Abstract:
The present invention enhances the dynamic frequency selection 9DFS) algorithms used in Wireless LANs by adding a channel swapping mechanism. The aim of the traditional DFS algorithm is to dynamically select channels in a wireless LAN in such a way that the best performance is achieved. However, not always the optimal channel selection is achieved. This invention describes an addition to the DFS algorithm in such a way that two APs can decide to swap channels instead of one AP switching to another channel. To avoid the problem of sub-optimal channel selection, a requesting AP sends Swap Requests to other APs in order to sense the willingness of other APs to swap channels with the requesting AP.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims priority of European Patent Application No. 01304146.2, which was filed on May 8, 2001. 
   FIELD OF THE INVENTION 
   The present invention relates to a communication system comprising a plurality of access points (APs) and network stations, each said network station being arranged to communicate with one of said access points through a wireless communication protocol. The invention also relates to access points for such a communication system. 
   BACKGROUND OF THE INVENTION 
   Wireless local area networks (LANs) have been developed as an enhanced replacement for wired LANs. In a wireless LAN for data-communication a plurality of (mobile) network stations (e.g., personal computers, telecommunication devices, etc.) are present that are capable of wireless communication. As compared to wired LANs, data-communication in a wireless LAN can be more versatile, due to the flexibility of the arrangement of network stations in the area covered by the LAN, and due to the absence of cabling connections. 
   Wireless LANs are generally implemented according to the standard as defined by the ISO/IEC 8802-11 international standard (IEEE 802.11). IEEE 802.11 describes a standard for wireless LAN systems that will operate in the 2.4-2.5 GHz ISM (industrial, scientific and medical) band. This ISM band is available worldwide and allows unlicensed operation for spread spectrum systems. For both the US and Europe, the 2,400-2,483.5 MHz band has allocated, while for some other countries, such as Japan, another part of the 2.4-2.5 GHz ISM ban has been assigned. The IEEE 802.11 standard focuses on the MAC (medium access control) and PHY (physical layer) protocols for AP based networks and ad-hoc networks. 
   In AP based wireless networks, the stations within a group or cell can communicate only directly to the AP. This AP forwards messages to the destination station within the same cell or through the wired distribution system to another AP, from which such messages arrive finally at the destination station. In ad-hoc networks, the stations operate on a peer-to-peer level and there is no AP or (wired) distribution system. 
   The 802.11 standard supports three PHY protocols: DSSS (direct sequence spread spectrum), FHSS (frequency hopping spread spectrum), and infrared with PPM (pulse position modulation). All these three PHYS provide bit rates of 1 and 2 Mbit/s. Furthermore, IEEE 802.11 includes extensions  11   a  and  11   b  which allow for additional higher bit rates: Extension  11   b  provides bit rates 5.5 and 11 Mbit&#39;s as well as the basic DSSS bit rates of 1 and 2 Mbit/s within the same 2.4-2.5 GHz ISM band. Extension  11   a  provides a high bit rate OFDM (orthogonal Frequency Division Multiplexing modulation) PHY standard providing bit rates in the range of 6 to 54 Mbit/s in the 5 GHz band. 
   The IEEE 802.11 basic MAC protocol allows interoperability between compatible PHYs through the use of the CSMA/CA (carrier sense multiple access with collision avoidance) protocol and a random back-off time following a busy medium condition. The IEEE 802.11 CSMA/CA protocol is designed to reduce the collision probability between multiple stations accessing the medium at the same time. Therefore, a random back-off arrangement is used to resolve medium contention conflicts. In addition, the IEEE 802.11 MAC protocol defines special functional behaviour for fragmentation of packets, medium reservation via RTS/CTS (request-to-send/clear-to-send) polling interaction and point coordination (for time-bounded services). 
   Moreover, the IEEE 802.11 MAC protocol defines Beacon frames sent at regular intervals by the AP to allow stations to monitor the presence of the AP. The IEEE 802.11 MAC protocol also gives a set of management frames including Probe Request frames which are sent by a station and are followed by the Probe Response frames sent by an available AP. This protocol allows a station to actively scan for APs operating on other frequency channels and for the APs to show to the stations what parameter settings the APs are using. 
   Every DSSS AP operates on one channel. The number of channels depends on the regulatory domain in which the wireless LAN is used (e.g. 11 channels in the US in the 2.4 GHz band). The number can be found in ISO/IEC 8802-011, ANSI/IEEE Std 802.11 Edition 1999-00-00. Overlapping cells using different channels can operate simultaneously without interference if the channel distance is at least 3. Non-overlapping cells can always use the same channels simultaneously without interference. Channel assignment can be dynamic or fixed. Dynamic channel assignment is preferable, as the environment itself is dynamic as well. 
   SUMMARY OF THE INVENTION 
   The present invention relates to an access point for a wireless LAN communication network, arranged to:
         monitor its access point traffic load   send probe requests and probe responses to other access points   receive probe requests and probe responses from other access points   include information on the traffic load in the probe responses   calculate and store an interference parameter for each of a plurality of its possible channels   calculate and store a channel sharing parameter for each of the plurality of channels   calculate a regular channel quality parameter for each of the plurality of channels, indicative of the amount of interference and channel sharing on each of the plurality of channels, using the interference and channel sharing parameters   dynamically select an optimum channel from the plurality of possible channels using the regular channel quality parameters,
 
