Abstract:
A system and method to emulate any TDM circuit on a Real-Time Scheduled Packet Network. The TDM circuit can be any serial or parallel bit stream, of any bit rate, and can either be synchronized to the Real-Time Scheduled Packet Network, or can be asynchronous to the network. The present system and method determines the requisite descriptors of a scheduled IP itinerary for any emulated TDM circuit.

Description:
[0001]    A TDM circuit, once established, offers a bandwidth that is completely free of contention from other circuits. If an application or service has a dedicated TDM circuit, then it has guaranteed bandwidth at all times.  
           [0002]    A conventional IP network cannot make such claims for any of the flows in its network, as long as there is more than one flow that contends for bandwidth somewhere along the path. Various prioritization and traffic engineering schemes have been proposed and implemented to combat this problem, but the result remains that jitter-free bandwidth cannot be guaranteed.  
           [0003]    Real-Time Scheduled Packet Networks provide deterministic, scheduled flow paths for IP packets with minimal queuing delay and no jitter or packet loss. This technology is ideal for real-time IP traffic and for emulating TDM circuits.  
         SUMMARY OF THE INVENTION  
         [0004]    TDM circuits can be mapped across scheduled networks using one of the following methods:  
           [0005]    1. Synchronous Method.  
           [0006]    In the Synchronous Method, all TDM circuits are synchronized to the scheduled network. For each TDM circuit, a specified number of TDM circuit bytes that occur in an integer number of 125 microsecond (μs) periods, are mapped into each scheduled packet. This method has been previously described in a patent application—entitled “Systems and Methods for the Emulation of TDM Circuits Over a Real-Time Scheduled Packet Network,” Docket No. 21340/3, filed Mar. 7, 2002—which is incorporated herein by reference in its entirety.  
           [0007]    2. Asynchronous Method.  
           [0008]    In the Asynchronous Method, each TDM circuit is allowed to be asynchronous relative to the scheduled network. Each TDM circuit is accumulated into a buffer for a provisionable amount of time (the Accumulation Interval), and the number of accumulated bits truncated to an integer number of bytes, (in all instances in this document, a byte refers to an 8-bit octet) are placed into each scheduled packet. The time of the Accumulation Interval is referenced to the scheduled network clock. Since the TDM circuits are not synchronized to the scheduled network, the number of bytes per scheduled packet is expected to vary by a small amount.  
           [0009]    TDM circuits can be categorized into five categories:  
           [0010]    1. The 24-channel Plesiochronous Digital Hierarchy, named because the primary interface, DS1, includes 24 individual 64 kbit/s payload channels.  
           [0011]    2. The 30-channel Plesiochronous Digital Hierarchy, named because the primary interface, E1, includes 30 individual 64 kbit/s payload channels.  
           [0012]    3. Synchronous Optical Network (SONET).  
           [0013]    4. Synchronous Digital Hierarchy (SDH).  
           [0014]    5. All other serial or parallel bit streams.  
           [0015]    Table 1 and Table 2 list examples of these PDH, SONET, and SDH circuits, their interface rates, and examples of some payloads that each can transport. Many of these interfaces can have several different payload options, and all are candidates for the present invention.  
                                               TABLE 1                           PDH Circuit Interfaces            PDH Interface   TDM Interface Rate   Channelized Payload                    DS1   1.544   Mbps   24 channels @ 64 kbps       DS1c   3.152   Mbps   2 DS1s       DS2   6.312   Mbps   4 DS1s       DS3   44.736   Mbps   7 DS2s       DS4NA   139.264   Mbps   3 DS3s       DS4   274.176   Mbps   6 DS3s       E1   2.048   Mbps   30 channels @ 64 kbps       E2   8.448   Mbps   4 E1s       E3   34.368   Mbps   4 E2s       E4   139.264   Mbps   4 E3s       E5   565.148   Mbps   4 E4s                  
 
