previously set to the vacant band specification device  100 . Specifically, the plurality of transmission rates is transmission rates between the maximum transmission rate and the minimum transmission rate which are previously set to the vacant band specification device  100 . 
     For example, the maximum transmission rate is the maximum value of the data amount capable of being transmitted by the vacant band specification device  100  for a unit time. For example, the minimum transmission rate is, for example, 0.1 mega bits per second (Mbps). For example, the vacant band specification device  100  transmits a plurality of packets to the second device  140  from the vacant band specification device  100  at the plurality of transmission rates. 
     ( 1 - 2 ) The vacant band specification device  100  acquires an index value indicating of the amount of packet loss at each transmission rate. The index value indicating the amount of packet loss is, for example, a packet loss rate indicating a percentage of packets which are not received by the second device  140  with respect to the transmitted packets. For example, the vacant band specification device  100  receives the packet loss rate when the packets are transmitted at the plurality of transmission rates from the second device  140 . An example in which the vacant band specification device  100  uses the packet loss rate as the index value indicating the amount of packet loss may refer to Embodiment 1 or Embodiment 2 to be described below. 
     In a case where the network  150  includes the radio section, a device as one end of the radio section may retransmit the packets when the packet loss occurs in the radio section, and the second device  140  may be difficult to recognize the packet loss. Meanwhile, since the device as one end of the radio section retransmits the packets, a time taken for the packets transmitted from the first device  130  to be received by the second device  140  increases, and a time taken for the second device  140  to respond to the first device  130  tends to increase. 
     Thus, the index value indicating the amount of packet loss may be, for example, the round trip time (RTT). An example in which the vacant band specification device  100  uses the RTT as the index value indicating the amount of packet loss may refer to Embodiment 3 to be described below. 
     ( 1 - 3 ) The vacant band specification device  100  specifies the transmission rate, among the plurality of transmission rates, in a case where the transmission rate and the index value indicating the amount of packet loss have a dependence relation, based on the index value for each transmission rate. For example, the dependence relation is a proportional relation. An example in which the vacant band specification device  100  uses the proportional relation as the dependence relation may refer to Embodiment 1 to be described below. 
     The dependence relation may be, for example, a correlation. For example, in a case where a correlation coefficient between a transmission rate group and an index value group corresponding to the transmission rate group is equal to or greater than a threshold, the vacant band specification device  100  specifies the transmission rate of the transmission rate group as the transmission rates in a case where the transmission rate and the index value have the correlation. An example in which the vacant band specification device  100  uses the correlation as the dependence relation may refer to Embodiment 2 to be described below. 
     ( 1 - 4 ) The vacant band specification device  100  specifies the upper limit of the vacant band between the first device  130  and the second device  140  based on the specified result. Here, as illustrated in the graph  120 , if the transmission rate increases, the packets tend to be randomly discarded until the transmission rate reaches the upper limit of the vacant band. In other words, the transmission rate and the index value indicating the amount of packet loss are difficult to have the dependence relation until the transmission rate reaches the upper limit of the vacant band. Thus, the vacant band specification device  100  may determine that the transmission rate other than the transmission rate in a case where the transmission rate and the index value have the specified dependence relation is equal to or less than the upper limit of the vacant band. 
     As illustrated in the graphs  110  and  120 , if the transmission rate increases, the packets tends to be discarded as many as the transmission rate exceeds the upper limit of the vacant band after the transmission rate reaches the upper limit of the vacant band. In other words, in a case where the transmission rate exceeds the upper limit of the vacant band, the transmission rate and the index value indicating the amount of packet loss tend to have the dependence relation. Thus, the vacant band specification device  100  may determine that the transmission rates in a case where the transmission rate and the index value have the specified dependence relation is equal to or greater than the upper limit of the vacant band. 
     Based on these factors, for example, the vacant band specification device  100  specifies the minimum value of the transmission rates in a case where the transmission rate and the index value have the specified dependence relation, as the upper limit of the vacant band between the vacant band specification device and the second device  140  as the opposing device. For example, the vacant band specification device  100  may specify a value which is less than the transmission rate in a case where the transmission rate and the index value have the specified dependence relation and is greater than the transmission rate other than the transmission rate in a case where the transmission rate and the index value have the specified dependence relation, as the upper limit of the vacant band. 
     Accordingly, the vacant band specification device  100  can specify the upper limit of the vacant band of the network  150  even without referring to the reception rate. Therefore, the vacant band specification device  100  can improve accuracy in specifying the upper limit of the vacant band of the network  150  in which the packet loss easily occurs and the reception rate is easily disturbed. For example, the vacant band specification device  100  can keep a range of reference sign  111  of the graph  110  from being specified as the upper limit of the vacant band. 
     The vacant band specification device  100  may transmit, to the second device  140 , the packets at a new transmission rate which is less than the transmission rate in a case where the transmission rate and the index value have the specified dependence relation and is greater than the transmission rate other than the transmission rate in a case where the transmission rate and the index value have the specified dependence relation. The vacant band specification device  100  may further improve accuracy in specifying the upper limit of the vacant band by acquiring the index value corresponding to the new transmission rate and specifying whether or not the new transmission rate is the transmission rate in a case where the transmission rate and the index value have the dependence relation. 
     Description of Embodiment 1 
     Hereinafter, Embodiment 1 will be described. In Embodiment 1, a case where the vacant band specification device  100  uses the proportional relation as the dependence relation between the transmission rate and the index value indicating the amount of packet loss will be described. 
     Example of Communication System  200  According to Embodiment 1 
     Hereinafter, an example of the communication system  200  according to Embodiment 1 to which the vacant band specification device  100  illustrated in  FIG. 1  is applied will be described with reference to  FIG. 2 . 
       FIG. 2  is an explanatory diagram illustrating an example of the communication system  200  according to Embodiment 1. In  FIG. 2 , the communication system  200  includes a first calculation device  201 , a first acceleration device  202 , a second calculation device  203 , and a second acceleration device  204 . 
     In the communication system  200 , the first acceleration device  202  and the second acceleration device  204  are connected via a wired or wireless network  210 . The network  210  is, for example, a local area network (LAN), a wire area network (WAN), or the Internet. 
     The first calculation device  201  is connected to the first acceleration device  202 . The first calculation device  201  is a computer which communicates with the first acceleration device  202  by a transmission control protocol (TCP) and transmits or receives packets to or from the second calculation device  203  via the first acceleration device  202 . 
     The first acceleration device  202  is a computer that increases the transmission rate up to the upper limit of the vacant band of the network  210  by replacing the TCP with a high-speed communication protocol and utilizes the network  210  more efficiently. Thus, the first acceleration device  202  tends to be desired to specify the upper limit of the vacant band of the network  210 . For example, the first acceleration device  202  corresponds to the first device  130  illustrated in  FIG. 1 . 
     The second calculation device  203  is a computer that is connected to the second acceleration device  204 , communicates with the second acceleration device  204  by the TCP, and transmits or receives the packets to or from the first calculation device  201  via the second acceleration device  204 . 
     The second acceleration device  204  is a computer that increases the transmission rate up to the upper limit of the vacant band of the network  210  by replacing the TCP with a high-speed communication protocol and utilizes the network  210  more efficiently. Thus, the second acceleration device  204  tends to be desired to specify the upper limit of the vacant band of the network  210 . For example, the second acceleration device  204  corresponds to the second device  140  illustrated in  FIG. 1 . 
     In the following description, a case where the first acceleration device  202  operates as the vacant band specification device  100  and specifies the upper limit of the vacant band of the network  210  will be described. The second acceleration device  204  may also operate as the vacant band specification device  100 . 
     (Hardware Configuration Example of First Acceleration Device  202 ) 
     Hereinafter, a hardware configuration example of the first acceleration device  202  included in the communication system  200  illustrated in  FIG. 2  will be described with reference to  FIG. 3 . 
       FIG. 3  is a block diagram illustrating the hardware configuration example of the first acceleration device  202 . In  FIG. 3 , the first acceleration device  202  includes a central processing unit (CPU)  301 , a memory  302 , an interface (I/F)  303 , a disk drive  304 , and a disk  305 . The respective elements are connected via a bus  300 . 
     Here, the CPU  301  controls the entire first acceleration device  202 . For example, the memory  302  includes a read-only memory (ROM), a random-access memory (RAM), and a flash ROM. Specifically, the flash ROM or the ROM stores various programs, and the RAM is used as a work area of the CPU  301 . The program stored in the memory  302  is loaded to the CPU  301 , and causes the CPU  301  to perform a process on which coding is already performed. 
     The I/F  303  is connected to the network  210  through a communication channel, and is connected to another computer (for example, the second acceleration device  204  illustrated in  FIG. 2 ) via the network  210 . The I/F  303  controls input and output of data from another computer through the network  210  and an internal interface. The I/F  303  is, for example, a network interface card (NIC), or a LAN card. 
     The disk drive  304  controls reading or writing of data in the disk  305  under the control of the CPU  301 . The disk drive  304  is, for example, a magnetic disk drive. The disk  305  is a non-volatile memory that stores data written under the control of the disk drive  304 . The disk  305  is, for example, a magnetic disk or an optical disk. 
     The first acceleration device  202  may include, for example, a solid state drive (SSD), a semiconductor memory, a keyboard, a mouse, and a display in addition to the above-mentioned elements. The first acceleration device  202  may include the SSD and the semiconductor memory instead of the disk drive  304  and the disk  305 . 
     (Hardware Configuration Example of Second Acceleration Device  204 ) 
     For example, the hardware configuration example of the second acceleration device  204  included in the communication system  200  illustrated in  FIG. 2  is the same as the hardware configuration example of the first acceleration device  202  illustrated in  FIG. 3 , and thus, the description thereof will be omitted. 
     (Hardware Configuration Example of First Calculation Device  201  or Second Calculation Device  203 ) 
     For example, the hardware configuration example of the first calculation device  201  or the second calculation device  203  included in the communication system  200  illustrated in  FIG. 2  is the same as the hardware configuration example of the first acceleration device  202  illustrated in  FIG. 3 , and thus, the description thereof will be omitted. 
     (Functional Configuration Example of Vacant Band Specification Device  100 ) 
     Hereinafter, a functional configuration example of the vacant band specification device  100  according to Embodiment 1 will be described with reference to  FIG. 4 . 
       FIG. 4  is a block diagram illustrating a functional configuration example of the vacant band specification device  100 . The vacant band specification device  100  includes an instruction unit  401 , a measurement unit  402 , a setting unit  403 , a specification unit  404 , and a storage unit  405 . For example, the instruction unit  401  to the storage unit  405  are functions of a control unit, and the functions thereof are realized by causing the CPU  301  to execute the programs stored in a storage device such as the memory  302  or the disk  305  illustrated in  FIG. 3  or by the I/F  303 . The processing results of the respective functional units are stored in, for example, a storage area of the memory  302  or the disk  305 . 
     The instruction unit  401  notifies the measurement unit  402  of a measurement request for measurement of the index value indicating the amount of packet loss. For example, in a case where the communication between the first device  130  and the second device  140  is time out and the communication between the first device  130  and the second device  140  is not performed, the instruction unit  401  notifies the measurement unit  402  of the measurement request. The first device  130  and the second device  140  are the device as one end of the network  210  and the device as the other end thereof which are targets for specifying the upper limit of the vacant band. For example, the second device  140  has at least any one of a function of measuring the reception rate, a function of measuring the packet loss rate, and a function of responding that the packets are received. 
     Any one of the first device  130  and the second device  140  may be the vacant band specification device  100 . The first device  130  is, for example, the first acceleration device  202  illustrated in  FIG. 2 . The second device  140  is, for example, the second acceleration device  204  illustrated in  FIG. 2 . Accordingly, the instruction unit  401  can generate a trigger for starting the measurement of the measurement unit  402 . The vacant band specification device  100  may not include the instruction unit  401 , and the function of the instruction unit  401  may be included in the measurement unit  402  or the specification unit  404 . 
     The measurement unit  402  transmits the packets from the first device  130  to the second device  140  at the plurality of transmission rates. The plurality of transmission rates is the transmission rates calculated by dividing the transmission rate into sections from preset maximum transmission rate S n  to minimum transmission rate S 1 . For example, the measurement unit  402  transmits the packets from the first device  130  to the second device  140  at the plurality of transmission rates S 1  to S n  under the control of the setting unit  403 . 
     Specifically, if the vacant band specification device  100  is the first acceleration device  202 , the measurement unit  402  transmits test packets from the vacant band specification device to the second acceleration device  204  at the plurality of transmission rates S 1  to S n . The test packets are, for example, a plurality of packets. The test packet is, for example, a packet prepared by the vacant band specification device  100  in order to specify the upper limit of the vacant band. For example, the test packet may be a packet transmitted from the first calculation device  201  to the second calculation device  203  during an operation of the first calculation device  201 . Accordingly, the measurement unit  402  can check whether or not the amount of packet loss occurring in the network  210  by sending the packets to the network  210 . 
     Specifically, if the vacant band specification device  100  is the second acceleration device  204 , the measurement unit  402  transmits a transmission request for the test packets at the plurality of transmission rates S 1  to S n , to the first acceleration device  202 . Accordingly, the measurement unit  402  can transmit the test packets from the first acceleration device  202  to the vacant band specification device. Accordingly, the measurement unit  402  can check whether or not the amount of packet loss occurring in the network  210  by sending the packets to the network  210 . 
     Specifically, if the vacant band specification device  100  is a management device, the measurement unit  402  transmits a transmission request for the test packets at the plurality of transmission rates S 1  to S n  to the second acceleration device  204 , to the first acceleration device  202 . The management device is a device that is neither the first device  130  nor the second device  140 , and is, for example, a device that is neither the first acceleration device  202  nor the second acceleration device  204 . Accordingly, the measurement unit  402  can transmit the test packets to the second acceleration device  204  from the first acceleration device  202 . Accordingly, the measurement unit  402  can check whether or not the amount of packet loss occurring in the network  210  by sending the packets to the network  210 . 
     For example, the measurement unit  402  may acquire a reception rate corresponding to the transmission rate when the packets are transmitted whenever the packets are transmitted. The measurement unit  402  transmits the packets to the second device  140  from the first device  130  while gradually increasing the transmission rate from the minimum transmission rate by a predetermined amount until at least a ratio of an increase in the reception rate to an increase in the transmission rate is equal to or less than a predetermined value. 
     More specifically, the measurement unit  402  transmits the test packets while gradually increasing the transmission rate from the minimum transmission rate by the predetermined amount. In this case, the measurement unit  402  determines whether or not the ratio of the increase in the reception rate to the increase in the transmission rate is equal to or less the predetermined value. The predetermined value is, for example, a value when the increase in the reception rate with respect to the increase in the transmission rate halves. The measurement unit  402  transmits the test packets a predetermined number of times after the ratio of the increase in the reception rate to the increase in the transmission rate is equal to or less than the predetermined value, and then stops transmitting the test packets. Accordingly, the measurement unit  402  may change the transmit rate until the transmission rate reaches the maximum transmission rate and may not transmit the packets, and thus, it is possible to reduce the number of times the packets are transmitted. 
     For example, the measurement unit  402  may acquire a reception rate corresponding to the transmission rate when the packets are transmitted whenever the packets are transmitted. The measurement unit  402  transmits the packets from the first device  130  to the second device  140  while gradually decreasing the transmission rate from the maximum transmission rate by a predetermined amount until at least a ratio of a decrease in the reception rate to a decrease in the transmission rate is equal to or greater than a predetermined value. 