wherein the access point is arranged to select the optimum channel by mutually swapping channels with another access point using a swapping mechanism.
       

   By introducing a swapping option between adjacent access points, the present invention provides a better overall performance for the wireless LAN. 
   Moreover, the present invention relates to a wireless LAN communication network, comprising at least two access points as described above. 
   Furthermore, the present invention relates to a method of selecting an optimum channel by an access point in a wireless LAN communication network, comprising the steps of:
         monitor its access point traffic load   send probe requests and probe responses to other access points   receive probe requests and probe responses from other access points   include information on the traffic load in the probe responses   calculate and store an interference parameter for each of a plurality of its possible channels   calculate and store a channel sharing parameter for each of the plurality of channels   calculate a regular channel quality parameter for each of the plurality of channels, indicative of the amount of interference and channel sharing on each of the plurality of channels, using the interference and channel sharing parameters   dynamically select an optimum channel from the plurality of possible channels using the regular channel quality parameters,
 
wherein the access point is arranged to select the optimum channel by mutually swapping channels with another access point using a swapping mechanism.
       

   The present invention also relates to a computer program product to be loaded by an access point for a wireless LAN communication network, the computer program product providing the access point with the capacity to:
         monitor its access point traffic load   send probe requests and probe responses to other access points   receive probe requests and probe responses from other access points   include information on the traffic load in the probe responses   calculate and store an interference parameter for each of a plurality of its possible channels   calculate and store a channel sharing parameter for each of the plurality of channels   calculate a regular channel quality parameter for each of the plurality of channels, indicative of the amount of interference and channel sharing on each of the plurality of channels, using the interference and channel sharing parameters   dynamically select an optimum channel from the plurality of possible channels using the regular channel quality parameters,
 
wherein the access point is arranged to select the optimum channel by mutually swapping channels with another access point using a swapping mechanism.
       

   Moreover, the present invention relates to a data carrier provided with a computer program product as described above. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Below, the invention will be explained with reference to some drawings, which are, intended for illustration purposes only and not to limit the scope of protection as defined in the accompanying claims. 
       FIG. 1   a  shows the cells of three APs in a wireless LAN in the Prior Art. 
       FIG. 1   b  shows the cells of four APs in a wireless LAN in the Prior Art. 
       FIG. 1   c  shows the cells of four APs in a wireless LAN as described in the invention. 
       FIG. 2  shows a block diagram of the arrangement of the present invention for a wireless LAN interface card. 
       FIG. 3  shows a schematic block diagram of a network station in the present invention. 
       FIG. 4  shows a schematic block diagram of an access point (AP) in the present invention. 
       FIG. 5  shows a flow diagram of the swapping procedure of a requesting AP in the present invention. 
       FIG. 6  shows a flow diagram of the swapping procedure of a responding AP in the present invention. 
   