           [0016]    [0016]                                                                                                               TABLE 2                       SONET and SDH Circuit Interfaces                                SONET   Full TDM Interface   Synchronous           Interface   Rate   Payload Envelope   Payload Capacity                    OC-1   51.840   Mpbs   50.112   Mpbs   49.536   Mpbs       OC-3   155.520   Mpbs   150.336   Mpbs   149.760   Mpbs       OC-12   622.080   Mpbs   601.344   Mpbs   599.040   Mpbs       OC-48   2488.320   Mpbs   2405.376   Mpbs   2396.160   Mpbs       OC-192   9953.280   Mpbs   9621.504   Mpbs   9584.640   Mpbs       OC-768   39813.120   Mpbs   38486.016   Mpbs   38338.560   Mpbs                    SDH   Full TDM Interface   Synchronous           Interface   Rate   Payload Envelope   Payload Capacity                    STM-1   155.520   Mpbs   150.336   Mpbs   149.760   Mpbs       STM-4   622.080   Mpbs   601.344   Mpbs   599.040   Mbps       STM-16   2488.320   Mpbs   2405.376   Mpbs   2396.160   Mpbs       STM-64   9953.280   Mpbs   9621.504   Mpbs   9584.640   Mpbs       STM-256   39813.120   Mpbs   38486.016   Mpbs   38338.560   Mpbs                    
           [0017]    The descriptors for a TDM circuit schedule itinerary include the following:  
           [0018]    Total number of appointments required for the TDM circuit.  
           [0019]    Number of appointments for each scheduled IP packet.  
           [0020]    In the Synchronous Method, the number of 125 microsecond (Ps) TDM frames per scheduled IP packet (or the number of TDM payload bytes per scheduled IP packet).  
           [0021]    In the Asynchronous Method, the Accumulation Interval, which is the time to accumulate an integer number of TDM circuit bytes into each scheduled packet.  
           [0022]    Schedule efficiency across the scheduled IP network, which is the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network.  
           [0023]    Bandwidth efficiency across the scheduled IP network, which is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet, including IP and higher layer (e.g., UDP) overhead.  
           [0024]    Packetization delay. This is the time required to accumulate TDM circuit bits into a packet.  
           [0025]    It will be shown that for any TDM circuit, the formulas in the present invention offer several choices of scheduled packet sizes. If the formulas produce more than one choice, a choice is made by balancing schedule efficiency, bandwidth efficiency and packetization delay.  
           [0026]    Circuit emulation represents one of the most difficult—if not the most difficult—service of any packet network. The circuit must appear as a bit stream with zero—near zero—packet loss, and zero—or near zero—jitter. Since an emulated circuit can support many applications, no inferences can be made by the packet network as to which application is operating. Therefore, only the strictest performance measures apply. An emulated TDM circuit on a Real-Time Scheduled Packet Network according to the invention has zero packet loss and zero jitter, offering the highest performance.  
           [0027]    The method according to the present invention calculates the requisite descriptors of a scheduled IP itinerary for an emulated TDM circuit, given virtually any TDM bit rate. Such a scheduled IP itinerary can be as described in U.S. patent application Ser. No. 09/746,744, filed Dec. 22, 2000, entitled “Scheduled Network Packet Switch,” which is incorporated herein by reference in its entirety. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0028]    The foregoing and other features and advantages of the present invention will be more fully understood by the following detailed description of illustrative embodiments taken in conjunction with the accompanying drawings in which:  
         [0029]    [0029]FIG. 1 is a process flow diagram for determining the minimum required number of appointments for any TDM circuit according to a specific synchronous method of at least one illustrative embodiment of the present invention;  
         [0030]    [0030]FIG. 2 is a process flow diagram for determining the minimum required number of appointments for any TDM circuit according to a specific asynchronous method of at least one embodiment of the present invention;  
         [0031]    [0031]FIG. 3 is a process flow diagram for determining the minimum required number of appointments for any TDM circuit according to an alternative general synchronous method embodiment of the present invention; and  
         [0032]    [0032]FIG. 4 is a process flow diagram for determining the minimum required number of appointments for any TDM circuit according to an alternative general asynchronous method embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0033]    The following sections describe specific illustrative embodiments (Section I) of a synchronous (Section IA) and asynchronous (Section IB) implementation according to the invention, based on certain applicable assumptions (as specified preceding the pertinent Sections). The specific implementations describe synchronous and asynchronous embodiments based on a specific schedule interval (20 ms) and specific appointment size (250 bytes). One skilled in the art will appreciate that the specific illustrative embodiments are only illustrative of the invention which has more general applicability.  
         [0034]    General illustrative embodiments are also described (Section II). The general illustrative embodiments or methodology demonstrate a detailed synchronous method for any schedule interval and appointment size (Section IIA) and two derived embodiments including one (Section IIB) with a specific schedule interval (20 ms) and specific appointment size (250 bytes) that is the same as the specific synchronous implementation described in Section IA. The second synchronous derived embodiment (Section IIC) has a different specific schedule interval (120 ms) and specific appointment size (50 bytes), which demonstrates the general applicability of the systems and methods according to the invention. A generalized asynchronous system and method is also described (Section IID) for any schedule interval and appointment size. First and second derived asynchronous embodiments are also presented including one (Section IIE) with a specific schedule interval (20 ms) and specific appointment size (250 bytes) that is the same as the specific asynchronous implementation described in Section IB. The second asynchronous derived embodiment (Section IIF) has a different specific schedule interval (120 ms) and specific appointment size (50 bytes), which, again, demonstrates the general applicability of the systems and methods according to the invention.  
         [0035]    I. Specific Illustrative Embodiments  
         [0036]    In a specific implementation, there are several variables to be considered for mapping TDM circuits into scheduled IP packets, including the packet protocols, the size of the packet, and the boundaries between packets. The assumptions for the formulas given in the following Specific Illustrative embodiment sections are as follows:  
         [0037]    1. The schedule interval (cycle time of appointments) is assumed to be 20 milliseconds (ms).  
         [0038]    2. The appointment size is assumed fixed on all links at 2000 bits, which is also equal to 250 bytes.  
         [0039]    3. It is assumed that TDM circuits are converted to scheduled UDP/IP packets. The packets can then be transported over Ethernet, SONET, or any other type of network media formats. Since Ethernet has more frame overhead than Packet-over-SONET and other Optical mappings, it represents the worst case. The calculations shown in the present invention assume that Ethernet transport is a possible media for the scheduled packets, and the maximum payload is adjusted accordingly for this worst case. It is straightforward to adjust this maximum payload by using media other than Ethernet.  
         [0040]    4. Packet Payloads.  
         [0041]    a. For the synchronous method, each scheduled IP packet should contain an integer number of 125 μs TDM frames for TDM circuits less than 91 Mbps. DS3 TDM frames are unique in that they do not repeat every 125 μs, but a DS3 does represent an integer number of bytes every 125 μs. Individual DS0s do not have a frame; they represent a single byte every 125 μs. DS1s have a 193-bit frame every 125 μs, which is not an integer number of bytes; therefore, an optimal DS1 solution should convert every N×8 frames into a scheduled IP packet. For TDM circuit speeds higher than 91 Mbps, each scheduled IP packet should contain a fraction of a 125 μs TDM frame. This is intended to simplify the packetization design and timing recovery.  
         [0042]    b. For the asynchronous method, each scheduled IP packet can contain any number of bytes, subject to the maximum packet size in Assumption 5, below.  
         [0043]    5. A maximum sized packet on Ethernet (1538 bytes including the minimum interframe gap of 12 bytes), requires seven 250-byte appointments, but only a small fraction of the 7 th  appointment is used. The maximum IP packet size should span at most 6 appointments; the limit of 6 appointments per scheduled IP packet helps to keep schedule efficiency high for TDM circuits over IP. Therefore, the packet should be no larger than 1500 bytes including Ethernet overhead (and Ethernet&#39;s 12-byte minimum interframe gap), or 1462 bytes including all overhead except Ethernet. Assuming a 250-byte appointment size, the possible number of appointments per packet is therefore 1, 2, 3, 4, 5, or 6.  
         [0044]    It should be appreciated by those skilled in the art that other assumptions may be made in using the formulas as a function of the application. More specifically, other assumptions may be made based on different network configurations (i.e. other than Ethernet), and timing considerations. For example, the appointment size could be other than 250 bytes; that affects the method by changing the values for the maximum payload in a scheduled packet, which will be shown in Table 3. Another example could be a schedule interval other than 20 ms; this would simply change the ratio of Schedule interval to 125 μs frame time, from 160 to another number.  
         [0045]    IA. Specific Illustrative Embodiment of the Synchronous Method  
         [0046]    The key starting formula for the Synchronous Method is found by matching the number of TDM circuit bytes in a 20 ms schedule interval with the number of payload bytes in a scheduled itinerary in the same 20 ms.  
               F   ×   160     =       A   ×   P     G             (   1   )                               
 