     More specifically, the measurement unit  402  transmits the test packets while gradually decreasing the transmission rate from the maximum transmission rate by the predetermined amount. In this case, the measurement unit determines whether or not the ratio of the decrease in the reception rate to the decrease in the transmission rate is equal to or greater than the predetermined value. The predetermined value is, for example, a value when the decrease in the reception rate with respect to the decrease in the transmission rate halves. The measurement unit  402  transmits the test packets a predetermined number of times after the ratio of the decrease in the reception rate to the decrease in the transmission rate is equal to or greater than the predetermined value, and then stops transmitting the test packets. Accordingly, the measurement unit  402  may change the transmit rate until the transmission rate reaches the maximum transmission rate and may not transmit the packets, and thus, it is possible to reduce the number of times the packets are transmitted. 
     The setting unit  403  receives the transmission rate used when the measurement unit  402  transmits the packets, and controls the transmission rate used when the measurement unit  402  transmits the packets. Accordingly, the setting unit  403  can cause the measurement unit  402  to transmit the packets at the plurality of transmission rates. The vacant band specification device  100  may not include the setting unit  403 , and the function of the setting unit  403  may be included in the measurement unit  402 . 
     The measurement unit  402  acquires the index value indicating the amount of packet loss for each transmission rate. The index value is, for example, a value indicating a percentage of packets which are not received by the second device  140  with respect to the packets transmitted from the first device  130  to the second device  140 . The index value is, for example, a packet loss rate. 
     Specifically, if the vacant band specification device  100  is the first acceleration device  202 , the measurement unit  402  receives the packet loss rates corresponding to the plurality of transmission rates S 1  to S n  from the second acceleration device  204 . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     Specifically, if the vacant band specification device  100  is the second acceleration device  204 , the measurement unit  402  measures the packet loss rates corresponding to the plurality of transmission rates S 1  to S n  in response to the reception of the test packets at the plurality of transmission rates S 1  to S n . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     Specifically, if the vacant band specification device  100  is the management device, the measurement unit  402  receives the packet loss rates corresponding to the plurality of transmission rates S 1  to S n  from the second acceleration device  204 . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     For example, the index value may be a value indicating a time from when the packets are transmitted from the first device  130  to when a response from the second device  140  in response to the packets transmitted from the first device  130  is received. The index value is, for example, the RTT. 
     Specifically, if the vacant band specification device  100  is the first acceleration device  202 , the measurement unit  402  receives a response from the second acceleration device  204  which receives the test packets at the plurality of transmission rates S 1  to S n . The measurement unit  402  measures the RTTs corresponding to the plurality of transmission rates S 1  to S n  based on the response from the second acceleration device  204 . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     Specifically, if the vacant band specification device  100  is the second acceleration device  204 , the measurement unit  402  transmits a response to the first acceleration device  202  in response to the reception of the test packets at the plurality of transmission rates S 1  to S n . The measurement unit  402  receives the RTTs corresponding to the plurality of transmission rates S 1  to S n  which are measured by the first acceleration device  202  from the first acceleration device  202 . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     Specifically, if the vacant band specification device  100  is the management device, the measurement unit  402  receives the RTTs corresponding to the plurality of transmission rates S 1  to S n  from the first acceleration device  202 . Accordingly, the measurement unit  402  can ascertain the amount of packet loss occurring in the network  210 . 
     The specification unit  404  specifies the transmission rate, among the plurality of transmission rates, in a case where the transmission rate and the index value indicating the amount of packet loss have the dependence relation, based on the index value for each transmission rate. The transmission rates in a case where the transmission rate and the index value have the dependence relation is a transmission rate of the plurality of transmission rates S 1  to S n , which is included in a range in which the index value indicating the amount of packet loss monotonously increases depending on the increase in the transmission rate. 
     For example, the specification unit  404  calculates slopes of the packet loss rates of the transmission rates including the minimum transmission rate S 1  to the predetermined transmission rate S n  (n=2, 3, . . . , and n) among the plurality of transmission rates S 1  to S n . Subsequently, the specification unit  404  specifies any combination of adjacent transmission rates S k−1  and S k  of which the slopes are comparatively greatly changed. Specifically, the specification unit  404  specifies the combination of the transmission rate S k−1  and the transmission rate S k  of which an absolute value of a difference between the slopes is equal to or greater than a threshold e. 
     The specification unit  404  specifies a range of the specified transmission rate S k  to the maximum transmission rate S n , as a range of transmission rates S max  to S n  in a case where the transmission rate and the index value have the proportional relation. S max  means a maximum value of the values which may become the upper limit of the vacant band. The specification unit  404  specifies a range of the minimum transmission rate S 1  to the specified transmission rate S k−1 , as a range of transmission rates S 1  to S min  in a case where the transmission rate and the index value do not have the correlation. S min  means a minimum value of the values which may become the upper limit of the vacant band. Accordingly, the specification unit  404  can specify a range of S min  to S max  of the values which may become the upper limit of the vacant band. 
     the transmission rates in a case where the transmission rate and the index value have the dependence relation may be a transmission rate of the plurality of transmission rates S 1  to S n , which is included in the range in which the correlation coefficient between the transmission rate and the index value indicating the amount of packet loss has a comparatively greatly fixed value. The specification unit  404  calculates the correlation coefficients of the minimum transmission rate S 1  to the predetermined transmission rate S n  (n=2, 3, . . . , and n) among the plurality of transmission rates S 1  to S n . Subsequently, the specification unit  404  specifies any combination of adjacent transmission rates S k−1  and S k  of which the correlation coefficients are comparatively greatly changed. 
     Specifically, the specification unit  404  specifies the combination of the transmission rate S k−1  and the transmission rate S k  of which an absolute value of a difference between the correlation coefficients is equal to or greater than a threshold e. Specifically, the specification unit  404  may specify the combination of the transmission rate S k−1  and the transmission rate S k  of which the correlation coefficient corresponding to the transmission rate S k  is equal to or greater than a threshold R and the absolute value of the difference between the correlation coefficients is equal to or greater than the threshold e. 
     The specification unit  404  specifies the specified range of the transmission rate S k  to the maximum transmission rate S n , as a range of transmission rates S max  to S n  in a case where the transmission rate and the index value have the correlation. The specification unit  404  specifies a range of the minimum transmission rate S 1  to the transmission rate S k−1 , as a range of transmission rates S 1  to S min  in a case where the transmission rate and the index value do not have the correlation. Accordingly, the specification unit  404  can specify a range of S min  to S max  of the values which may become the upper limit of the vacant band. 
     For example, the specification unit  404  may specify the transmission rates in a case where the transmission rate and the index value have the dependence relation based on the index value, among the index values for the respective transmission rates, in a case where the ratio of the increase in the reception rate to the increase in the transmission rate is equal to or less than the predetermined value. For example, the specification unit  404  calculates a difference between reception rates of the adjacent transmission rates S k−1  and S k  among the plurality of transmission rates S 1  to S n  in sequence from the minimum transmission rate S 1 . The specification unit  404  specifies the transmission rates in a case where the transmission rate and the index value have the dependence relation based on the index values corresponding to the transmission rates between the minimum transmission rate S 1  and the transmission rate S k+a  after “a” number of transmission rates from the transmission rate S k  when the difference between the reception rates is equal to or less than a predetermined value. Accordingly, the specification unit  404  can reduce a processing amount by reducing the number of index values used for calculating the correlation coefficient. 
     The specification unit  404  specifies the transmission rate, among the plurality of transmission rates, in a case where the transmission rate and the index value indicating the amount of packet loss have the dependence relation based on other index values acquired by removing components having a predetermined frequency or more from the index values for the respective transmission rates. For example, the specification unit  404  calculates signals acquired by reducing components having a predetermined frequency or more by inputting signals acquired by arranging the index values for the respective transmission rates in a sequence of time to a low-pass filter. The low-pass filter may be realized by hardware, or may be realized by software. 
     The specification unit  404  uses the detected signals as the index values for the respective transmission rates. Accordingly, the specification unit  404  can change the index value to an index value of which the fluctuation is suppressed in a case where the index value indicating the amount of packet loss is fluctuated due to a factor randomly occurring in the network  210 . For example, the randomly occurred factor is communication of another device that uses the network  210 . 
     The specification unit  404  specifies the upper limit of the vacant band between the first device  130  and the second device  140  based on the specified result. For example, in a case where the range of the transmission rates S max  to S n  in a case where the transmission rate and the index value have the correlation, the specification unit  404  specifies the transmission rate S max  as the upper limit of the vacant band. For example, the specification unit  404  may specify a center value (S min  S max )/2 of the range of S min  to S max  of the values which may become the upper limit of the vacant band, as the upper limit of the vacant band. Accordingly, the specification unit  404  may accurately specify the upper limit of the vacant band for the network  210  in which the packet loss easily occurs and which is difficult to ascertain a change in the reception rate depending on a change in the transmission rate with accuracy. 
     The storage unit  405  stores the result specified by the specification unit  404 . For example, the storage unit  405  stores the result specified by the specification unit  404  in a management table to be described below in  FIG. 5 . Accordingly, the storage unit  405  can cause the result specified by the specification unit  404  to be referred to. The vacant band specification device  100  may not include the storage unit  405 , and the function of the storage unit  405  may be included in the specification unit  404 . 
     The measurement unit  402  may transmit the packets from the first device  130  to the second device  140  at another transmission rate which is less than the transmission rate in a case where the transmission rate and the index value have the dependence relation and is greater than the transmission rate in a case where the transmission rate and the index value do not have the dependence relation. 
     For example, the measurement unit  402  transmits the packets from the first device  130  to the second device  140  at the transmission rate S a  which is less than the transmission rate S max  in a case where the transmission rate and the index value have the dependence relation and is greater than the transmission rate S min  in a case where the transmission rate and the index value do not have the dependence relation. Accordingly, the measurement unit  402  can transmit the test packets in order to acquire the index value used when the range of S min  to S max  of the values which may become the upper limit of the vacant band is further narrowed. 
     The measurement unit  402  may acquire the index value indicating the amount of packet loss at another transmission rate. For example, the measurement unit  402  acquires the packet loss rate at the transmission rate S a . For example, the measurement unit  402  may not acquire the RTT at the transmission rate S a . Accordingly, the measurement unit  402  can acquire the index value used when the range of S min  to S max  of the values which may become the upper limit of the vacant band is further narrowed. 
     The specification unit  404  may specify whether or not another transmission rate is the transmission rate in a case where the transmission rate and the index value have the dependence relation based on the index value at another transmission rate. The specification unit  404  may determine whether or not the transmission rate S a  is the transmission rate in a case where the transmission rate and the index value have the dependence relation and the transmission rate as S max . Accordingly, the measurement unit  402  can further narrow the range of S min  to S max  of the values which may become the upper limit of the vacant band. 
     The specification unit  404  specifies the upper limit of the vacant band between the first device  130  and the second device  140  based on the range of S min  to S max  of the values with which the upper limit of the narrowed vacant band can be acquired. For example, the specification unit  404  specifies a center value (S min  S max )/2 of the range of S min  to S max  of the values which may become the upper limit of the vacant band. Accordingly, the specification unit  404  can specify the upper limit of the vacant band with more accuracy. 
     (Flow for Specifying Upper Limit of Vacant Band of Network  210 ) 
     Hereinafter, a flow for specifying the upper limit of the vacant band of the network  210  according to Embodiment 1 will be described with reference to  FIGS. 5 to 10 . 
       FIG. 5  is an explanatory diagram illustrating an example of the stored content of a management table  500  according to Embodiment 1. For example, the management table  500  is realized by the storage area such as the memory  302  or the disk  305  illustrated in  FIG. 3 . As illustrated in  FIG. 5 , the management table  500  includes fields such as the transmission rate, the reception rate, the packet loss rate, and proportion determination. 
     The proportion determination is a flag indicating whether or not the transmission rate, the reception rate, and the packet loss rate associated with the proportion determination are information in a case where the transmission rate and the packet loss rate have the proportional relation. For example, the proportion determination is “o” in a case where the transmission rate and the packet loss rate have the proportional relation, and is “x” in a case where the transmission rate and the packet loss rate do not have the proportional relation. The transmission rate is a transmission rate range in a case where the proportional relation is expressed by the proportion determination. The reception rate is a reception rate range in a case where the proportional relation is expressed by the proportion determination. The packet loss rate is a packet loss rate range in a case where the proportional relation is expressed by the proportion determination. 
     The management table  500  may classify the transmission rates into a range of the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation and a range of the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation, and may manage the classified transmission rate ranges. In other words, the management table  500  may classify the transmission rates into a range of the transmission rates which are equal to or greater than the upper limit of the vacant band and a range of the transmission rates which are less than the upper limit of the vacant band, and may manage the classified transmission rate ranges. 
       FIG. 6  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 1 is specified. In  FIG. 6 , ( 6 - 1 ) the first acceleration device  202  acquires the preset maximum transmission rate S n  and minimum transmission rate S 1 . Subsequently, the first acceleration device  202  divides the transmission rates between the maximum transmission rate S n  and the minimum transmission rate S 1 , and calculates n number of transmission rates S 1  to S n . 
     As illustrated in  FIG. 6 , an example in which the transmission rates S 1  to S k−1  of n number of transmission rates S 1  to S n  are equal to or less than the vacant band and the transmission rates S k  to S n  thereof are equal to or greater than the vacant band will be described. In the following description, the first acceleration device  202  may classify n number of transmission rates S 1  to S n  into the transmission rates S 1  to S k−1  which are equal to or less than the vacant band and the transmission rates S k  to S n  which are equal to or greater than the vacant band. 
     Here, the first acceleration device  202  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204 . The first acceleration device  202  transmits the test packets to the second acceleration device  204  at n number of calculated transmission rates S 1  to S n  after the measurement request is transmitted. The test packets are, for example, a plurality of packets. 
     Meanwhile, the second acceleration device  204  measures reception rates P 1  to P n  and packet loss rates Per 1  to Per n  which correspond to the transmission rates S 1  to S n , and transmits the measured values to the first acceleration device  202 . The first acceleration device  202  receives the reception rates P 1  to P n  and the packet loss rates Per 1  to Per n  which correspond to the transmission rates S 1  to S n . 
     ( 6 - 2 ) The first acceleration device  202  specifies the transmission rate of the transmission rates S 1  to S n , in a case where the transmission rate and the packet loss rate have the proportion relation based on the received packet loss rate Per 1  to Per n . In other words, the first acceleration device  202  specifies the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportion relation. Here,  FIG. 7  will be described. 
       FIG. 7  is an explanatory diagram illustrating an example in which the transmission rate in a case where the transmission rate and the packet loss rate have the proportion relation is specified. In  FIG. 7 , ( 7 - 1 ) the first acceleration device  202  substitutes the transmission rate S n , the transmission rate S x , the packet loss rate Per n , and the packet loss rate Per k  in the following expression (1) while sequentially changing a variable x to n−1, n−2, . . . , and 1. Accordingly, the first acceleration device  202  calculates the slope I x,n  of the packet loss rate between the transmission rate S n  and the transmission rate S x  for each of x=n−1, n−2, . . . , and 1. 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       x 
                       , 
                       n 
                     