   DESCRIPTION OF PREFERRED EMBODIMENTS 
   In the co-owned, co-pending, U.S. patent application Ser. No. 10/140,689, filed 8 May 2002, entitled “Network System Comprising Access Point” (our reference Awater 12-23-14), the contents of which are incorporated by reference herein, dynamic assignment of channels is called dynamic frequency selection (DFS). The aim of the DFS algorithm is to dynamically assign channels in a wireless LAN in such a way that the best performance is achieved. Performance can be expressed in terms of throughput, delay and fairness. An AP with dynamic frequency selection is able to switch its channel in order to obtain a better operating channel. It will usually choose a channel with less interference and channel sharing than that on the current channel. 
   In the algorithm of the Awater 12-23-14 application, the amount of interference an AP is experiencing on a certain channel X, is expressed by a parameter I(X). Channel sharing is expressed by a parameter CS(X). The values of CS(X) are combined to calculate a so-called Channel Sharing and Interference Quality CSIQ(X). The value of CSIQ(X) is a measure for the amount of interference and channel sharing belonging to a certain channel X. In one embodiment:
 
 CS ( X )=Share ( RX L ( X ))*Load( X )
 
and
 
             I   ⁡     (   X   )       =       Noise   ⁢           ⁢     L   ⁡     (   j   )         +       ∑     j   =   1       X   -   1       ⁢           ⁢     Y   ⁡     (   j   )         +       ∑     j   =     X   +   1       N     ⁢           ⁢     Y   ⁡     (   j   )                 
where:
         Y(j)=(RX_L(j)−RJ(j−X))*Load(j),   RX L(X) corresponds to a reception level of a response signal with channel frequency X,   Share(RX L(X)) equals 0 if RX L(X) is below 10 dB under the signal detection threshold,   Share(RX L(X)) equals 0.1 if RX L(X) is above 10 dB and under 9 dB below the signal detection threshold,   Share(RX L(X)) equals i/10 if RX L(X) is above 10-i+1 dB and under 10-i dB below the signal detection threshold, for i=2, . . . , 8,   Share(RX L(X)) equals 0.9 if RX L(X) is above 2 dB and under 1 dB below the signal detection threshold,   Share(RX L(X)) equals 1 if RX L(X) is above 1 dB below the signal detection threshold,   Load(X) corresponds to the load on channel frequency X,   Noise L(j) corresponds to the noise level of channel frequency j,   N is the total number of channel frequencies,   RX L(j) corresponds to a reception level of a response signal with channel frequency j,   RJ(j-X) corresponds to a rejection level of a signal with channel frequency j on channel frequency X, and   Load(j) corresponds to the load on channel frequency j.       
   In the Awater 12-23-14 application, an AP will switch to a channel Y if the value of CSIQ(Y) is the highest of all the values CSIQ(X) of the channels X=1, . . . N with the number of available channels. So the best channel quality is represented by the highest CSIQ(X). The functioning of the DFS algorithm in the Awater 12-23-14 application, will be explained in an example with help of  FIG. 1   a  and  1   b . The wireless LAN  1 , shown in  FIG. 1   a , comprises a number of access points of which three access points AP 1 , AP 2 , AP 3  are shown. These access points serve as access point for their respective cells  3 , 5 , 7  which are each schematically depicted by a circle around their respective access point. In the initial situation, the access points AP 1 , AP 2 , AP 3  are communicating with their network stations on channels C 1 , C 2 , C 3 , respectively. The cells  3 , 5 , 7  may have different sizes. Cell size is depending on the desired coverage area of an access point and on the requirements of data throughput in the cell. The cell size can be controlled by suitable setting of the levels of the defer behaviour threshold and carrier sense detection threshold as known from EP-A-0903891. For example, a cell may comprise a number of network stations, NS 1 , NS 2  that require high throughputs. In that case, the cell size should be small such that other network stations will be left out of the cell as much as possible. In another case, for example, in a cell only few network stations with low throughput requirements will be present. Then, a single large cell comprising these network stations will be sufficient to handle all data traffic related to that cell.  