         [0047]    F is the number of TDM bytes in a 125 μs frame.  
         [0048]    A is the number of appointments in the scheduled IP itinerary.  
         [0049]    P is the size of each scheduled IP packet payload, in bytes. The IP packet payload does not include any overhead bytes for RTP, UDP, IP, or Ethernet.  
         [0050]    G is the group of appointments that each packet requires. Gε{1,2,3,4,5,6}.  
         [0051]    160 is the ratio of the schedule interval (20 ms) to the TDM frame interval (125 μs. For other schedule intervals or TDM frame intervals, enter the ratio of the schedule interval to the TDM frame interval. F should then represent the number of bytes in this TDM frame interval.  
         [0052]    Solving for A, we get:  
             A   =       F   ×   G   ×   160     P             (   2   )                               
 
         [0053]    It is known from Assumption 4a that the size of each scheduled IP packet payload is an integer number of bytes in a 125 μs TDM frame. Substituting this into Equation (1), results in:  
             A   =       G   ×   160     N             (   3   )                               
 
         [0054]    N is the number of 125 μs TDM frames in each scheduled IP packet.  
         [0055]    There are two additional constraints that can be placed on Equation (3) to converge on a solution. First, there is a minimum number of appointments per schedule interval (A) required, based on the number of TDM frames to be mapped and packet size. Second, both A and N must be integers, so a lookup function can be used to determine the final values of A and N, for each of the 6 possibilities of G, for any TDM signal. These methods are described in the following paragraphs.  
         [0056]    There are two conditions that set the minimum number of appointments required; there must be at least the number of appointments taken up by a packet (group size, G), and for each group size there is a maximum packet payload size, P max  that also sets a minimum number of appointments per schedule interval, A′. The term A′ is used because this is an interim value which is used to determine the actual minimum number of appointments required.  
                              For                 i     =         {     1   :   6     }     ,                A   i   ′       =     max        (       G   i     ,                  F   ×     G   i     ×   160       P     max                 i           )                
          or                 specifically   ,                            A   1   ′     =            max        (     1   ,                  F   ×   160       P     max                 i           )                     A   2   ′     =            max        (     2   ,                  F   ×   320       P     max                 2           )                     A   3   ′     =            max        (     3   ,                  F   ×   480       P     max                 3           )                     A   4   ′     =            max        (     4   ,                  F   ×   640       P     max                 4           )                     A   5   ′     =            max        (     5   ,                  F   ×   800       P     max                 5           )                     A   6   ′     =            max        (     6   ,                  F   ×   960       P     max                 6           )                         (   4   )                               
 
         [0057]    The maximum packet payload size (P max ) for each of the six group sizes of appointments depends on the format chosen for scheduled packet transport. It has already been assumed, for calculation purposes, that packets should be sized so that transport over Ethernet networks is allowed. There are three optional header fields that should be considered:  
         [0058]    1. Ethernet has an optional 4-byte Virtual LAN (VLAN) header.  
         [0059]    2. The Real Time Protocol (RTP) can be used, which provides time stamping and sequencing. RTP might benefit the performance through a Scheduled IP network, or it could be chosen for compatibility with mappings over non-scheduled packet networks. The RTP overhead field is 12 bytes, if present.  
         [0060]    3. Another optional overhead can be included for TDM Control. This field can indicate conventional circuit conditions such as Loss of Signal, Remote Defect, or Alarm Indication Signal (AIS), but the details of this field are outside the scope of the present invention. The TDM Control field could be any size, but a field of 4 bytes is assumed if it is present.  
         [0061]    Table 3 and Table 4 show the maximum capacity of TDM payload per scheduled packet (P max ) for each of the six appointment group sizes. Ethernet, IP, and UDP represent 38, 20, and 8 bytes of overhead, respectively, totaling 66 bytes. [VLAN 4 ] refers to the 4-byte VLAN field, if present. [RTP 12 ] refers to the 12-byte RTP field, if present. [TDMC 4 ] refers to the 4-byte TDM Control field, if present.  
                         TABLE 3                           Maximum Packet Payloads (P max ) vs.       Appointment Groups per Packet (G)            G   P max  (in Bytes)               1   P max1  = (250 − 66) − [VLAN 4 ] − [RTP 12 ] − [TDMC 4 ]       2   P max2  = P max1  + 250       3   P max3  = P max2  + 250       4   P max4  = P max3  + 250       5   P max5  = P max4  + 250       6   P max6  = P max5  + 250                  
 