                   
                   = 
                   
                     
                       
                         Per 
                         n 
                       
                       - 
                       
                         Per 
                         x 
                       
                     
                     
                       
                         S 
                         n 
                       
                       - 
                       
                         S 
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Here, when the variable x is sequentially changed to n−1, n−2, . . . , and 1, since the transmission rate in which the transmission rate and the packet loss rate have the proportional relation is within a section “upper limit of vacant band to S n ” for a period during which the transmission rate S x  is equal to or greater than the upper limit of the vacant band, the slop I x,n  tends to have a fixed value. When the transmission rate S x  is less than the upper limit of the vacant band, the slope I x,n  tends to be comparatively greatly changed. 
     ( 7 - 2 ) Thus, the first acceleration device  202  specifies the transmission rates S k  to S n  until the slope I x,n  has a fixed value and the slope I x,n  is changed, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation, based on the slope I x,n . Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. 
     For example, the first acceleration device  202  calculates a difference between the slope I x,n  and a slope I x-1,n , and determines whether or not the difference is equal to or greater than the threshold e. The threshold e is, for example, 20. The first acceleration device  202  specifies the transmission rate S x  to the maximum transmission rate S n  corresponding to the slope I x,n  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the minimum transmission rate S 1  to the transmission rate S x-1  corresponding to the slope I x-1,n  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. 
     ( 7 - 3 ) The first acceleration device  202  may substitute the transmission rate S x , the transmission rate S 1 , the packet loss rate Per k , and the packet loss rate Per 1  in the following expression (2) while sequentially changing the variable x to 2, 3, . . . , and n. Accordingly, the first acceleration device  202  calculates a slope I 1,x  between the transmission rates S x  and S 1  for each x=2, 3, . . . , and n. 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       1 
                       , 
                       x 
                     
                   
                   = 
                   
                     
                       
                         Per 
                         x 
                       
                       - 
                       
                         Per 
                         1 
                       
                     
                     
                       
                         S 
                         x 
                       
                       - 
                       
                         S 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, when the variable x is sequentially changed to 2, 3, . . . , and n, since the transmission rate in which the transmission rate and the packet loss rate do not have the proportional relation is within a section of “S 1  to upper limit of vacant band” for a period during which the transmission rate S x  is less than the upper limit of the vacant band, the slope I 1,x  tends to have a fixed value. When the transmission rate S x  is greater than the upper limit of the vacant band, the slope I 1,x  tends to be comparatively greatly changed. 
     ( 7 - 4 ) Thus, the first acceleration device  202  specifies the transmission rates S 1  to S k−1  until the slope I 1,x  has a fixed value and the slope I 1,x  is changed, based on the slope I 1,x . The first acceleration device  202  sets the specified transmission rates S 1  to S k−1  as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S k  to S n  as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. 
     For example, the first acceleration device  202  calculates a difference between the slope I 1,x  and the slope I 1,x−1 , and determines whether or not the difference is equal to or greater than the threshold e. The first acceleration device  202  specifies the transmission rate S x  to the maximum transmission rate S n  corresponding to the slope I 1,x  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the minimum transmission rate S 1  to the transmission rate S x-1  corresponding to the slope I 1,x−1  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. 
     Although it has been described in this example that the first acceleration device  202  specifies the transmission rate in which the transmission rate and the packet loss rate have the proportional relation by using Expression (1) or Expression (2), the disclosure is not limited thereto. For example, in a case where the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation is not able to be specified by using Expression (1), the first acceleration device  202  may use Expression (2). 
     For example, the first acceleration device  202  may specify the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation by using Expression (1), and may specify the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation by using Expression (2). The first acceleration device  202  may improve the accuracy in specifying the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation based on the specified transmission rate in a case where the transmission rate and the packet loss rate have the proportional relation. Here,  FIG. 8  will be described. 
       FIG. 8  is an explanatory diagram illustrating another example in which the transmission rate in a case where the transmission rate and the packet loss rate have the proportional relation is specified. A table illustrated in  FIG. 8  is a measurement result using the test packets, and data of the transmission rates and the packet loss rates at measurement points of time defined by the respective item number are stored. 
     In  FIG. 8 , ( 8 - 1 ) the first acceleration device  202  uses Expression (3) instead of Expression (1). The first acceleration device  202  substitutes the transmission rate S n , the transmission rate S k , the packet loss rate Per n , and the packet loss rate Per k  in the following expression (3) while sequentially changing the variable x to n−1, n−2, . . . , and 1. Accordingly, the first acceleration device  202  calculates the slope I x,n  between the transmission rate S n  and the transmission rate S k  for each of x=n−1, n−2, . . . , and 1. 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       x 
                       , 
                       n 
                     
                   
                   = 
                   
                     
                       
                         Per 
                         n 
                       
                       - 
                       
                         Per 
                         x 
                       
                     
                     
                       
                         
                           log 
                           10 
                         
                         ⁢ 
                         
                           S 
                           n 
                         
                       
                       - 
                       
                         
                           log 
                           10 
                         
                         ⁢ 
                         
                           S 
                           x 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     ( 8 - 2 ) Thus, the first acceleration device  202  specifies the transmission rates S k  to S n  until the slope I x,n  has a fixed value and the slope I x,n  is changed, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation, based on the slope I x,n . Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. 
     For example, the first acceleration device  202  calculates a difference between the slope I x,n  and the slope I x-1,n , and determines whether or not the difference is equal to or greater than the threshold e. The first acceleration device  202  specifies the transmission rate S x  to the maximum transmission rate S n  corresponding to the slope I x,n  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the minimum transmission rate S 1  to the transmission rate S x-1  corresponding to the slope I x-1,n  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. 
     ( 8 - 3 ) The first acceleration device  202  uses Expression (4) instead of Expression (2). The first acceleration device  202  may substitute the transmission rate S x , the transmission rate S 1 , the packet loss rate Per k , and the packet loss rate Per 1  in the following expression (4) while sequentially changing the variable x to 2, 3, . . . , and n. Accordingly, the first acceleration device  202  calculates the slope I 1,x  between the transmission rate S x  and the transmission rate S 1  for each of x=2, 3, . . . , and n. 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       1 
                       , 
                       x 
                     
                   
                   = 
                   
                     
                       
                         Per 
                         x 
                       
                       - 
                       
                         Per 
                         1 
                       
                     
                     
                       
                         