FIG. 1   a  shows the initial situation of a wireless LAN  1  comprising three DFS-capable Aps. In the LAN  1  a plurality of network stations NS 1 , NS 2  is present of which only two are shown. In  FIG. 1   a , for example, the network station NS 1  is communicating with the access point AP 1  for all its data traffic. The network station NS 1  itself continuously monitors the communication quality (i.e. the difference between signal reception level and average noise level) of its communication with the access point API. As long as a good communication quality for the associated access point AP 1  is maintained, the network station NS 1  stays communicating with AP 1 . When the communication quality decreases below a predetermined level, the network station NS 1  starts to search for another cell  5  (an access point AP 2 ) with a better communication quality. To this purpose, the network station NS 1  is probing the associated access point AP 1  and all other access points (i.e. AP 2 ) within range, as known to persons skilled in the art. In this procedure the network station NS 1  uses the signal reception level of Beacon frames received from the associated access point AP 1  and Probe Response frames from the other access point AP 2 . The Probe Response frames are received by the network station NS 1  following Probe Request frames sent by the network station NS 1 . As known from IEEE 802.11, the other access point AP 2  will be operating on a channel with another frequency than the one of access point AP 1 . Network station NS 2 , shown in  FIG. 1   a , is communicating with AP 2 . When the communication quality decreases, this network station NS 2  also will start to search for another cell with a better communication quality but will not be able to find a better AP so network station NS 2  will stay communicating with AP 2 . 
     FIG. 1   b  shows the situation where a non-DFS access point AP 4  using, for example channel  9 , has arrived within the range of the DFS-capable API. With the DFS algorithm of the Awater 12-23-14 application, access point AP 1 , operating on channel  10 , will switch to channel  4  or to channel  11  in order to have at least a channel distance of 2 with every neighboring cell. 
   A problem of the DFS algorithm described in the Awater 12-23-14 application is the inability to optimize the overall performance. All Aps in a wireless LAN will currently optimize their own performance and will not take performance of other APs into consideration. It may well be that, from a network point of view, the division of the channels over the difference APs is not optimal. 
   In  FIG. 1   c  a schematic overview of a preferred embodiment is shown. A wireless LAN  1  comprises a set of access points AP 1 , AP 2 , AP 3  which have overlapping cells  3 , 5 , 7 . In this way (mobile) network stations are able to communicate with an AP in a continuous area. Besides LAN  1  a fourth access point AP 4  is present having an accompanying cell  9 . As in the situation described with reference to  FIG. 1   b , it is assumed that AP 4  is a non-DFS AP. However, it should be understood that AP 4  may be any kind of radio source acting on channel C 4 . The circles  43  and  45  depict the positions in which the receive level equals the lowest possible carrier detect threshold of respectively AP 1  and AP 2 . 
     FIG. 2  shows an example of a block diagram of an arrangement of the present invention for a medium access controller (MAC) device  11  on a wireless LAN interface card  30  installed in network station NS 1 , NS 2  or on a similar wireless LAN interface card  130  installed in access point AP 1 , AP 2 , respectively. 
   Here, the MAC device  11  is schematically depicted, showing only a signal-processing unit  12 , a signal reception level detection circuit  13 , an antenna  31  and an on-board memory  14  as needed for the description of this embodiment of the invention. The MAC device  11  may comprise other components not shown here. Also, the components  12 , 13 , 14  which are shown, may be separate devices or integrated into one device. As desired, the devices also may be implemented in the form of analog or digital circuits. The on-board memory  14  may comprise RAM,ROM, FlashROM and/or other types of memory devices, as are known in the art. 