         [0062]    [0062]                                 TABLE 4                           Maximum Payload (P max1 ) of A Single Appointment Packet                    TDM Control           VLAN Header   RTP Header   Header   Resulting P max1                 None   None   None   184 Bytes       None   None   4 Bytes   180 Bytes       None   12 Bytes   None   172 Bytes       None   12 Bytes   4 Bytes   168 Bytes       4 Bytes   None   None   180 Bytes       4 Bytes   None   4 Bytes   176 Bytes       4 Bytes   12 Bytes   None   168 Bytes       4 Bytes   12 Bytes   4 Bytes   164 Bytes                    
         [0063]    As previously noted, A, G, and N must all be integers. Since Assumption 5 limits the group size (G) to 6 appointments, there are only six possible values for G. Equation (3) can now be simplified for the six possible instances of G:  
                   G   =              1   :     A   1       =     160     N   1                     G   =              2   :     A   2       =     320     N   2                     G   =              3   :     A   3       =     480     N   3                     G   =              4   :     A   4       =     640     N   4                     G   =              5   :     A   5       =     800     N   5                     G   =              6   :     A   6       =     960     N   6                       (   5   )                               
 
         [0064]    There are only a finite number of integers that can satisfy the set of equations in (5) above. Table 5 shows these possible values for {A 1 :A 6 } and {N 1 :N 6 }. The highest number of appointments that can be used with this technique is 960, which limits the speed of each TDM circuit to about 960×250 bytes every 20 ms, or approximately 96 Mbps or less, depending on the chosen packet format. Those skilled in the art can easily modify the above equations to allow scheduled packets to contain fractions of TDM frames for higher-speed TDM circuits.  
                                                                                                                                             TABLE 5                           Possible Integer Values of A and N            G = 1   G = 2   G = 3   G = 4   G = 5   G = 6            A 1     N 1     A 2     N 2     A 3     N 3     A 4     N 4     A 5     N 5     A 6     N 6                      1   160   1   320   1   480   1   640   1   800   1   960       2   80   2   160   2   240   2   320   2   400   2   480       4   40   4   80   3   160   4   160   4   200   3   320       5   32   5   64   4   120   5   128   5   160   4   240       8   20   8   40   5   96   8   80   8   100   5   192       10   16   10   32   6   80   10   64   10   80   6   160       16   10   16   20   8   60   16   40   16   50   8   120       20   8   20   16   10   48   20   32   20   40   10   96       32   5   32   10   12   40   32   20   25   32   12   80       40   4   40   8   15   32   40   16   32   25   15   64       80   2   64   5   16   30   64   10   40   20   16   60       160   1   80   4   20   24   80   8   50   16   20   48               160   2   24   20   128   5   80   10   24   40               320   1   30   16   160   4   100   8   30   32                       32   15   320   2   160   5   32   30                       40   12   640   1   200   4   40   24                       48   10           400   2   48   20                       60   8           800   1   60   16                       80   6                   64   15                       96   5                   80   12                       120   4                   96   10                       160   3                   120   8                       240   2                   160   6                       480   1                   192   5                                               240   4                                               320   3                                               480   2                                               960   1                  
 
         [0065]    Packetization delay (Pack_Delay) is proportional to the number of 125 μs TDM frames in each scheduled IP packet:  
             Pack_Delay   =     N   ×   125                 µs             (   6   )                               
 
         [0066]    The schedule efficiency (Sched_Eff) of an emulated TDM circuit refers to the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network. This also equates to the number of TDM circuit bytes in a schedule interval (a 20 ms schedule interval=160 TDM frames @ 125 μs) divided by the number of reserved appointment bytes in that schedule interval. The TDM circuit bit rate is represented by the number of bytes per 125 μs TDM frame (F).  
             Sched_Eff   =         F   ×   160       A   ×   250       =       0.64   ×   F     A               (   7   )                               
 
         [0067]    The Bandwidth Efficiency across the scheduled IP network is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet, including IP and higher layer (e.g., UDP) overhead. Alternatively, the Bandwidth Efficiency is the ratio of packet payload to overall packet size (including IP and higher overhead). The Bandwidth Efficiency (BW_Eff) can be calculated by the following equation:  
             BW_Eff   =       N   ×   F         N   ×   F     +     [     TDMC   4     ]     +     [     RTP   12     ]     +     [     VLAN   4     ]     +   28               (   8   )                               
 