                           log 
                           10 
                         
                         ⁢ 
                         
                           S 
                           x 
                         
                       
                       - 
                       
                         
                           log 
                           10 
                         
                         ⁢ 
                         
                           S 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     ( 8 - 4 ) The first acceleration device  202  specifies the transmission rates S 1  to S k−1  until the slope I 1,x  has a fixed value and the slope I 1,x  is changed, as the transmission rates in a case where the transmission rate and the packet loss rate do have the proportion relation, based on the slope I 1,X . Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S k  to S n  as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. 
     For example, the first acceleration device  202  calculates a difference between the slope I 1,x  and the slope I 1,x−1 , and determines whether or not the difference is equal to or greater than the threshold e. The first acceleration device  202  specifies the transmission rate S x  to the maximum transmission rate S n  corresponding to the slope I 1,x  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the minimum transmission rate S 1  to the transmission rate S x-1  corresponding to the slope I 1,x−1  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. Now, the description is referred back to  FIG. 6 . 
     In  FIG. 6 , ( 6 - 3 ) the first acceleration device  202  stores the specified result in the management table  500 . For example, the first acceleration device  202  sets the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the transmission rates corresponding to the proportion determination “o”. 
     For example, the first acceleration device  202  sets the reception rates P k  to P n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the reception rates corresponding to the proportion determination “o”. For example, the first acceleration device  202  sets the packet loss rates Per k  to Per n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the packet loss rates corresponding to the proportion determination “o”. 
     Meanwhile, for example, the first acceleration device  202  sets the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate do not have the specified proportional relation in the fields of the transmission rates corresponding to the proportion determination “x”. 
     For example, the first acceleration device  202  sets the reception rates P 1  to P k−1  in a case where the transmission rates S 1  to S k−1  and the packet loss rate do not have the specified proportional relation in the fields of the reception rates corresponding to the proportion determination “x”. For example, the first acceleration device  202  sets the packet loss rates Per 1  to Per k−1  in a case where the transmission rates S 1  to S k−1  and the packet loss rate do not have the specified proportional relation in the fields of the packet loss rates corresponding to the proportion determination “x”. 
     Accordingly, the first acceleration device  202  can manage the transmission rates S k  to S n  which are equal to or greater than the upper limit of the vacant band and the transmission rates S 1  to S k−1  which are less than the upper limit of the vacant band. In other words, the first acceleration device  202  can store the range of the transmission rates S k−1  to S k , as the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. 
     Here, the first acceleration device  202  may specify any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. For example, the first acceleration device  202  may specify (S min +S max )/2, the upper limit of the vacant band. 
     As a result, the first acceleration device  202  can accurately specify the upper limit of the vacant band of the network  210  in which the packet loss easily occurs and the reception rate is easily disturbed. The first acceleration device  202  may further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, and may further improve the accuracy in specifying the upper limit of the vacant band. Here,  FIG. 9  will be described. 
       FIGS. 9 and 10  are explanatory diagrams illustrating examples in which the upper limit of the vacant band according to Embodiment 1 is more accurately specified. In  FIG. 9 , ( 9 - 1 ) the first acceleration device  202  acquires the packet loss rates of the transmission rate S a =(S min +S max )/2 which is a center value of the range of the transmission rates S min  to S max =S k−1  to S k  which may become the upper limit of the vacant band. 
     For example, the first acceleration device  202  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204 . The first acceleration device  202  transmits the test packets to the second acceleration device  204  at the transmission rate S a  after the measurement request is transmitted. Meanwhile, the second acceleration device  204  measures the packet loss rate Per a  and the reception rate P a  corresponding to the transmission rate S a , and transmits the measured result to the first acceleration device  202 . The first acceleration device  202  receives the packet loss rate Per a  and the reception rate P a  corresponding to the transmission rate S a . 
     ( 9 - 2 ) The first acceleration device  202  specifies whether the transmission rate Sa is the transmission rate in a case where the transmission rate and the packet loss rate have the proportional relation or the transmission rate in which the transmission rate and the packet loss rate do not have the proportional relation, based on the received packet loss rate Per a . Specifically, the first acceleration device  202  calculates the slope I a,n  between the transmission rates S n  and the transmission rate S a , similarly to  FIG. 7 or 8 . 
     The first acceleration device  202  specifies whether the range of the transmission rates S min  to S max  that may be the upper limit of the vacant band is the range of the transmission rates S k−1  to S a  or the range of the transmission rates S a  to S k . 
     ( 9 - 3 ) If a change between the slope I x,k  and the slope I x,a  is comparatively small, the first acceleration device  202  specifies the transmission rates S a  to S n  as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. For example, if the difference between the slope I x,k  and the slope I x,a  is less than the threshold e, the first acceleration device  202  specifies the transmission rates S a  to S n  as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. 
     The first acceleration device  202  updates the management table  500  based on the specified result. For example, since the transmission rates S a  to S n  are specified as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation, the first acceleration device  202  updates the fields of the transmission rates corresponding to the proportion determination “o” with the transmission rates S a  to S n . 
     For example, the first acceleration device  202  sets the reception rates P a  to P n  corresponding to the transmission rates S a  to S n  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the reception rates corresponding to the proportion determination “o”. For example, the first acceleration device  202  sets the packet loss rates Per a  to Per n  corresponding to the transmission rates S a  to S n  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the packet loss rates corresponding to the proportion determination “o”. 
     ( 9 - 4 ) If the change between the slope I x,k  and the slope I x,a  is comparatively great, the first acceleration device  202  specifies the transmission rates S k  to S n  as the transmission rate in which the transmission rate and the packet loss rate have the proportional relation. If the difference between the slope I x,k  and the slope I x,a  is equal to or greater than the threshold e, the first acceleration device  202  specifies the transmission rates S k  to S n  as the transmission rate in which the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the remaining transmission rates S 1  to S a , as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. 
     For example, since the transmission rates S 1  to S a  are specified as the transmission rate in which the transmission rate and the packet loss rate do not have the proportion relation, the first acceleration device  202  updates the fields of the transmission rates corresponding to the proportion determination “x” with the transmission rates S 1  to S a . 
     For example, the first acceleration device  202  sets the reception rates P 1  to P a  corresponding to the transmission rates S 1  to S a  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the reception rates corresponding to the proportion determination “x”. For example, the first acceleration device  202  sets the packet loss rates Per 1  to Per a  corresponding to the transmission rates S 1  to S a  in a case where the transmission rate and the packet loss rate have the specified proportional relation in the fields of the packet loss rates corresponding to the proportion determination “x”. 
     Accordingly, the first acceleration device  202  can specify whether the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band is the range of the transmission rates S a  to S k  or the range of the transmission rates S k−1  to S a , and can store the specified range. In other words, the first acceleration device  202  can narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band to the range of the transmission rates S a  to S k  or the range of the transmission rates S k−1  to S a  from the range of the transmission rates S k−1  to S k . 
     Here, the first acceleration device  202  may specify any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. Here,  FIG. 10  will be described. 
     In  FIG. 10 , ( 10 - 1 ) the first acceleration device  202  determines whether or not to further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. For example, if the difference between S min  and S max  is equal to or greater than a threshold T, the first acceleration device  202  determines to further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. In a case where it is determined to further narrow the range, the first acceleration device  202  further narrows the range of the transmission rates S min  to S max , similarly to  FIG. 9 . 
     Meanwhile, if the difference between S min  and S max  is less than the threshold T, the first acceleration device  202  determines not to narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. 
     ( 10 - 2 ) If it is determined not to narrow the range, the first acceleration device  202  specifies any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. 
     As a result, the first acceleration device  202  can more accurately specify the upper limit of the vacant band of the network  210  in which the packet loss easily occurs and the reception rate is easily disturbed. Thus, the first acceleration device  202  can efficiently utilize the network  210 . 
     Example of Specification Process Procedure According to Embodiment 1 
     Hereinafter, an example of a specification process procedure according to Embodiment 1 for specifying the upper limit of the vacant band of the network  210  will be described with reference to  FIGS. 11 and 12 . 
       FIGS. 11 and 12  are flowcharts illustrating examples of the specification process procedure according to Embodiment 1. In  FIG. 11 , the first acceleration device  202  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204  (step S 1101 ). Subsequently, the first acceleration device  202  determines whether or not the response is received from the second acceleration device  204  (step S 1102 ). Here, in a case where the response is not received (step S 1102 : No), the first acceleration device  202  returns the process to step S 1101 . 
     Meanwhile, in a case where the response is received (step S 1102 : Yes), the first acceleration device  202  determines n number of transmission rates S 1  to S n  used when the test packets are transmitted based on the preset maximum transmission rate and minimum transmission rate (step S 1103 ). 
     Subsequently, the first acceleration device  202  increments a variable i, and selects a transmission rate S i  from the transmission rate S 1  to S n  (step S 1104 ). An initial value of the variable i is 0. The first acceleration device  202  transmits the test packets to the second acceleration device  204  at the selected transmission rate S i  (step S 1105 ). 
     Subsequently, the first acceleration device  202  receives a reception rate P i  and a packet loss rate Per i  measured by the second acceleration device  204  from the second acceleration device  204  (step S 1106 ). The first acceleration device  202  determines whether or not i≧n is satisfied (step S 1107 ). Here, in a case where i≧n is not satisfied (step S 1107 : No), the first acceleration device  202  returns the process to step S 1104 . 
     Meanwhile, in a case where i≧n is satisfied (step S 1107 : Yes), the first acceleration device  202  classifies the transmission rates S 1  to S n , and stores the classified transmission rates in the management table  500  (step S 1108 ). Here, for example, the first acceleration device  202  classifies the transmission rates S 1  to S n  into the transmission rates S max  to S n  in a case where the transmission rate and the packet loss rate have the proportional relation and the transmission rates S 1  to S min  in a case where the transmission rate and the packet loss rate do not have the proportional relation. Thereafter, the first acceleration device  202  performs the process of step S 1201  of  FIG. 12 . 
     In  FIG. 12 , the first acceleration device  202  determines whether or not S max −S min &lt;T is satisfied (step S 1201 ). Here, in a case where S max −S min &lt;T is satisfied (step S 1201 : Yes), the first acceleration device  202  specifies the upper limit of the vacant band based on the management table  500 , and stores the specified upper limit (step S 1202 ). The first acceleration device  202  ends the specification process. 
     Meanwhile, in a case where S max −S min &lt;T is not satisfied (step S 1201 : No), the first acceleration device  202  sets the transmission rate S a =(S min +S max )/2, and transmits the test packets to the second acceleration device  204  at the transmission rate S a  (step S 1203 ). Subsequently, the first acceleration device  202  receives a reception rate P a  and a packet loss rate Per a  measured by the second acceleration device  204  from the second acceleration device  204  (step S 1204 ). The first acceleration device  202  calculates the slope I a,n  between the transmission rate S a  and the transmission rate S n  (step S 1205 ). 
     Subsequently, the first acceleration device  202  determines whether or not a difference between the slope I a,n  and the slope of the transmission rate in which the transmission rate and the packet loss rate have the proportional relation is less than the threshold e (step S 1206 ). Here, in a case where the difference is not less than the threshold e (step S 1206 : No), the first acceleration device  202  updates the fields of the transmission rates associated with the proportion determination “x” of the management table  500 , and sets S min =S a  (step S 1207 ). The first acceleration device  202  returns the process to step S 1201 . 
     Meanwhile, in a case where the difference is less than the threshold e (step S 1206 : Yes), the first acceleration device  202  updates the fields of the transmission rates associated with the proportion determination “o” of the management table  500 , and sets S max =S a  (step S 1208 ). The first acceleration device  202  returns the process to step S 1201 . Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Operation Example of Communication System  200  According to Embodiment 1 
     Hereinafter, an operation example of the communication system  200  according to Embodiment 1 will be described with reference to  FIGS. 13 and 14 . 
       FIGS. 13 and 14  are sequence diagrams illustrating operation examples of the communication system  200  according to Embodiment 1. In  FIG. 13 , the first acceleration device  202  further includes a detection unit  1300 . For example, the detection unit  1300  generates triggers for causing the instruction unit  401  to the storage unit  405  to start the processes. 
     In  FIG. 13 , the detection unit  1300  of the first acceleration device  202  detects that the communication with the second acceleration device  204  is time out (step S 1301 ). If the time-out is detected, the detection unit  1300  inputs the measurement request to the instruction unit  401  (step S 1302 ). If the measurement request is received, the instruction unit  401  determines n number of transmission rates S 1  to S n , and notifies the measurement unit  402  of the transmission rate S i  of the transmission rates S 1  to S n  (step S 1303 ). 
     If the transmission rate S i  is notified, the measurement unit  402  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204  (step S 1304 ). Meanwhile, if the measurement request is received, the second acceleration device  204  transmits the response to the measurement unit  402  (step S 1305 ). 
     If the response is received, the measurement unit  402  notifies the setting unit  403  of the transmission rates S i  (step S 1306 ). Subsequently, the measurement unit  402  accepts the control of the transmission rate S i  performed by the setting unit  403  (step S 1307 ). The measurement unit  402  transmits the test packets to the second acceleration device  204  at the transmission rate S i  under the control of the setting unit  403  (step S 1308 ). 
     If the test packets are received, the second acceleration device  204  measures the reception rates P i  and the packet loss rate Per i  corresponding to the transmission rate S i  (step S 1309 ). The second acceleration device  204  transmits the reception rate P i  and the packet loss rate Per i  corresponding to the measured transmission rate S i  to the measurement unit  402  (step S 1310 ). 
     If the reception rate P i  and the packet loss rate Per i  corresponding to the transmission rate S i  are received, the measurement unit  402  notifies the instruction unit  401  of the measurement result including the reception rate P i  and the packet loss rate Per i  (step S 1311 ). 
     If the measurement result is received, the instruction unit  401  determines whether or not n number of times of the measurement is ended by using the transmission rates S 1  to S n  (step S 1312 ). Here, in a case where n number of times of the measurement is not ended (step S 1312 : No), the instruction unit  401  returns the process to step S 1303 . 
     Meanwhile, in a case where n number of times of the measurement is ended (step S 1312 : Yes), the instruction unit  401  notifies the specification unit  404  of a specification request for the range of the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation and the measurement result (step S 1313 ). Here,  FIG. 14  will be described. 
     In  FIG. 14 , if the specification request and the measurement result are received, the specification unit  404  specifies the range of the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation (step S 1401 ). The specification unit  404  notifies the storage unit  405  of the specification result, and stores the management table  500  in the storage unit  405  (step S 1402 ). 
     The specification unit  404  notifies the instruction unit  401  of the specification result (step S 1403 ). If the specification result is received, the instruction unit  401  determines whether or not S max −S min &lt;T is satisfied (step S 1404 ). Here, in a case where S max −S min &lt;T is satisfied (step S 1404 : Yes), the instruction unit  401  performs the process of step S 1418 . 
     Meanwhile, in a case where S max −S min &lt;T is not satisfied (step S 1404 : No), the instruction unit  401  notifies the measurement unit  402  of the transmission rate S a =(S min +S max )/2 (step S 1405 ). 
     If the transmission rate S a  is notified, the measurement unit  402  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204  (step S 1406 ). Meanwhile, if the measurement request is received, the second acceleration device  204  transmits the response to the measurement unit  402  (step S 1407 ). 
     If the response is received, the measurement unit  402  notifies the setting unit  403  of the transmission rates S a  (step S 1408 ). Subsequently, the measurement unit  402  accepts the control of the transmission rate S a  performed by the setting unit  403  (step S 1409 ). The measurement unit  402  transmits the test packets to the second acceleration device  204  at the transmission rate S a  under the control of the setting unit  403  (step S 1410 ). 
     If the test packets are received, the second acceleration device  204  measures the reception rates P a  and the packet loss rate Per a  corresponding to the transmission rate S a  (step S 1411 ). The second acceleration device  204  transmits the reception rate P a  and the packet loss rate Per a  corresponding to the measured transmission rate S a  to the measurement unit  402  (step S 1412 ). 
     If the reception rate P a  and the packet loss rate Per a  corresponding to the transmission rate S a  are received, the measurement unit  402  notifies the instruction unit  401  of the measurement result including the reception rate P a  and the packet loss rate Per a  (step S 1413 ). 
     In a case where the measurement result is received, the instruction unit  401  notifies the specification unit  404  of a specification request for the range of the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation and the measurement result (step S 1414 ). 
     If the specification request and the measurement result are received, the specification unit  404  refers to the management table  500  stored in the storage unit  405  (step S 1415 ). If the management table  500  is referred to, the specification unit  404  specifies whether or not the transmission rate S a  is the transmission rate in a case where the transmission rate and the packet loss rate have the proportional relation (step S 1416 ). The specification unit  404  notifies the storage unit  405  of the specification result, and updates the management table  500  in the storage unit  405  (step S 1417 ). The specification unit  404  returns the process to step S 1403 . 
     In a case where S max −S min &lt;T is satisfied and the process of step S 1418  is performed, the instruction unit  401  outputs the upper limit of the vacant band (step S 1418 ). Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Description of Embodiment 2 
     Hereinafter, Embodiment 2 will be described. In the following description, the same elements as those of Embodiment 1 will be assigned the same reference signs as those of Embodiment 1, and the redundant description thereof will be omitted in some cases. 
     Example of Communication System  200  According to Embodiment 2 
     Hereinafter, an example of the communication system  200  according to Embodiment 2 to which the vacant band specification device  100  illustrated in  FIG. 1  is applied will be described with reference to  FIG. 15 . 
       FIG. 15  is an explanatory diagram illustrating an example of the communication system  200  according to Embodiment 2. In  FIG. 15 , the communication system  200  includes the first calculation device  201 , the first acceleration device  202 , the second calculation device  203 , and the second acceleration device  204 . In the communication system  200 , the first acceleration device  202  and the second acceleration device  204  are connected via a wired or wireless network  210 . 
     Here, similarly to  FIG. 2 , the first acceleration device  202  tends to be desired to specify the upper limit of the vacant band of the network  210 . Thus, in the following description, a case where the first acceleration device  202  operates as the vacant band specification device  100  and specifies the upper limit of the vacant band of the network  210  will be described. 
     Here, in the network  210 , if the transmission rate is increased, the index value indicating the amount of packet loss tends to be also increased. However, the index value indicating the amount of packet loss is not necessarily increased in a straight line with respect to the increase in the transmission rate in some types of the index value indicating the amount of packet loss or some statuses of the network  210 . The packet loss is comparatively small immediately after the transmission rate exceeds the upper limit of the vacant band in some cases. Thus, it is difficult to specify the range of the transmission rates in a case where the transmission rate and the index value indicating the amount of packet loss have the proportional relation. 
     Thus, in Embodiment 2, the first acceleration device  202  uses the correlation between the transmission rate and the index value indicating the amount of packet loss instead of the proportional relation, as the dependence relation between the transmission rate and the index value indicating the amount of packet loss. Accordingly, the first acceleration device  202  can improve the accuracy in specifying the upper limit of the vacant band. 
     (Functional Configuration Example of Vacant Band Specification Device  100 ) 
     Hereinafter, a functional configuration example of the vacant band specification device  100  according to Embodiment 2 will be described. Similarly to  FIG. 4 , the vacant band specification device  100  includes the instruction unit  401 , the measurement unit  402 , the setting unit  403 , the specification unit  404 , and the storage unit  405 . The functional units are the same as those of  FIG. 4 , and thus, the description thereof will be described. 
     (Flow for Specifying Upper Limit of Vacant Band of Network  210 ) 
     Hereinafter, a flow for specifying the upper limit of the vacant band of the network  210  according to Embodiment 2 will be described with reference to  FIGS. 16 to 20 . 
       FIG. 16  is an explanatory diagram illustrating an example of the stored content of the management table  1600  according to Embodiment 2. For example, the management table  1600  is realized by the storage area such as the memory  302  or the disk  305  illustrated in  FIG. 3 . As illustrated in  FIG. 16 , the management table  1600  includes fields such as the transmission rate, the reception rate, the packet loss rate, and correlation determination. 
     The correlation determination is a flag indicating whether or not the transmission rate, the reception rate, and the packet loss rate associated with the correlation determination are information in a case where the transmission rate and the packet loss rate have the correlation. For example, the correlation determination is “o” if the transmission rate and the packet loss rate have the correlation, and is “x” if the transmission rate and the packet loss rate do not have the correlation. The transmission rate is a transmission rate range in a case where the correlation is expressed by the correlation determination. The reception rate is a reception rate range in a case where the correlation is expressed by the correlation determination. The packet loss rate is a packet loss rate in which the correlation is expressed by the correlation determination. 
     The management table  1600  may classify the transmission rates into a range of the transmission rates in a case where the transmission rate and the packet loss rate have the correlation and a range of the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation, and may manage the classified ranges. In other words, the management table  1600  may classify the transmission rates into a range of transmission rates which are equal to or greater than the upper limit of the vacant band and a range of transmission rates which are less than the upper limit of the vacant band, and may manage the classified ranges. 
       FIG. 17  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 2 is specified. In  FIG. 17 , ( 17 - 1 ) the first acceleration device  202  receives the packet loss rates Per 1  to Per n  and the reception rates P 1  to P n  corresponding to n number of transmission rates S 1  to S n  from the second acceleration device  204 , similarly to  FIG. 6 . 
     As illustrated in  FIG. 17 , a case where the transmission rates S 1  to S k−1  of n number of transmission rates S 1  to S n  are equal to or less than the vacant band and the transmission rates S k  to S n  are equal to or greater than the vacant band will be described. In the following description, the first acceleration device  202  may classify n number of transmission rates S 1  to S n  into the transmission rates S 1  to S k−1  which are equal to or less than the vacant band and the transmission rates S k  to S n  which are equal to or greater than the vacant band. 
     Here, the first acceleration device  202  specifies the transmission rate of the transmission rates S 1  to S n , in a case where the transmission rate and the packet loss rate have the correlation based on the received packet loss rates Per 1  to Per n . In other words, the first acceleration device  202  may specify the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation. Here,  FIG. 18  will be described. 
       FIG. 18  is an explanatory diagram illustrating an example in which the transmission rate in a case where the transmission rate and the packet loss rate have the correlation is specified. A table illustrated in  FIG. 18  is a measurement result using the test packets, and data of the transmission rates and the packet loss rates at measurement points of time defined by the respective item number are stored. 
     In  FIG. 18 , ( 18 - 1 ) the first acceleration device  202  calculates the correlation coefficient r x,n  between the transmission rate S n  and the transmission rate S k  by using Expression (5) while sequentially changing the variable x to n−1, n−2, . . . , and 1. 
     For example, the first acceleration device  202  substitutes the transmission rates S k  to S n , an average value S avg  of the transmission rates S k  to S n , the packet loss rates Per k  to Per n , and an average Per avg  of the packet loss rates Per k  to Per n  in the following expression (5). Accordingly, the first acceleration device  202  calculates the correlation coefficient r x,n  between the transmission rate S n  and the transmission rate S k  for each of x=n−1, n−2, . . . , and 1. 
     