     FIG. 3  shows a schematic block diagram of an embodiment of a network station NS 1 , NS 2  comprising processor means  21  with peripherals. The processor means  21  is connected to memory units  18 , 22 , 23 , 24  which store instructions and data, one or more reading units  25  (to read, e.g., floppy disks  19 , CD ROM&#39;s  20 , DVD&#39;s, etc.), a keyboard  26  and a mouse  27  as input devices, and as output devices, a monitor  28  and a printer  29 . Other input devices, like a trackball and a touch screen, and output devices may be provided for. For data-communication over the wireless LAN  1 , and interface card  30  is provided. The interface card  30  connects to an antenna  31 . 
   The memory units shown comprise RAM  22 , (E)EPROM  23 , ROM  24  and hard disk  18 . However, it should be understood that there may be provided more and/or other memory units known to persons skilled in the art. Moreover, one or more of them may be physically located remote from the processor means  21 , if required. The processor means  21  are shown as one box, however, they may comprise several processing units functioning in parallel or controlled by one main processor, that may be located remote from one another, as is known to persons skilled in the art. 
   In an alternative embodiment of the present invention, the network station  5 , 6  may be a telecommunication device in which the components of interface card  30  are incorporated as known to those skilled in the art. 
     FIG. 4  shows a schematic block diagram of an embodiment of an access point AP 1 , AP 2 ,AP 3  comprising processor means  121  with peripherals. The processor means  121  are connected to memory units  118 , 122 , 123 , 124  which store instructions and data, one or more reading units  125  (to read, e.g., floppy disks  119 , CD ROM&#39;s  120 , DVD&#39;s, etc.), a keyboard  126  and a mouse  127  as input devices, and a output devices, a monitor  128  and a printer  129 . For data-communication over the wireless LAN  1 , an interface card  130  is provided. The interface card  130  connects to an antenna  131 . Furthermore, the access point AP 1 , AP 2 , AP 3  is connected to a wired distribution network  140  through I/O means  132  for communication with, e.g., other access points. The memory units shown comprise RAM  133 , (E)EPROM  123 , ROM  124  and hard disk  118 . However, it should be understood that there may be provided more and/or other memory units known to persons skilled in the art. Moreover, one or more of them may be physically located remote from the processor means  121 , if required. The processor means  121  are shown as one box, however, they may comprise several processing units functioning in parallel or controlled by one main processor, that may be located remote from one another, as is known to persons skilled in the art. Moreover, other input/output devices than those shown (i.e.  126 , 127 , 128 , 129 ) may be provided. 
   In an alternative embodiment of the present invention, the access point AP AP 2 , AP 3  may be a telecommunication device in which the components of interface card  130  are incorporated as known to those skilled in the art. 
   The appearance of a new access point AP 4  shown in  FIG. 1   c  will cause sudden interference to AP 1  because it is using channel C 4 =9 which has a channel distance less than 3 to the channel C 1 =10 of AP 1 . Now, in accordance with the invention, access point AP 1  decides to start a swapping procedure. 
     FIG. 5  shows a flow diagram of the swapping procedure for the requesting access point API. In the procedure of  FIG. 5  the following parameters are used:
     regCSIQ this is a quality parameter calculated for every possible channel on which the AP can operate; its value is a measure for both channel sharing and interference for the channel concerned. The formula is given by:
 