         [0068]    [TDMC 4 ] refers to the 4-byte TDM Control field, and assumed equal to 4 if present, else 0.  
         [0069]    [RTP 12 ] refers to the 12-byte RTP field, and is equal to 12 if present, else 0.  
         [0070]    [VLAN 4 ] refers to the 4-byte VLAN field, and is equal to 4 if present, else 0.  
         [0071]    The number 28 represents the number of overhead bytes in IP (20 bytes) and UDP (8 bytes).  
         [0072]    Delay and Efficiency Considerations  
         [0073]    Equations (1) through (8) in the previous section may result in up to 6 possible configurations of the total number of Appointments per schedule interval (A), the number of TDM frames per IP packet (F), and group of appointments per packet (G). Although it is usually best to choose the configuration with the minimum number of appointments, it may be preferable to choose a configuration with less packetization delay.  
         [0074]    Consider the E1 circuit, which is used extensively outside of the U.S. The E1 bit rate, including overhead, is 2.048 Mbps. Therefore F=32 bytes every 125 μs. Equations (4), (5), (6), and (7) are then used to calculate the values shown in Table 6, below. To keep the number of possibilities to a minimum, the values in Table 7 were calculated assuming that the RTP header and TDM Control header are used, but not the VLAN header. As previously noted, other header combinations can easily be used, which may alter the results.  
         [0075]    Although there are two resulting configurations in Table 7 that have the highest Schedule Efficiency (G=3 and G=6), the former has much less packetization delay and is therefore the better choice. If packetization delay needs to be lower, G=1 or G=2 may be the better choices.  
         [0076]    Examples of common TDM circuits are shown in the table below. Note that the high speed of OC-3/STM-1 limits the conversion to ½ of the bytes in each TDM frame.  
                                                                                                           TABLE 6                           Examples of TDM Circuit Mappings - Synchronous Method       Cells in the table containing “—” indicate no solution for that packet size.                                            Schedule   Bandwidth   Packetization       Circuit   TDM Bit Rate   F   G   A′   A × N   A   N   Efficiency   Efficiency   Delay                    DS1    1.544 Mbps   24.125 Bytes   1   22.44   160   32   5   48.3%   73.3%   0.6 ms                   2   18.29   320   20   16   77.2%   89.8%   2.0 ms                   3   17.23   480   20   24   77.2%   92.9%   3.0 ms                   4   16.75   640   20   32   77.2%   94.6%   4.0 ms                   5   16.47   800   20   40   77.2%   95.6%   5.0 ms                   6   16.29   960   20   48   77.2%   96.3%   6.0 ms       E1    2.048 Mbps   32 Bytes   1   29.77   160   32   5   64.0%   78.4%   0.6 ms                   2   24.27   320   32   10   64.0%   87.9%   1.3 ms                   3   22.86   480   24   20   85.3%   93.6%   2.5 ms                   4   22.21   640   32   20   64.0%   93.6%   2.5 ms                   5   21.84   800   25   32   81.9%   95.9%   4.0 ms                   6   21.60   960   24   40   85.3%   96.7%   5.0 ms       E3   34.368 Mbps   537 Bytes   1   499.53   160   —   —   —   —   —                   2   407.20   320   —   —   —   —   —                   3   383.57   480   480   1   71.6%   92.4%   0.1 ms                   4   372.75   640   640   1   53.7%   92.4%   0.1 ms                   5   366.55   800   400   2   85.9%   96.1%   0.3 ms                   6   362.53   960   480   2   71.6%   96.1%   0.3 ms       DS3   44.736 Mbps   699 Bytes   1   650.23   160   —   —   —   —   —                   2   530.05   320   —   —   —   —   —                   3   499.29   480   —   —   —   —   —                   4   485.21   640   640   1   69.9%   94.1%   0.1 ms                   5   477.13   800   800   1   55.9%   94.1%   0.1 ms                   6   471.90   960   480   2   93.2%   96.9%   0.3 ms       EC-1   51.840 Mbps   810 Bytes   1   753.49   160   —   —   —   —   —       (STS-1)           2   614.22   320   —   —   —   —   —                   3   578.57   480   —   —   —   —   —                   4   562.26   640   640   1   81.0%   94.8%   0.1 ms                   5   552.90   800   800   1   64.8%   94.8%   0.1 ms                   6   546.84   960   960   1   54.0%   94.8%   0.1 ms       OC-3/   155.520 Mbps    2430 Bytes   1   2260.47   160   —   —   —   —   —       STM-1           2   1842.65   320   —   —   —   —   —                   3   1735.71   480   —   —   —   —   —                   4   1686.77   640   —   —   —   —   —                   5   1658.70   800   —   —   —   —   —                   6   1640.51   960   1920   0.5   81.0%   96.5%   0.1 ms                  
 
         [0077]    [0077]                                                                                   TABLE 7                           Example: E1 Circuit Examples - Synchronous Method                                Schedule   Bandwidth   Packetization       G   A′   A × N   A   N   Efficiency   Efficiency   Delay                    1   30.48   160   32   5   64.0%   78.4%   0.6 ms       2   24.50   320   32   10   64.0%   87.9%   1.3 ms       3   22.99   480   24   20   85.3%   93.6%   2.5 ms       4   22.31   640   32   20   64.0%   93.6%   2.5 ms       5   21.92   800   25   32   81.9%   95.9%   4.0 ms       6   21.66   960   24   40   85.3%   96.7%   5.0 ms                    
         [0078]    Those skilled in the art now have enough information to determine the minimum required number of appointments for any TDM circuit. The steps to process are shown in FIG. 1 for the synchronous method.  
         [0079]    First, the number of bytes per 125 μs frame is determined 12. Next, a format of the scheduled packet is chosen 14 and the value of the maximum payload of the first packet is determined. Then, six values of interim minimum appointment size (A′) are calculated 16 for each of the six values of appointment groups per packet (G). Six values of the number of appointments required (A) are then determined 18 corresponding to G={1,2,3,4,5,6}.  
         [0080]    Packetization delay is then considered 20. If packetization delay is an issue at this bit rate 22, then a value for the number of appointments required (A) is chosen with the best combination of schedule efficiency, bandwidth efficiency and packetization delay.  
         [0081]    If packetization delay is not an issue at this bit rate 24, then a value for the number of appointments required (A) is chosen with the best combination of schedule efficiency and bandwidth efficiency.  
         [0082]    IB. Specific Illustrative Embodiment of the Asynchronous Method  
         [0083]    In the Asynchronous Method, TDM circuits are no longer synchronized to the scheduled network. One can theoretically choose any Accumulation Interval to accumulate bytes from TDM circuits into scheduled packets; the only restrictions are:  
         [0084]    1. The number of accumulated bytes in the Accumulation Interval must be less than a defined maximum. Practical considerations of schedule efficiency usually set the maximum number of accumulated bytes per packet equal to the maximum payload of 6 appointments.  
         [0085]    2. The resulting number of appointments must be within the capacity of the scheduled network. Practically, This restriction only applies to TDM circuits that have similar or higher bit rates than interfaces on the scheduled network.  
         [0086]    There is a more practical method than having an infinitely adjustable Accumulation Interval. For constant bit rate flows such as emulated TDM circuits, there are a constant number of packets per schedule interval. The Asynchronous. Method calculates the minimum number of packets per schedule interval, which is limited by the maximum TDM circuit bit rate (relative to the scheduled network) and the maximum scheduled packet size.  
         [0087]    Although TDM circuits have a constant bit rate, the Asynchronous Method assumes that the TDM circuit is not synchronized to the scheduled network. Therefore, the maximum TDM circuit bit rate relative to the scheduled network is calculated by using the following formula:  
               TDM_BR   max     =       TDM_BR   nom     ×     [     1   +     (         ΔTDM_Clock   max     +     ΔAccum_Clock   max       1000000     )       ]               (   9   )                               
 