       
         
           
             
               
                 
                   
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     Here, when the variable x is sequentially changed to n−1, n−2, . . . , and 1, since the transmission rate in which the transmission rate and the packet loss rate have the correlation is within a section “upper limit of vacant band to S n ” for a period during which the transmission rate S x  is equal to or greater than the upper limit of the vacant band, the correlation coefficient r x,n  tends to have a fixed value or to be comparatively great. When the transmission rate S x  is less than the upper limit of the vacant band, the correlation coefficient r x,n  tends to be changed. 
     ( 18 - 2 ) Thus, the first acceleration device  202  specifies the transmission rates S k  to S n  until the correlation coefficient r x,n  has a fixed value and the correlation coefficient r x,n  is changed, based on the correlation coefficient r x,n . The first acceleration device  202  sets the specified transmission rates S k  to S n  as the transmission rate in which the transmission rate and the packet loss rate have the correlation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation. 
     For example, the first acceleration device  202  calculates the difference between the correlation coefficient r x,n  and the correlation coefficient r x-1,n  and determines whether or not the correlation coefficient r x,n  is equal to or greater than the threshold R and the difference is equal to or greater than the threshold e. The threshold R is, for example, 0.9. The threshold e is, for example, 0.4. Here, since the difference is not equal to or greater than the threshold e, the first acceleration device  202  is not able to specify the transmission rates in a case where the transmission rate and the packet loss rate have the correlation. 
     ( 18 - 3 ) The first acceleration device  202  is not able to specify the transmission rate in a case where the transmission rate and the packet loss rate have the correlation, the first acceleration device calculates the correlation coefficient r 1,x  between the transmission rates S x  and S 1  by using the following expression (6) while sequentially changing the variable x to 2, 3, . . . , and n. 
     For example, the first acceleration device  202  substitutes the transmission rates S 1  to S x , an average value S avg  of the transmission rates S 1  to S x , the packet loss rates Per 1  to Per k , and an average Per avg  of the packet loss rates Per 1  to Per k  in the following expression (6). Accordingly, the first acceleration device  202  calculates the correlation coefficient r 1,x  between the transmission rate S x  and the transmission rate S 1  for each of x=2, 3, . . . , and n. 
     
       
         
           
             
               
                 