reg CSIQ ( X )= CS ( X )+CorFac× I ( X )
    In contrast with the CSIQ in the Awater 12-23-14 application, the lower the value for regCSIQ(X), the better the channel X. The formulas for CS (X) and l(X) are found in the Awater 12-23-14application; the parameter CorFac is a correction factor that is preferably equal to 1.   ssCSIQ swap specific CSIQ; this is a specially calculated quality paramter.   
   The formula is given by:
 
 ssCSIQ ( X )=reg CSIQ ′( X )+SwapPenalty
      where regCSIQ′(X) is calculated in the same was as regCSIQ(X) but under the assumption that a responding AP already uses the channel of a requesting AP, i.e., a situation is assumed in which swapping has already occurred. The SwapPenalty is a parameter indicating that swapping is associated with a certain penalty. It may be zero but preferably it has a positive value, e.g. 10.   

   At the start of the swapping procedure, access point AP 1  is using channel C 1 =10. At step  51  the requesting access point AP 1  collects interference and sharing information by means of sending Probe Requests to other APs. Then at step  52 , AP 1  calculates the regCSIQ values for all possible channels. At step  53 , AP 1  calculates a swap specific CSIQ (ssCSIQ) for every channel used by any AP responding to the Probe Request. For the calculation of the swap specific CSIQ values, the formula for regCSIQ is used, but with the assumption that the responding access points AP 2 , AP 3  are not using the channel on which they are actually operating, but the channel on which the requesting AP is operating. 
   The swap specific CSIQ value is increased by a certain amount, (e.g., by 10). A swap should not be executed when it is not necessary, because of possible overhead costs. By increasing the ssCSIQ by e.g. 10, it becomes more likely that a channel with a regular CSIQ is selected for switching and swapping is not necessary. 
   Now at step  55 , the lowest CSIQ is determined out of all the calculated regCSIQ values and all the ssCSIQ values. If the lowest ssCSIQ is smaller than the lowest regCSIQ the procedure will go on to step  57 . If this in not the case step  69  will be executed. At step  57 , AP 1  calculates the difference between the lowest regCSIQ and the lowest ssCSIQ. This difference, named SwapBinP AP1 , is the benefit in performance for AP 1  if AP 1  would swap channels (with the AP corresponding to the lowest ssCSIQ) instead of switching its channel to the channel corresponding to the lowest regCSIQ. At step  59 , a Swap Request is sent using the channel corresponding to the lowest ssCSIQ value. The swap request contains the channel C 1  of AP 1  requesting the swap, and it also contains the value for SwapBinP AP1 . 
   Now at step  61 , the access point AP 1  will wait for a Swap Response during a predefined time period T_wait. If API has received a Swap Response within T_wait ms, the result of step  63  is YES and step  65  follows. If the result of the test at step  63  is NO, then the next step will be step  69  and the channel will be switched to a channel C 5 , corresponding to the lowest regCSIQ. 
   At step  65 , the Swap Response is checked. If the Swap Response is ‘yes’, then step  67  follows. This means that AP 1  will change its channel to the value of the one of the responding access point AP 2  (i.e., C 2 ). If at step  65  the Swap Response is ‘no’, step  69  will be executed and AP 1  will switch to said channel C 5 . 
     FIG. 6  shows a flow diagram of the swapping procedure for the responding access point AP 2 . At the start of the procedure, access point AP 2  is using channel C 2 =6. At step  75 , access point AP 2  is operating normally and is stand-by for any Swap Request. If, at step  77 , a request is received, AP 2  will proceed to step  79 . If no Swap Request is received AP 2  will stay at step  75 . At step  79 , the access point AP 2  will rescan all the channels in order to get the Probe Responses of neighbouring APs. During the scan of a channel X, AP 2  switches to the channel in question (i.e. X) and configures itself temporarily to the lowest defer threshold and bit rate to allow communication over as large as possible distance, see circle  45  in  FIG. 1   c . AP 2  sends a Probe Request frame to evoke a probe Response from all APs tuned to the channel in question and within radio range. The Probe Response packets sent by the APs responding to the Probe Request, carry information on load factors from each AP using the channel in question. The gathered load information from all the probe-responding APs together with the receive levels of the Probe Responses, are stored by AP 2 . This is done for all the channels and in the same way as m the Awater 12-23-14 application. 
   Next, at step  80 , the regCSIQ value for the operating channel of AP 2  is calculated. This means regCSIQ(C 2 ) is calculated. At step  81 , the value of ssCSIQ is calculated for the channel that is used by the swap requesting AP 1 . This means ssCSIQ(C 1 ) is calculated using the load and receive level information stored by AP 2  at step  79 . Then at step  83 , access point AP 2  switches its channel to the one of the swap requesting AP 1  (i.e., C 1 ). At step  85 , the value of ssCSIQ(C 1 ) is compared to the value of regCSIQ(C 2 ). If ssCSIQ(C 1 ) is lower than regCSIQ(C 2 ), then access point AP 2  will send a Swap Response ‘yes’ at step  87 . If ssCSIQ(C 1 ) is not lower than regCSIQ(C 2 ) the procedure will go to step  88 . In step  88  the administrative domain (e.g. company or organization) of AP 1  is compared with the one of AP 2 . If the domains are not the same, step  90  is executed. If the two domains match, then step  89  will follow in which another, so-called ‘sacrifice’ test is done. At this step the benefit in performance for, and predicted by, requesting AP 1  (i.e., SwapBinP AP1 , e.g., the difference between the lowest of all regular channel quality parameters (regCSIQ) and the lowest of all swap specific channel quality parameters (ssCSIO)) is compared to the predicted decrease in performance for AP 2  (i.e., ssCSIQ(C 1 )-regCSIQ(c 2 )). If the benefit in performance for AP 1  is higher than the decrease in performance for AP 2 , access point AP 2  will sacrifice its channel and will agree to swap channels. This means that step  87  will follow. If the answer to the test in step  88  is NO, then step  90  follows. This means that AP 2  will send a Swap Response ‘no’ to the swap requesting AP 1 . After this, AP 2  will switch its channel back to CS=6, see step  91 . 
   The swapping procedure described above is not a low-overhead solution. Therefore, it should not be attempted frequently. It should only be attempted once per channel change. Once a swap has failed for a certain AP, it should not be attempted in the near future. Therefore, the information record that exists for every DFS-capable AP, also contains a timer. This timer is used to ensure that swap requests to the same AP are separated by a certain number of hours (i.e., 24).