         [0088]    TDM_BR max  is the maximum bit rate of the TDM circuit, in bits/sec, with respect to the Accumulator clock.  
         [0089]    TDM_BR nom  is the nominal bit rate of the TDM circuit, in bits/sec, with respect to the Accumulator clock.  
         [0090]    ΔTDM_Clock max  is the maximum frequency drift of the TDM circuit clock, in parts per million (ppm). For example, if the accuracy of the TDM clock is ±50 ppm, then ΔTDM_Clock max =50.  
         [0091]    ΔAccum_Clock max  is the maximum frequency drift of the Accumulator clock, in parts per million (ppm).  
         [0092]    The minimum number of packets per schedule interval is calculated by using the following formula:  
               K   min     =     Roundup   [         TDM_BR   max     ×   20                 ms         P   max     ×   8       ]             (   10   )                               
 
         [0093]    Roundup is a function(x) that rounds up the value “x” to the next highest integer that is greater than or equal to x.  
         [0094]    K min  is the minimum number of packets per 20 millisecond (ms) Schedule Interval.  
         [0095]    P max  is the maximum payload per scheduled packet (in bytes). P max  depends on the specific packet formats chosen, and the maximum frame size on the scheduled network. We have previously used the assumption that Ethernet will limit packet sizes to 1500 bytes, excluding Ethernet overhead. IP and UDP add 20 bytes and 8 bytes of overhead to the packet size, respectively, resulting in a maximum packet size of 1500−28=1472 bytes, if there is no other overhead.  
         [0096]    The maximum packet payload is shown in Table 8 below for several possible packet formats. The values in Table 8 are not the only choices; those skilled in the art will recognize that other combinations are possible, especially with the TDM control header, which can be virtually any size.  
                                 TABLE 8                           Maximum Payload of A Scheduled Packet (P max )                    TDM Control           VLAN Header   RTP Header   Header   Resulting P max                 None   None   None   1472 Bytes       None   None   4 Bytes   1468 Bytes       None   12 Bytes   None   1460 Bytes       None   12 Bytes   4 Bytes   1456 Bytes       4 Bytes   None   None   1468 Bytes       4 Bytes   None   4 Bytes   1464 Bytes       4 Bytes   12 Bytes   None   1456 Bytes       4 Bytes   12 Bytes   4 Bytes   1452 Bytes                  
 
         [0097]    Once K min  is calculated, larger values K (number of packets per schedule interval) can be chosen to optimize the following parameters:  
         [0098]    Schedule Efficiency  
         [0099]    Bandwidth Efficiency  
         [0100]    Packetization Delay (also equal to the Accumulation Interval)  
         [0101]    Before the above optimization parameters are calculated, other important parameters should be calculated for each value of K:  
         [0102]    Maximum Expected Packet Size  
         [0103]    Required Number of Appointments  
         [0104]    The Maximum Expected Packet Size (MEPS), in bytes, is calculated by the following equation:  
                     MEPS   =              Roundup        [         TDM_BR   max     ×   SI       8   ×   K       ]       +     [     TDMC   4     ]     +     [     RTP   12     ]     +     [     VLAN   4     ]     +     66                 or   ,              given                 a                 Schedule                   Interval   (   SI   )                   of                 20                                  ms        (     0.02                 sec     )       ,                                MEPS   =              Roundup   [       TDM_BR   max       400   ×   K       ]     +     {     TDMC   4     ]     +     [     RTP   12     ]     +     [     VLAN   4     ]     +   66                   (   11   )                               
 