                   
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     Here, when the variable x is sequentially changed to 2, 3, . . . , and n, since the transmission rate in which the transmission rate and the packet loss rate do not have the correlation is within a section of “S 1  to upper limit of vacant band” for a period during which the transmission rate S x  is less than the upper limit of the vacant band, there are many packet loss rates having no regularity, and the correlation coefficient r 1,x  tends to be decreased. When the transmission rate S x  is greater than the upper limit of the vacant band, the correlation coefficient r 1,x  tends to be comparatively greatly changed. 
     ( 18 - 4 ) Thus, the first acceleration device  202  specifies the transmission rates S 1  to S k−1  until the correlation coefficient r 1,x  is decreased and the correlation coefficient r 1,x  is comparatively greatly changed, based on the correlation coefficient r 1,x . The first acceleration device  202  sets the specified transmission rates S 1  to S k−1  as the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S k  to S n , as the transmission rates in a case where the transmission rate and the packet loss rate have the correlation. 
     For example, the first acceleration device  202  calculates the difference between the correlation coefficient r 1,x  and the correlation coefficient r 1,x−1 , and determines whether or not the correlation coefficient r 1,x  is equal to or greater than the threshold R and the difference is equal to or greater than the threshold e. Here, the first acceleration device  202  determines that the correlation coefficient r 1,x  is equal to or greater than the threshold R and the difference is equal to or greater than the threshold e. The first acceleration device  202  specifies the transmission rate S x  to the maximum transmission rate S n  corresponding to the correlation coefficient r 1,x  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate have the proportional relation. The first acceleration device  202  specifies the minimum transmission rate S 1  to the transmission rate S x-1  corresponding to the correlation coefficient r 1,x−1  when the difference is equal to or greater than the threshold e, as the transmission rates in a case where the transmission rate and the packet loss rate do not have the proportional relation. Now, the description is referred back to  FIG. 17 . 
     In  FIG. 17 , ( 17 - 2 ) the first acceleration device  202  stores the specified result in the management table  1600 , similarly to  FIG. 6 . For example, the first acceleration device  202  sets the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the transmission rates corresponding to the correlation determination “o”. 
     For example, the first acceleration device  202  sets the reception rates P k  to P n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the reception rates corresponding to the correlation determination “o”. The first acceleration device  202  sets the packet loss rates Per k  to Per n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the packet loss rates corresponding to the correlation determination “o”. 
     Meanwhile, for example, the first acceleration device  202  sets the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the transmission rates corresponding to the correlation determination “x”. 
     For example, the first acceleration device  202  sets the reception rates P 1  to P k−1  corresponding to the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the reception rates corresponding to the correlation determination “x”. For example, the first acceleration device  202  sets the packet loss rates Per 1  to Per k−1  corresponding to the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate do not have the specified correlation in the fields of the packet loss rates corresponding to the correlation determination “x”. 
     Accordingly, the first acceleration device  202  can manage the transmission rates S k  to S n  which are equal to or greater than the upper limit of the vacant band and the transmission rates S 1  to S k−1  which are less than the upper limit of the vacant band. In other words, the first acceleration device  202  can store the range of the transmission rates S k−1  to S k , as the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. 
     Here, the first acceleration device  202  may specify any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. For example, the first acceleration device  202  may specify (S min +S max )/2, the upper limit of the vacant band. 
     As a result, the first acceleration device  202  can accurately specify the upper limit of the vacant band of the network  210  in which the packet loss easily occurs and the reception rate is easily disturbed. The first acceleration device  202  can accurately specify the upper limit of the vacant band even though the change in the slope of the graph of the transmission rate and the index value indicating the amount of packet loss is comparatively small immediately after the transmission rate exceeds the upper limit of the vacant band. The first acceleration device  202  may further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, and may further improve the accuracy in specifying the upper limit of the vacant band. Here,  FIGS. 19 and 20  will be described. 
       FIGS. 19 and 20  are explanatory diagrams illustrating examples in which the upper limit of the vacant band according to Embodiment 2 is more accurately specified. In  FIG. 19 , ( 19 - 1 ) the first acceleration device  202  acquires the packet loss rates of the transmission rate S a  which is a center value of the range of the transmission rates S min  to S max =S k−1  to S k  which may become the upper limit of the vacant band. 
     For example, the first acceleration device  202  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204 . The first acceleration device  202  transmits the test packets to the second acceleration device  204  at the transmission rate S a  after the measurement request is transmitted. 
     Meanwhile, the second acceleration device  204  measures the packet loss rate Per a  and the reception rate P a  corresponding to the transmission rate S a , and transmits the measured result to the first acceleration device  202 . The first acceleration device  202  receives the packet loss rate Per a  and the reception rate P a  corresponding to the transmission rate S a . 
     ( 19 - 2 ) The first acceleration device  202  specifies whether the transmission rate S a  is the transmission rate in a case where the transmission rate and the packet loss rate have the correlation or the transmission rate in which the transmission rate and the packet loss rate do not have the correlation, based on the received packet loss rate Per a . Specifically, the first acceleration device  202  calculates the correlation coefficient r a,n  between the transmission rate S n  and the transmission rate S a , similarly to  FIG. 18 . 
     The first acceleration device  202  specifies whether the range of the transmission rates S min  to S max  that may be the upper limit of the vacant band is the range of the transmission rates S k−1  to Sa or the range of the transmission rates S a  to S k . 
     ( 19 - 3 ) if the correlation coefficient r x,a  is equal to or greater than threshold R and the change between the correlation coefficient r x,k  and the correlation coefficient r x,a  is comparatively small, the first acceleration device  202  specifies the transmission rates S a  to S n , as the transmission rates in which the transmission rate and the packet loss rate have the correlation. For example, if the correlation coefficient r x,a  is equal to or greater than the threshold R and the difference between the correlation coefficient r x,k  and the correlation coefficient r x,a  is less than the threshold e, the first acceleration device  202  specifies the transmission rates S a  to S n , as the transmission rates in a case where the transmission rate and the packet loss rate have the correlation. The first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation. 
     The first acceleration device  202  updates the management table  1600  based on the specified result. For example, since the transmission rates S a  to S n  are specified as the transmission rates in a case where the transmission rate and the packet loss rate have the correlation, the first acceleration device  202  updates the fields of the transmission rates corresponding to the correlation determination “o” with the transmission rates S a  to S n . 
     For example, the first acceleration device  202  sets the reception rates P a  to P n  corresponding to the transmission rates S a  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the reception rates corresponding to the correlation determination “o”. The first acceleration device  202  sets the packet loss rates Per a  to Per n  corresponding to the transmission rates S a  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the packet loss rates corresponding to the correlation determination “o”. 
     ( 19 - 4 ) if the correlation coefficient r x,a  is less than threshold R and the change between the correlation coefficient r x,k  and the correlation coefficient r x,a  is comparatively great, the first acceleration device  202  specifies the transmission rates S k  to S n , as the transmission rates in which the transmission rate and the packet loss rate have the correlation. For example, if the correlation coefficient r x,a  is less than the threshold R and the difference between the correlation coefficient r x,k  and the correlation coefficient r x,a  is equal to or greater than the threshold e, the first acceleration device  202  specifies the transmission rates S k  to S n , as the transmission rates in a case where the transmission rate and the packet loss rate have the correlation. The first acceleration device  202  specifies the remaining transmission rates S 1  to S a , as the transmission rates in a case where the transmission rate and the packet loss rate do not have the correlation. 
     For example, since the transmission rates S 1  to S a  are specified as the transmission rate in which the transmission rate and the packet loss rate do not have the correlation, the first acceleration device  202  updates the fields of the transmission rates corresponding to the correlation determination “x” with the transmission rates S 1  to S a . 
     For example, the first acceleration device  202  sets the reception rates P 1  to P a  corresponding to the transmission rates S 1  to S a  in a case where the transmission rate and the packet loss rate do not have the specified correlation in the fields of the reception rates corresponding to the correlation determination “x”. For example, the first acceleration device  202  sets the packet loss rates Per 1  to Per a  corresponding to the transmission rates S 1  to S a  in a case where the transmission rate and the packet loss rate do not have the specified correlation in the fields of the packet loss rates corresponding to the correlation determination “x”. 
     Accordingly, the first acceleration device  202  can specify whether the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band is the range of the transmission rates S a  to S k  or the range of the transmission rates S k−1  to S a , and may store the specified range. In other words, the first acceleration device  202  can narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band to the range of the transmission rates S a  to S k  or the range of the transmission rates S k−1  to S a  from the range of the transmission rates S k−1  to S k . 
     Here, the first acceleration device  202  may specify any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. Here,  FIG. 20  will be described. 
     In  FIG. 20 , ( 20 - 1 ) the first acceleration device  202  determines whether or not to further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. For example, if the difference between S min  and S max  is equal to or greater than a threshold T, the first acceleration device  202  determines to further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. In a case where it is determined to further narrow the range, the first acceleration device  202  further narrows the range of the transmission rates S min  to S max , similarly to  FIG. 19 . 
     Meanwhile, if the difference between S min  and S max  is less than the threshold T, the first acceleration device  202  determines not to narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. 
     ( 20 - 2 ) If it is determined not to narrow the range, the first acceleration device  202  specifies any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. 
     As a result, the first acceleration device  202  can more accurately specify the upper limit of the vacant band of the network  210  in which the packet loss easily occurs and the reception rate is easily disturbed. Thus, the first acceleration device  202  can efficiently utilize the network  210 . 
     Example of Specification Process Procedure According to Embodiment 2 
     Hereinafter, an example of a specification process procedure according to Embodiment 2 for specifying the upper limit of the vacant band of the network  210  will be described with reference to  FIGS. 21 and 22 . 
       FIGS. 21 and 22  are flowcharts illustrating examples of the specification process procedure according to Embodiment 2. In  FIG. 21 , the processes of steps S 2101  to S 2107  are the same as the processes of steps S 1101  to S 1107  illustrated in  FIG. 11 , and thus, the description thereof will be omitted. Here, the process of step S 2108  will be described. 
     The first acceleration device  202  classifies the transmission rates S 1  to S n , and stores the classified transmission rates in the management table  1600  (step S 2108 ). Here, for example, the first acceleration device  202  classifies the transmission rates S 1  to S n  into the transmission rates S max  to S n  in a case where the transmission rate and the packet loss rate have the correlation and the transmission rates S 1  to S min  in a case where the transmission rate and the packet loss rate do not have the correlation. Thereafter, the first acceleration device  202  performs the process of step S 2201  of  FIG. 22 . 
     In  FIG. 22 , the first acceleration device  202  determines whether or not S max −S min &lt;T is satisfied (step S 2201 ). Here, in a case where S max −S min &lt;T is satisfied (step S 2201 : Yes), the first acceleration device  202  specifies the upper limit of the vacant band based on the management table  1600 , and stores the specified upper limit (step S 2202 ). The first acceleration device  202  ends the specification process. 
     Meanwhile, in a case where S max −S min &lt;T is not satisfied (step S 2201 : No), the first acceleration device  202  sets the transmission rate S a =(S min  S max )/2, and transmits the test packets to the second acceleration device  204  at the transmission rate S a  (step S 2203 ). Subsequently, the first acceleration device  202  receives the reception rate P a  and the packet loss rate Per a  measured by the second acceleration device  204  from the second acceleration device  204  (step S 2204 ). The first acceleration device  202  calculates the correlation coefficient r a,n  between the transmission rate S a  and the transmission rate S n  (step S 2205 ). 
     Subsequently, the first acceleration device  202  determines whether or not the correlation coefficient r a,n  is equal to or greater than the threshold R, and the difference between the correlation coefficient r a,n  and the correlation coefficient of the transmission rate in a case where the transmission rate and the packet loss rate have the correlation is less than threshold e and have the correlation (step S 2206 ). Here, in a case where the transmission rate and the packet loss rate do not have the correlation (step S 2206 : No), the first acceleration device  202  updates the fields of the transmission rates associated with the correlation determination “x” of the management table  1600 , and sets S min =S a  (step S 2207 ). The first acceleration device  202  returns the process to step S 2201 . 
     Meanwhile, in a case where the transmission rate and the packet loss rate have the correlation (step S 2206 : Yes), the first acceleration device  202  updates the fields of the transmission rates associated with the correlation determination “o” of the management table  1600 , and sets S max =S a  (step S 2208 ). The first acceleration device  202  returns the process to step S 2201 . Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Operation Example of Communication System  200  According to Embodiment 2 
     Hereinafter, an operation example of the communication system  200  according to Embodiment 2 will be described with reference to  FIGS. 23 and 24 . 
       FIGS. 23 and 24  are sequence diagrams illustrating operation examples of the communication system  200  according to Embodiment 2. In  FIG. 23 , the processes of steps S 2301  to S 2312  are the same as the processes of steps S 1301  to S 1312  illustrated in  FIG. 13 , and thus, the description thereof will be omitted. Here, the process of step S 2313  will be described. 
     The instruction unit  401  notifies the specification unit  404  of the specification request for the range of the transmission rates in a case where the transmission rate and the packet loss rate have the correlation and the measurement result (step S 2313 ). Here,  FIG. 24  will be described. 
     In  FIG. 24 , if the specification request and the measurement result are received, the specification unit  404  specifies the range of the transmission rates in a case where the transmission rate and the packet loss rate have the correlation (step S 2401 ). The specification unit  404  notifies the storage unit  405  of the specification result, and updates the management table  1600  in the storage unit  405  (step S 2402 ). 
     The specification unit  404  notifies the instruction unit  401  of the specification result (step S 2403 ). If the specification result is received, the instruction unit  401  determines whether or not S max −S min &lt;T is satisfied (step S 2404 ). Here, in a case where S max −S min &lt;T is satisfied (step S 2404 : Yes), the instruction unit  401  performs the process of step S 2418 . 
     Meanwhile, in a case where S max −S min &lt;T is not satisfied (step S 2404 : No), the instruction unit  401  notifies the measurement unit  402  of the transmission rate S a =(S min +S max )/2 (step S 2405 ). 
     If the transmission rate S a  is notified, the measurement unit  402  transmits the measurement request of the reception rate and the packet loss rate to the second acceleration device  204  (step S 2406 ). Meanwhile, if the measurement request is received, the second acceleration device  204  transmits the response to the measurement unit  402  (step S 2407 ). 
     If the response is received, the measurement unit  402  notifies the setting unit  403  of the transmission rates S a  (step S 2408 ). Subsequently, the measurement unit  402  accepts the control of the transmission rate S a  performed by the setting unit  403  (step S 2409 ). The measurement unit  402  transmits the test packets to the second acceleration device  204  at the transmission rate Sa under the control of the setting unit  403  (step S 2410 ). 
     If the test packets are received, the second acceleration device  204  measures the reception rates P a  and the packet loss rate Per a  corresponding to the transmission rate S a  (step S 2411 ). The second acceleration device  204  transmits the reception rate P a  and the packet loss rate Per a  corresponding to the measured transmission rate S a  to the measurement unit  402  (step S 2412 ). 
     If the reception rate P a  and the packet loss rate Per a  corresponding to the transmission rate S a  are received, the measurement unit  402  notifies the instruction unit  401  of the measurement result including the reception rate P a  and the packet loss rate Per a  (step S 2413 ). 
     In a case where the measurement result is received, the instruction unit  401  notifies the specification unit  404  of a specification request for the range of the transmission rates in a case where the transmission rate and the packet loss rate have the correlation and the measurement result (step S 2414 ). 
     If the specification request and the measurement result are received, the specification unit  404  refers to the management table  1600  stored in the storage unit  405  (step S 2415 ). If the management table  1600  is referred to, the specification unit  404  specifies whether or not the transmission rate S a  is the transmission rate in a case where the transmission rate and the packet loss rate have the correlation (step S 2416 ). The specification unit  404  notifies the storage unit  405  of the specification result, and updates the management table  1600  in the storage unit  405  (step S 2417 ). The specification unit  404  returns the process to step S 2403 . 
     In a case where S max −S min &lt;T is satisfied and the process of step S 2418  is performed, the instruction unit  401  outputs the upper limit of the vacant band (step S 2418 ). Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Description of Embodiment 3 
     Hereinafter, Embodiment 3 will be described. In the following description, the same elements as those of Embodiment 1 or Embodiment 2 will be assigned the same reference signs as those of Embodiment 1 or Embodiment 2, and the redundant description thereof will be omitted in some cases. 
     Example of Communication System  200  According to Embodiment 3 
     Hereinafter, an example of the communication system  200  according to Embodiment 3 to which the vacant band specification device  100  illustrated in  FIG. 1  is applied will be described with reference to  FIG. 25 . 
       FIG. 25  is an explanatory diagram illustrating an example of the communication system  200  according to Embodiment 3. In  FIG. 25 , the communication system  200  includes the first calculation device  201 , the first acceleration device  202 , a first base station  205 , the second calculation device  203 , the second acceleration device  204 , and a second base station  206 . In the communication system  200 , the first base station  205  and the second base station  206  are connected via a wireless network  210 . 
     Here, similarly to  FIG. 2 , the first acceleration device  202  tends to be desired to specify the upper limit of the vacant band of the network  210 . Thus, in the following description, a case where the first acceleration device  202  operates as the vacant band specification device  100  and specifies the upper limit of the vacant band of the network  210  will be described. 
     Here, a case where the first base station  205  or the second base station  206  have functions of Automatic Repeat reQuest (ARQ), or hybrid ARQ (HARQ) is considered. For example, in a case the packet loss occurs in the wireless network  210 , the first base station  205  may retransmit the packets. 
     However, in this case, the second acceleration device  204  is difficult to detect that the packet loss occurs, and is difficult to accurately measure the packet loss rate. As a result, the first acceleration device  202  is difficult to use the packet loss rate as the index value indicating the amount of packet loss. 
     Meanwhile, in a case where the packet loss occurs and the first base station  205  retransmits the packets, a time taken for the packets transmitted from the first acceleration device  202  to be received by the second acceleration device  204  tends to be further increased than that in a case where the first base station does not retransmit the packets. As a result, a time taken for the second acceleration device  204  to transmit a response indicating that the packets are received to the first acceleration device  202  tends to be increased. 
     As stated above, as the packet loss is increased, the RTT which is a time taken for the second acceleration device  204  to transmit the response indicating that the packets are received to the first acceleration device  202  tends to be increased. In other words, the RU may become the index value indicating the amount of packet loss. 
     Thus, in Embodiment 3, the first acceleration device  202  uses the RU as the index value indicating the amount of packet loss, instead of the packet loss rate. Accordingly, the first acceleration device  202  can improve the accuracy in specifying the upper limit of the vacant band even though there is the wireless network  210 . 
     In Embodiment 3, the first acceleration device  202  may use the proportional relation as in Embodiment 1 as the dependence relation between the transmission rate and the index value indicating the amount of packet loss, or may use the correlation as in Embodiment 2. In the following description, a case where the first acceleration device  202  uses the correlation as in Embodiment 2 as the dependence relation between the transmission rate and the index value indicating the amount of packet loss will be described. 
     (Functional Configuration Example of Vacant Band Specification Device  100 ) 
     Hereinafter, a functional configuration example of the vacant band specification device  100  according to Embodiment 3 will be described. Similarly to  FIG. 4 , the vacant band specification device  100  includes the instruction unit  401 , the measurement unit  402 , the setting unit  403 , the specification unit  404 , and the storage unit  405 . The functional units are the same as those of  FIG. 4 , and thus, the description thereof will be described. 
     (Flow for Specifying Upper Limit of Vacant Band of Network  210 ) 
     Hereinafter, a flow for specifying the upper limit of the vacant band of the network  210  according to Embodiment 3 will be described with reference to  FIGS. 26 and 27 . 
       FIG. 26  is an explanatory diagram illustrating an example of the stored content of the management table  2600  according to Embodiment 3. For example, the management table  2600  is realized by the storage area such as the memory  302  or the disk  305  illustrated in  FIG. 3 . As illustrated in  FIG. 26 , the management table  2600  includes fields such as the transmission rate, the reception rate, the packet loss rate, the average RTT, and the correlation determination. 
     The correlation determination is a flag indicating whether or not the transmission rate, the reception rate, and the packet loss rate associated with the correlation determination are information in a case where the transmission rate and the packet loss rate have the proportional relation. For example, the correlation determination is “o” if the transmission rate and the packet loss rate have the correlation, and is “x” if the transmission rate and the packet loss rate do not have the correlation. The transmission rate is a transmission rate range in a case where the correlation is expressed by the correlation determination. The reception rate is a reception rate range in a case where the correlation is expressed by the correlation determination. The average RTT is an average RTT range in a case where the correlation is expressed by the correlation determination. 
     The management table  2600  may classify the transmission rates into a range of the transmission rates in a case where the transmission rate and the average RTT have the correlation and a range of the transmission rates in a case where the transmission rate and the average RTT do not have the correlation, and may manage the classified ranges. In other words, the management table  2600  may classify the transmission rates into a range of transmission rates which are equal to or greater than the upper limit of the vacant band and a range of transmission rates which are less than the upper limit of the vacant band, and may manage the classified ranges. 
       FIG. 27  is an explanatory diagram illustrating an example in which the upper limit of the vacant band according to Embodiment 3 is specified. In  FIG. 27 , ( 27 - 1 ) the first acceleration device  202  acquires the preset maximum transmission rate S n  and minimum transmission rate S 1 . Subsequently, the first acceleration device  202  divides the transmission rates between the maximum transmission rate S n  and the minimum transmission rate  51 , and calculates n number of transmission rates  51  to S n . 
     As illustrated in  FIG. 27 , a case where the transmission rates S 1  to S k−1  of n number of transmission rates S 1  to S n  are equal to or less than the vacant band and the transmission rates S k  to S n  are equal to or greater than the vacant band will be described. In the following description, the first acceleration device  202  may classify n number of transmission rates S 1  to S n  into the transmission rates S 1  to S k−1  which are equal to or less than the vacant band and the transmission rates S k  to S n  which are equal to or greater than the vacant band. 
     The first acceleration device  202  transmits a measurement request of the reception rate to the second acceleration device  204 . The first acceleration device  202  transmits the test packets to the second acceleration device  204  at n number of calculated transmission rates S 1  to S n  after the measurement request is transmitted. 
     Meanwhile, if the test packets is received, the second acceleration device  204  transmits a response indicating that the test packets are received to the first acceleration device  202 . If the response is received, the first acceleration device  202  calculates the RTT of the test packets, and calculates the average RTT of n number of transmission rates S 1  to S n . 
     The second acceleration device  204  measures the reception rates P 1  to P n  corresponding to the transmission rates S 1  to S n , and transmits the measurement rates to the first acceleration device  202 . The first acceleration device  202  receives the reception rates P 1  to P n  corresponding to the transmission rates S 1  to S n . 
     Here, the first acceleration device  202  specifies the transmission rate of the transmission rates S 1  to S n , in a case where the transmission rate and the average RTT have the correlation based on the calculated average RTTs t 1  to T n . In other words, the first acceleration device  202  may specify the transmission rates in a case where the transmission rate and the average RTT do not have the correlation. 
     The first acceleration device  202  substitutes the transmission rate S n , the transmission rates S x  to S n , the average value S avg  of the transmission rates S x  to S n , the average RTTs t x  to t n , and the average value t avg  of the average RTTs t x  to t n  in the following expression (7) while sequentially changing the variable x to n−1, n−2, . . . , and 1. Accordingly, the first acceleration device  202  calculates the correlation coefficients r x,n  of the transmission rates S x  to S n  for each of x=n−1, n−2, . . . , and 1. 
     