         [0105]    [TDMC 4 ] refers to the 4-byte TDM Control field, and assumed equal to 4 if present, else 0.  
         [0106]    [RTP 12 ] refers to the 12-byte RTP field, and is equal to 12 if present, else 0.  
         [0107]    [VLAN 4 ] refers to the 4-byte VLAN field, and is equal to 4 if present, else 0.  
         [0108]    The number 66 represents the total number of overhead bytes from UDP (8 bytes), IP (20 bytes), and Ethernet (38 bytes, including Ethernet&#39;s 12-byte minimum interframe gap).  
         [0109]    The total number of appointments required for the scheduled IP itinerary is calculated using the Maximum Expected Packet Size and the number of packets per Schedule Interval (K), as shown in Table 9. The size of the packet in Table 9 includes UDP/IP overhead, Ethernet overhead (including the 12-byte minimum interframe gap between Ethernet frames), and any of the optional headers shown in Table 8 (VLAN, RTP, and TDM Control Headers).  
                             TABLE 9                           Appointments            Maximum Expected Packet Size   Number of   Total Number of       (Including All Overhead   Appointments   Appointments       and Ethernet   Required per   Required per       Interframe Gap)   Packet   Itinerary (A)               [1-250] bytes   1    K       [251-500] bytes   2   2K       [501-750] bytes   3   3K       [751-1000] bytes   4   4K       [1001-1250] bytes   5   5K       [1251-1500] bytes   6   6K       [1501-1538] bytes or   7   7K       [1501-1542] bytes   Packet sizes should       The maximum size packet on   be limited to 6       Ethernet is 1538 bytes if there   appointments to       is no VLAN tag, and 1542 bytes   keep schedule       with a VLAN tag.   efficiency high, as           per Assumption 5.                  
 
         [0110]    The Schedule Efficiency is the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network. The Schedule Efficiency (Sched_Eff) can be calculated by the following equation:  
               Sched_Eff   =         TDM_BR   nom     ×   SI       Appt_Size   ×   A              
        or   ,              given                 an                 appointment                 size                 of                 250                   bytes   (     2000                 bits                 and                 a                            Schedule                   Interval        (   SI   )          of                 20                   ms        (     0.02                 sec     )       ,               Sched_Eff   =       TDM_BR   nom       100000   ×   A                                                 (   12   )        `                               
 
         [0111]    The Bandwidth Efficiency across the scheduled IP network is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet, including IP and higher layer (e.g., UDP) overhead. The Bandwidth Efficiency (BW_Eff) can be calculated by the following equation:  
                   BW_Eff   =         TDM_BR   nom     ×   SI           TDM_BR   nom     ×   SI     +       (       [     TDMC   4     ]     +     [     RTP   12     ]     +     [     VLAN   4     ]     +   28     )     ×   8   ×   K                
        or   ,              given                 a                 Schedule                   Interval   (   SI   )                   of                 20                   ms        (     0.02                 sec     )       ,                               BW_Eff   =       TDM_BR   nom         TDM_BR   nom     +       (       [     TDMC   4     ]     +     [     RTP   12     ]     +     [     VLAN   4     ]     +   28     )     ×   400   ×   K                                (   13   )                               
 
         [0112]    The number 28 represents the number of overhead bytes in IP (20 bytes) and UDP (8 bytes).  
         [0113]    The Packetization Delay is the same as the Accumulation Interval, and call be calculated using the number of packets per schedule interval:  
                 Packetization_Delay   =     Accumulation_Interval   =     SI   K              
          or   ,              given                 a                 Schedule                   Interval   (   SI   )        of                 20                   ms        (     0.02                 sec     )       ,                    Packetization_Delay   =     Accumulation_Interval   =       20                 ms     K                              (   14   )                               
 
         [0114]    Consider again the E1 circuit, 2.048 Mbps, where the entire E1 bit rate—including TDM overhead—is mapped into scheduled packets. A table of possible values can be created, once the clock accuracies are known and the packet format is chosen. Two assumptions will be made to proceed with the example; however, the present method can be used with any clock accuracies or packet formats:  
         [0115]    Assume ATDM_Clock max +ΔAccum_Clock max =150 ppm  
         [0116]    Assume the Packet format includes a 12-byte RTP header, a 4-byte TDM Control header, and no VLAN header.  
         [0117]    Using Table 8, P max  is equal to 1456 bytes. Using Equation (9), K min  (the minimum number of packets per Schedule Interval), is equal to 4. A table of parameters can now be created using various values of K (K≧K min ) using Equations (10) through (13), as shown in Table 10.  
                                                                           TABLE 10                           Example Schedule Parameters for E1 Circuits, Asynchronous Method            Packets per   Max                           Schedule   Expected   Appts.   Total       Interval   Packet   per   Appts.   Schedule   Bandwidth   Packetization       (K)   Size   Packet   (A)   Efficiency   Efficiency   Delay                    4   1363 bytes    6   24   85.3%   96.7%   5.00 ms       5   1107 bytes    5   25   81.9%   95.9%   4.00 ms       6   936 bytes   4   24   85.3%   95.1%   3.33 ms       7   814 bytes   4   28   73.1%   94.3%   2.86 ms       8   723 bytes   3   24   85.3%   93.6%   2.50 ms       9   651 bytes   3   27   75.9%   92.8%   2.22 ms       10   595 bytes   3   30   68.3%   92.1%   2.00 ms       11   548 bytes   3   33   62.1%   91.4%   1.82 ms       12   509 bytes   3   36   56.9%   90.7%   1.67 ms       13   476 bytes   2   26   78.8%   90.0%   1.54 ms       14   448 bytes   2   28   73.1%   89.3%   1.43 ms       15   424 bytes   2   30   68.3%   88.6%   1.33 ms       16   403 bytes   2   32   64.0%   87.9%   1.25 ms       17   384 bytes   2   34   60.2%   87.3%   1.18 ms       18   367 bytes   2   36   56.9%   86.6%   1.11 ms       19   352 bytes   2   38   53.9%   86.0%   1.05 ms       20   339 bytes   2   40   51.2%   85.3%   1.00 ms       21   326 bytes   2   42   48.8%   84.7%   0.95 ms       22   315 bytes   2   44   46.5%   84.1%   0.91 ms       23   305 bytes   2   46   44.5%   83.5%   0.87 ms       24   296 bytes   2   48   42.7%   82.9%   0.83 ms       25   287 bytes   2   50   41.0%   82.3%   0.80 ms       26   279 bytes   2   52   39.4%   81.7%   0.77 ms       27   272 bytes   2   54   37.9%   81.2%   0.74 ms       28   265 bytes   2   56   36.6%   80.6%   0.71 ms       29   259 bytes   2   58   35.3%   80.1%   0.69 ms       30   253 bytes   2   60   34.1%   79.5%   0.67 ms       31   248 bytes   1   31   66.1%   79.0%   0.65 ms       32   243 bytes   1   32   64.0%   78.4%   0.63 ms       33   238 bytes   1   33   62.1%   77.9%   0.61 ms       34   233 bytes   1   34   60.2%   77.4%   0.59 ms       35   229 bytes   1   35   58.5%   76.9%   0.57 ms                  
 