       
         
           
             
               
                 
                   
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     Here, when the variable x is sequentially changed to n−1, n−2, . . . , and  1 , since the transmission rate in which the transmission rate and the average RTT have the correlation is within a section “upper limit of vacant band to S n ” for a period during which the transmission rate S x  is equal to or greater than the upper limit of the vacant band, the correlation coefficient r x,n  tends to have a fixed value or to be comparatively great. When the transmission rate S x  is less than the upper limit of the vacant band, the correlation coefficient r x,n  tends to be changed. 
     Thus, the first acceleration device  202  specifies the transmission rates S k  to S n  until the correlation coefficient r x,n  has a fixed value and the correlation coefficient r x,n  is changed, based on the correlation coefficient r x,n . The first acceleration device  202  sets the specified transmission rates S k  to S n  as the transmission rate in which the transmission rate and the average RTT have the correlation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S 1  to S k−1 , as the transmission rates in a case where the transmission rate and the average RTT do not have the correlation. 
     The first acceleration device  202  may substitute the transmission rates S 1  to S x , the average value S avg  of the transmission rates S 1  to S x , the average RTTs t 1  to t x , and an average value t avg  of the average RTTs t 1  to t x  in the following expression (8) while sequentially changing the variable x to 2, 3, . . . , and n. Accordingly, the first acceleration device  202  calculates the correlation coefficient r 1,x  between the transmission rate S x  and the transmission rate S 1  for each of x=2, 3, . . . , and n. 
     
       
         
           
             
               
                 
                   
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     Here, when the variable x is sequentially changed to 2, 3, . . . , and n, since the transmission rate in which the transmission rate and the average RTT do not have the correlation is within a section of “S 1  to upper limit of vacant band” for a period during which the transmission rate S x  is less than the upper limit of the vacant band, there are many average RTT having no regularity, and the correlation coefficient r 1,x  tends to be decreased. When the transmission rate S x  is greater than the upper limit of the vacant band, the correlation coefficient r 1,x  tends to be comparatively greatly changed. 
     Thus, the first acceleration device  202  specifies the transmission rates S 1  to S k−1  until the correlation coefficient r 1,x  is decreased and the correlation coefficient r 1,x  is comparatively greatly changed, based on the correlation coefficient r 1,x . The first acceleration device  202  sets the specified transmission rates S 1  to S k−1  as the transmission rate in which the transmission rate and the average RTT do not have the correlation. Meanwhile, the first acceleration device  202  specifies the remaining transmission rates S k  to S n , as the transmission rates in a case where the transmission rate and the average RTT have the correlation. 
     ( 27 - 2 ) The first acceleration device  202  stores the specified result in the management table  2600 . For example, the first acceleration device  202  sets the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the transmission rates corresponding to the correlation determination “o”. 
     For example, the first acceleration device  202  sets the reception rates P k  to P n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the reception rates corresponding to the correlation determination “o”. For example, the first acceleration device  202  sets the average RTTs t k  to t n  corresponding to the transmission rates S k  to S n  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the average RTTs rates corresponding to the correlation determination “o”. 
     Meanwhile, for example, the first acceleration device  202  sets the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the transmission rates corresponding to the correlation determination “x”. 
     For example, the first acceleration device  202  sets the reception rates P 1  to P k−1  corresponding to the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the reception rates corresponding to the correlation determination “x”. For example, the first acceleration device  202  sets the average RTTs t 1  to t k−1  corresponding to the transmission rates S 1  to S k−1  in a case where the transmission rate and the packet loss rate have the specified correlation in the fields of the average RTTs corresponding to the correlation determination “x”. 
     Accordingly, the first acceleration device  202  can manage the transmission rates S k  to S n  which are equal to or greater than the upper limit of the vacant band and the transmission rates S 1  to S k−1  which are less than the upper limit of the vacant band. In other words, the first acceleration device  202  can store the range of the transmission rates S k−1  to S k , as the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band. 
     Here, the first acceleration device  202  may specify any one transmission rate within the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, as the upper limit of the vacant band. For example, the first acceleration device  202  specifies the S max =S k , as the upper limit of the vacant band. For example, the first acceleration device  202  may specify (S min  S max )/2, the upper limit of the vacant band. 
     As a result, the first acceleration device  202  can accurately specify the upper limit of the vacant band of the network  210  in which the packet loss easily occurs and the reception rate is easily disturbed. The first acceleration device  202  can accurately specify the upper limit of the vacant band even though the change in the slope of the graph of the transmission rate and the index value indicating the amount of packet loss is comparatively small immediately after the transmission rate exceeds the upper limit of the vacant band. 
     The first acceleration device  202  may further narrow the range of the transmission rates S min  to S max  which may become the upper limit of the vacant band, and may further improve the accuracy in specifying the upper limit of the vacant band. An example in which the upper limit of the vacant band is accurately specified is the same as that of  FIGS. 19 and 20 , and the description thereof will be omitted. 
     Example of Specification Process Procedure According to Embodiment 3 
     Hereinafter, an example of a specification process procedure according to Embodiment 3 for specifying the upper limit of the vacant band of the network  210  will be described with reference to  FIGS. 28 and 29 . 
       FIGS. 28 and 29  are flowcharts illustrating examples of the specification process procedure according to Embodiment 3. In  FIG. 28 , the first acceleration device  202  transmits a measurement request of the reception rate to the second acceleration device  204  (step S 2801 ). Subsequently, the first acceleration device  202  determines whether or not the response is received from the second acceleration device  204  (step S 2802 ). Here, in a case where the response is not received (step S 2802 : No), the first acceleration device  202  returns the process to step S 2801 . 
     Meanwhile, in a case where the response is received (step S 2802 : Yes), the first acceleration device  202  determines n number of transmission rates S 1  to S n  used when the test packets are transmitted based on the preset maximum transmission rate and minimum transmission rate (step S 2803 ). 
     Subsequently, the first acceleration device  202  increments a variable i, and selects a transmission rate S i  from the transmission rate S 1  to S n  (step S 2804 ). An initial value of the variable i is 0. The first acceleration device  202  transmits the test packets to the second acceleration device  204  at the selected transmission rate S i  (step S 2805 ). 
     Subsequently, the first acceleration device  202  receives the reception rate P i  measured by the second acceleration device  204  from the second acceleration device  204  (step S 2806 ). The first acceleration device  202  calculates an average RTT i  corresponding to the transmission rate S 1  based on the response which indicates that the test packets are received and is received from the second acceleration device  204  (step S 2807 ). 
     The first acceleration device  202  determines whether or not i≧n is satisfied (step S 2808 ). Here, in a case where i≧n is not satisfied (step S 2808 : No), the first acceleration device  202  returns the process to step S 2804 . 
     Meanwhile, in a case where i≧n is satisfied (step S 2808 : Yes), the first acceleration device  202  classifies the transmission rates S 1  to S n , and stores the classified transmission rates in the management table  2600  (step S 2809 ). Here, for example, the first acceleration device  202  classifies the transmission rates S 1  to S n  into the transmission rates S max  to S n  in a case where the transmission rate and the average RTT have the correlation and the transmission rates S 1  to S min  in a case where the transmission rate and the packet loss rate do not have the correlation. Thereafter, the first acceleration device  202  performs the process of step S 2901  of  FIG. 29 . 
     In  FIG. 29 , the first acceleration device  202  determines whether or not S max −S min &lt;T is satisfied (step S 2901 ). Here, in a case where S max −S min &lt;T is satisfied (step S 2901 : Yes), the first acceleration device  202  specifies the upper limit of the vacant band based on the management table  2600 , and stores the specified upper limit (step S 2902 ). The first acceleration device  202  ends the specification process. 
     Meanwhile, in a case where S max −S min &lt;T is not satisfied (step S 2901 : No), the first acceleration device  202  sets the transmission rate S a =(S min  S max )/2, and transmits the test packets to the second acceleration device  204  at the transmission rate S a  (step S 2903 ). Subsequently, the first acceleration device  202  receives the reception rate P a  measured by the second acceleration device  204  from the second acceleration device  204  (step S 2904 ). 
     The first acceleration device  202  calculates an average RTT t a  corresponding to the transmission rate S a  based on the response which indicates that the test packets are received and is received from the second acceleration device  204  (step S 2905 ). The first acceleration device  202  calculates the correlation coefficient r a,n  between the transmission rates S a  to S n  (step S 2906 ). 
     Subsequently, the first acceleration device  202  determines whether or not the correlation coefficient r a,n  is equal to or greater than the threshold R, and the difference between the correlation coefficient r a,n  and the correlation coefficient of the transmission rate in a case where the transmission rate and the packet loss rate have the correlation is less than threshold e and have the correlation (step S 2907 ). Here, in a case where the transmission rate and the packet loss rate do not have the correlation (step S 2907 : No), the first acceleration device  202  updates the fields of the transmission rates associated with the correlation determination “x” of the management table  2600 , and sets S min =S a  (step S 2908 ). The first acceleration device  202  returns the process to step S 2901 . 
     Meanwhile, in a case where the transmission rate and the packet loss rate have the correlation (step S 2907 : Yes), the first acceleration device  202  updates the fields of the transmission rates associated with the correlation determination “o” of the management table  2600 , and sets S max =S a  (step S 2909 ). The first acceleration device  202  returns the process to step S 2901 . Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Operation Example of Communication System  200  According to Embodiment 3 
     Hereinafter, an operation example of the communication system  200  according to Embodiment 3 will be described with reference to  FIGS. 30 and 31 . 
       FIGS. 30 and 31  are sequence diagrams illustrating operation examples of the communication system  200  according to Embodiment 3. In  FIG. 30 , the detection unit  1300  of the first acceleration device  202  detects that the communication with the second acceleration device  204  is time out (step S 3001 ). 
     If the time-out is detected, the detection unit  1300  inputs the measurement request to the instruction unit  401  (step S 3002 ). If the measurement request is received, the instruction unit  401  determines n number of transmission rates S 1  to S n , and notifies the measurement unit  402  of the transmission rate Si of the transmission rates S 1  to S n  (step S 3003 ). 
     If the transmission rate S i  is notified, the measurement unit  402  transmits the measurement request of the reception rate to the second acceleration device  204  (step S 3004 ). Meanwhile, if the measurement request is received, the second acceleration device  204  transmits the response to the measurement unit  402  (step S 3005 ). 
     If the response is received, the measurement unit  402  notifies the setting unit  403  of the transmission rates S i  (step S 3006 ). Subsequently, the measurement unit  402  accepts the control of the transmission rate S i  performed by the setting unit  403  (step S 3007 ). The measurement unit  402  transmits the test packets to the second acceleration device  204  at the transmission rate S i  under the control of the setting unit  403  (step S 3008 ). 
     If the test packets are received, the second acceleration device  204  measures the reception rate P i  corresponding to the transmission rate S i  (step S 3009 ). The second acceleration device  204  transmits the response indicating that the test packets are received to the measurement unit  402  (step S 3010 ). The measurement unit  402  calculates an average RTT t corresponding to the transmission rate Si based on the response which indicates that the test packets are received and is received from the second acceleration device  204  (step S 3011 ). 
     The second acceleration device  204  transmits the reception rate P i  corresponding to the measured transmission rate S i  to the measurement unit  402  (step S 3012 ). If the reception rate P i  corresponding to the transmission rate S i  is received and the average RTT i  is calculated, the measurement unit  402  notifies the instruction unit  401  the measurement result including the average RTT i  and the reception rate P i  corresponding to the transmission rates S i  (step S 3013 ). 
     If the measurement result is received, the instruction unit  401  determines whether or not n number of times of the measurement is ended by using the transmission rates S 1  to S n  (step S 3014 ). Here, in a case where n number of times of the measurement is not ended (step S 3014 : No), the instruction unit  401  returns the process to step S 3003 . 
     Meanwhile, in a case where n number of times of the measurement is ended (step S 3014 : Yes), the instruction unit  401  notifies the specification unit  404  of a specification request for the range of the transmission rates in a case where the transmission rate and the average RTT have the correlation and the measurement result (step S 3015 ). Here,  FIG. 31  will be described. 
     In  FIG. 31 , if the specification request and the measurement result are received, the specification unit  404  specifies the range of the transmission rates in a case where the transmission rate and the average RTT have the correlation (step S 3101 ). The specification unit  404  notifies the storage unit  405  of the specification result, and updates the management table  2600  in the storage unit  405  (step S 3102 ). 
     The specification unit  404  notifies the instruction unit  401  of the specification result (step S 3103 ). If the specification result is received, the instruction unit  401  determines whether or not S max −S min &lt;T is satisfied (step S 3104 ). Here, in a case where S max −S min &lt;T is satisfied (step S 3104 : Yes), the instruction unit  401  performs the process of step S 3120 . 
     Meanwhile, in a case where S max −S mm &lt;T is not satisfied (step S 3104 : No), the instruction unit  401  notifies the measurement unit  402  of the transmission rate S a =(S min  S max )/2 (step S 3105 ). 
     If the transmission rate S a  is notified, the measurement unit  402  transmits the measurement request of the reception rate to the second acceleration device  204  (step S 3106 ). Meanwhile, if the measurement request is received, the second acceleration device  204  transmits the response to the measurement unit  402  (step S 3107 ). 
     If the response is received, the measurement unit  402  notifies the setting unit  403  of the transmission rates S a  (step S 3108 ). Subsequently, the measurement unit  402  accepts the control of the transmission rate S a  performed by the setting unit  403  (step S 3109 ). The measurement unit  402  transmits the test packets to the second acceleration device  204  at the transmission rate S a  under the control of the setting unit  403  (step S 3110 ). 
     If the test packets are received, the second acceleration device  204  measures the reception rates P a  corresponding to the transmission rate S a  (step S 3111 ). The second acceleration device  204  transmits the response indicating that the test packets are received to the measurement unit  402  (step S 3112 ). The measurement unit  402  calculates an average RTT t a  corresponding to the transmission rate S a  based on the response which indicates that the test packets are received and is received from the second acceleration device  204  (step S 3113 ). 
     The second acceleration device  204  transmits the reception rate P a  corresponding to the measured transmission rate S a  to the measurement unit  402  (step S 3114 ). If the reception rate P a  corresponding to the transmission rate S a  is received and the average RTT t a  is calculated, the measurement unit  402  notifies the instruction unit  401  of the measurement result including the average RTT t a  and the reception rate P a  corresponding to the transmission rate S a  (step S 3115 ). 
     In a case where the measurement result is received, the instruction unit  401  notifies the specification unit  404  of a specification request for the range of the transmission rates in a case where the transmission rate and the average RTT have the correlation and the measurement result (step S 3116 ). 
     If the specification request and the measurement result are received, the specification unit  404  refers to the management table  2600  stored in the storage unit  405  (step S 3117 ). If the management table  2600  is referred to, the specification unit  404  specifies whether or not the transmission rate S a  is the transmission rate in a case where the transmission rate and the average RTT have the correlation (step S 3118 ). The specification unit  404  notifies the storage unit  405  of the specification result, and updates the management table  2600  in the storage unit  405  (step S 3119 ). The specification unit  404  returns the process to step S 3103 . 
     In a case where S max −S min &lt;T is satisfied and the process of step S 3120  is performed, the instruction unit  401  outputs the upper limit of the vacant band (step S 3120 ). Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Description of Embodiment 4 
     Hereinafter, Embodiment 4 will be described. In the following description, the same elements as those of Embodiments 1 to 3 will be assigned the same reference signs as those of Embodiments 1 to 3, and the redundant description thereof will be omitted in some cases. 
     Example of Communication System  200  According to Embodiment 4 
     Hereinafter, an example of the communication system  200  according to Embodiment 4 to which the vacant band specification device  100  illustrated in  FIG. 1  is applied will be described with reference to  FIG. 32 . 
       FIG. 32  is an explanatory diagram illustrating an example of the communication system  200  according to Embodiment 4. In  FIG. 32 , the communication system  200  includes the first calculation device  201 , the first acceleration device  202 , the second calculation device  203 , the second acceleration device  204 , and the management device  3200 . In the communication system  200 , the first acceleration device  202  and the second acceleration device  204  are connected via the wireless network  210 . 
     Here, similarly to  FIG. 2 , the first acceleration device  202  tends to be desired to specify the upper limit of the vacant band of the network  210 . Thus, in the following description, a case where the first acceleration device  202  operates as the vacant band specification device  100  and specifies the upper limit of the vacant band of the network  210  will be described. 
     In Embodiment 4, the first acceleration device  202  specifies the upper limit of the vacant band under the control of the management device  3200 . In  FIG. 32 , ( 32 - 1 ) the first calculation device  201  transmits an inquiry about channel quality to the management device  3200 . 
     ( 32 - 2 ) If the inquiry about the channel quality is received, the management device  3200  transmits the measurement request including the maximum transmission rate, the minimum transmission rate, and information for specifying the second acceleration device  204  to the first acceleration device  202 . The management device  3200  transmits the measurement request to the second acceleration device  204 . The management device  3200  causes the first acceleration device  202  to specify the upper limit of the vacant band, and receives the upper limit of the vacant band from the first acceleration device  202 . 
     ( 32 - 3 ) The management device  3200  transmits the upper limit of the vacant band to the first calculation device  201 . 
     (Functional Configuration Example of Vacant Band Specification Device  100 ) 
     Hereinafter, a functional configuration example of the vacant band specification device  100  according to Embodiment 4 will be described. Similarly to  FIG. 4 , the vacant band specification device  100  includes the instruction unit  401 , the measurement unit  402 , the setting unit  403 , the specification unit  404 , and the storage unit  405 . The functional units are the same as those of  FIG. 4 , and thus, the description thereof will be described. 
     (Flow for Specifying Upper Limit of Vacant Band of Network  210 ) 
     Hereinafter, a flow for specifying the upper limit of the vacant band of the network  210  according to Embodiment 4 will be described. 
     Example of Specification Process Procedure According to Embodiment 4 
     Hereinafter, an example of a specification process procedure according to Embodiment 4 for specifying the upper limit of the vacant band of the network  210  will be described with reference to  FIGS. 33 and 34 . 
       FIGS. 33 and 34  are flowcharts illustrating examples of the specification process procedure according to Embodiment 4. In  FIG. 33 , the first acceleration device  202  receives the measurement request including the maximum transmission rate, the minimum transmission rate, and the information for specifying the second acceleration device  204  from the management device  3200  that receives the inquiry about the channel quality from the first calculation device  201  (step S 3301 ). 
     Subsequently, the first acceleration device  202  specifies the second acceleration device  204  and stores the maximum transmission rate and the minimum transmission rate, based on the received measurement request (step S 3302 ). Here, the processes of steps S 3303  to S 3310  are the same as the processes of steps S 2101  to S 2108  illustrated in  FIG. 21 , and thus, the description thereof will be omitted. Thereafter, the first acceleration device  202  performs the process of step S 3401  of  FIG. 34 . 
     In  FIG. 34 , the processes of steps S 3401  to S 3408  are the same as the processes of steps S 2201  to S 2208  illustrated in  FIG. 22 , and thus, the description thereof will be omitted. Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     Operation Example of Communication System  200  According to Embodiment 4 
     Hereinafter, an operation example of the communication system  200  according to Embodiment 4 will be described with reference to  FIGS. 35 and 36 . 
       FIGS. 35 and 36  are sequence diagrams illustrating operation examples of the communication system  200  according to Embodiment 4. In  FIG. 35 , the first calculation device  201  detects that the communication of the second calculation device  203  is time out (step S 3501 ). 
     If the time-out is detected, the first calculation device  201  transmits an inquiry about channel quality to the management device  3200  (step S 3502 ). If the inquiry about the channel quality is received, the management device  3200  transmits the measurement request including the maximum transmission rate, the minimum transmission rate, and the information for specifying the second acceleration device  204  to the instruction unit  401  (step S 3503 ). Here, the processes of steps S 3504  to S 3514  are the same as the processes of steps S 2304  to S 2313  illustrated in  FIG. 23 , and thus, the description thereof will be omitted. Hereinafter,  FIG. 36  will be described. 
     In  FIG. 36 , the processes of steps S 3601  to S 3617  are the same as the processes of steps S 2401  to S 2417  illustrated in  FIG. 24 , and thus, the description thereof will be omitted. Here, the process of steps S 3618  and S 3619  will be described. 
     In a case where S max −S min &lt;T is satisfied and the process of step S 3618  is performed, the instruction unit  401  transmits the upper limit of the vacant band to the management device  3200  (step S 3618 ). If the upper limit of the vacant band is received, the management device  3200  transmits the upper limit of the vacant band to the first calculation device  201  (step S 3619 ). Accordingly, the first acceleration device  202  can accurately specify the upper limit of the vacant band. 
     As described in the respective embodiments, according to the vacant band specification device  100 , it is possible to acquire the index value indicating the amount of packet loss for each transmission rate by transmitting the packets from the first device  130  to the second device  140  at each of the plurality of transmission rates. According to the vacant band specification device  100 , it is possible to specify the transmission rate, among the plurality of transmission rates, in a case where the transmission rate and the index value indicating the amount of packet loss have the dependence relation based on the index value for each transmission rate. According to the vacant band specification device  100 , it is possible to specify the upper limit of the vacant band between the first device  130  and the second device  140  based on the specified result. 
     Accordingly, the vacant band specification device  100  can specify the range of the values which may become the upper limit of the vacant band. The vacant band specification device  100  can improve the accuracy in specifying the upper limit of the vacant band even though the packet loss easily occurs and it is difficult to ascertain the relationship between the transmission rate and the reception rate in magnitude. 
     According to the vacant band specification device  100 , it is possible to transmit the packets from the first device  130  to the second device  140  at another transmission rate which is less than the transmission rate in a case where the transmission rate and the index value have the dependence relation and is greater than the transmission rate in a case where the transmission rate and the index value do not have the dependence relation. According to the vacant band specification device  100 , it is possible to acquire the index value indicating the amount of packet loss at another transmission rate, and it is possible to specify whether or not another transmission rate is the transmission rate in a case where the transmission rate and the packet loss rate have the dependence relation based on the index value at another transmission rate. 
     Accordingly, the vacant band specification device  100  can further narrow the range of the values which may become the upper limit of the vacant band. The vacant band specification device  100  can specify the upper limit of the vacant band from the narrowed range, and can improve the accuracy in specifying the upper limit of the vacant band. 
     According to the vacant band specification device  100 , it is possible to acquire the reception rate corresponding to the transmission rate when the packets are transmitted whenever the packets are transmitted. According to the vacant band specification device  100 , it is possible to transmit the packets from the first device  130  to the second device  140  while gradually increasing the transmission rate from the minimum transmission rate by the predetermined amount until the ratio of the increase in the reception rate to the increase in the transmission rate is equal to or less than the predetermined value. Accordingly, the vacant band specification device  100  can reduce the number of times the packets are transmitted. 
     According to the vacant band specification device  100 , it is possible to transmit the packets from the first device  130  to the second device  140  while gradually decreasing the transmission rate from the maximum transmission rate by the predetermined amount until the ratio of the decrease in the reception rate to the decrease in the transmission rate is equal to or greater than the predetermined value. Accordingly, the vacant band specification device  100  can reduce the number of times the packets are transmitted. 
     According to the vacant band specification device  100 , it is possible to acquire the reception rate for each transmission rate. According to the vacant band specification device  100 , it is possible to specify the transmission rate in a case where the transmission rate and the packet loss rate have the dependence relation based on the index value of the index values of the respective transmission rates in a case where the ratio of the increase in the reception rate to the increase in the transmission rate is equal to or less than the predetermined value. Accordingly, the vacant band specification device  100  can reduce the number of index values used when the transmission rate in a case where the transmission rate and the packet loss rate have the dependence relation is specified, and can reduce the number of processes. 
     According to the vacant band specification device  100 , it is possible to use the proportional relation in which the index value indicating the amount of packet loss becomes great as the transmission rate becomes great, as the dependence relation. Accordingly, the vacant band specification device  100  can improve the accuracy in specifying the upper limit of the vacant band in the network in which the transmission rate and the index value have the proportional relation. 
     According to the vacant band specification device  100 , the relation in which the correlation coefficient between the transmission rate and the index value indicating the amount of packet loss is equal to or greater than the threshold can be used as the dependence relation. Accordingly, the vacant band specification device  100  can improve the accuracy in specifying the upper limit of the vacant band even in the network in which the transmission rate and the index value do not have the proportional relation. 
     According to the vacant band specification device  100 , it is possible to acquire the index value indicating a value indicating a percentage of packets which are not received by the second device  140  with respect to the packets transmitted from the first device  130  to the second device  140 . Accordingly, the vacant band specification device  100  can use the index value on which the amount of packet loss is comparatively accurately reflected, and can improve the accuracy in specifying the upper limit of the vacant band. 
     According to the vacant band specification device  100 , it is possible to acquire the index value indicating the time from which the packets are transmitted from the first device  130  to when the response which corresponds to the packets transmitted from the first device  130  and is received from the second device  140  is received. Accordingly, the vacant band specification device  100  can improve the accuracy in specifying the upper limit of the vacant band even in the network including the radio section. The vacant band specification device  100  can cause the second device  140  not to perform the process of measuring the packet loss rate. 
     According to the vacant band specification device  100 , it is possible to reduce the components having the predetermined frequency or more for the index value for each transmission rate, and it is possible to calculate another index value for each transmission rate. According to the vacant band specification device  100 , it is possible to specify the transmission rate, among the plurality of transmission rates, in a case where the transmission rate and the index value have the dependence relation based on another index value for each transmission rate. Accordingly, in a case where the index value indicating the amount of packet loss is fluctuated due to a randomly occurred factor, the vacant band specification device  100  can change the index value to an index value of which the fluctuation is suppressed, and can improve the accuracy in specifying the upper limit of the vacant band. 
     Although it has been described in the embodiment that the vacant band specification device  100  uses the packet loss rate or the RTT as the index value, the disclosure is not limited thereto. For example, the vacant band specification device  100  may specify the upper limit of the vacant band by using the packet loss rate as the index value, and may specify the upper limit of the vacant band by using the RTT as the index value. The vacant band specification device  100  may statistically specify the upper limit of the vacant band from the specified upper limits of the vacant band. 
     The vacant band specification method described in the present embodiment may be realized by causing a computer such as a personal computer or a workstation to execute a previously prepared program. The present vacant band specification program is recorded in a computer-readable recording medium such as a hard disk, a flexible disk, a CD-ROM, a MO, or a DVD, and is executed by the computer by being read from the recording medium. The present vacant band specification program may be distributed via a network such as the Internet. 
     All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.