         [0118]    It is now a simple matter of choosing the value of K with the best Schedule Efficiency and Bandwidth Efficiency that meets the customer&#39;s delay requirements.  
         [0119]    Several more examples are shown below for other common TDM circuits. The Asynchronous Method is in no way limited to the values shown.  
         [0120]    E1 mappings were shown in Table 10 for the asynchronous method. Note that many more combinations are possible than are shown in Table 11 below.  
                                                                                   TABLE 11                           Examples of TDM Circuit Mappings - Asynchronous Method                Packets   Maximum                           TDM Circuit   per   Expected   Appts.       Bit Rate to   Schedule   Packet   per   Total   Schedule   Bandwidth   Packetization       be Scheduled   Interval   Size   Packet   Appts.   Efficiency   Efficiency   Delay                    DS-1   3   1369 bytes   6   18   85.8%   96.7%   6.67 ms       1,544 Mbps   4   1048 bytes   5   20   77.2%   95.6%   5.00 ms           5    855 bytes   4   20   77.2%   94.6%   4.00 ms           6    726 bytes   3   18   85.8%   93.6%   3.33 ms           7    634 bytes   3   21   73.5%   92.6%   2.86 ms           8    565 bytes   3   24   64.3%   91.6%   2.50 ms           9    511 bytes   3   27   57.2%   90.7%   2.22 ms           10    469 bytes   2   20   77.2%   89.8%   2.00 ms           11    433 bytes   2   22   70.2%   88.9%   1.82 ms           12    404 bytes   2   24   64.3%   88.0%   1.67 ms           13    379 bytes   2   26   59.4%   87.1%   1.54 ms           14    358 bytes   2   28   55.1%   86.2%   1.43 ms           15    340 bytes   2   30   51.5%   85.4%   1.33 ms           16    324 bytes   2   32   48.3%   84.6%   1.25 ms           17    310 bytes   2   34   45.4%   83.8%   1.18 ms           18    297 bytes   2   36   42.9%   83.0%   1.11 ms           19    286 bytes   2   38   40.6%   82.2%   1.05 ms           20    276 bytes   2   40   38.6%   81.4%   1.00 ms           21    266 bytes   2   42   36.8%   80.7%   0.95 ms           22    258 bytes   2   44   35.1%   80.0%   0.91 ms           23    250 bytes   1   23   67.1%   79.2%   0.87 ms           24    243 bytes   1   24   64.3%   78.5%   0.83 ms           25    237 bytes   1   25   61.8%   77.8%   0.80 ms       E3   61   1491 bytes   6   366   93.9%   97.0%   0.33 ms       34.368 Mbps   62   1469 bytes   6   372   92.4%   96.9%   0.32 ms           63   1447 bytes   6   378   90.9%   96.9%   0.32 ms           64   1425 bytes   6   384   89.5%   96.8%   0.31 ms           65   1405 bytes   6   390   88.1%   96.8%   0.31 ms           66   1385 bytes   6   396   86.8%   96.7%   0.30 ms           67   1365 bytes   6   402   85.5%   96.7%   0.30 ms           68   1346 bytes   6   408   84.2%   96.6%   0.29 ms           69   1328 bytes   6   414   83.0%   96.6%   0.29 ms           70   1310 bytes   6   420   81.8%   96.5%   0.29 ms           71   1293 bytes   6   426   80.7%   96.5%   0.28 ms           72   1276 bytes   6   432   79.6%   96.4%   0.28 ms           73   1260 bytes   6   438   78.5%   96.4%   0.27 ms           74   1244 bytes   5   370   92.9%   96.3%   0.27 ms           75   1228 bytes   5   375   91.6%   96.3%   0.27 ms       DS-3   79   1498 bytes   6   474   94.4%   97.0%   0.25 ms       44.736 Mbps   80   1481 bytes   6   480   93.2%   96.9%   0.25 ms           81   1463 bytes   6   486   92.0%   96.9%   0.25 ms           82   1447 bytes   6   492   90.9%   96.9%   0.24 ms           83   1430 bytes   6   498   89.8%   96.8%   0.24 ms           84   1414 bytes   6   504   88.8%   96.8%   0.24 ms           85   1398 bytes   6   510   87.7%   96.8%   0.24 ms           86   1383 bytes   6   516   86.7%   96.7%   0.23 ms           87   1368 bytes   6   522   85.7%   96.7%   0.23 ms           88   1354 bytes   6   528   84.7%   96.7%   0.23 ms           89   1339 bytes   6   534   83.8%   96.6%   0.22 ms           90   1325 bytes   6   540   82.8%   96.6%   0.22 ms           91   1312 bytes   6   546   81.9%   96.5%   0.22 ms           92   1298 bytes   6   552   81.0%   96.5%   0.22 ms           93   1285 bytes   6   558   80.2%   96.5%   0.22 ms           94   1272 bytes   6   564   79.3%   96.4%   0.21 ms           95   1260 bytes   6   570   78.5%   96.4%   0.21 ms           96   1248 bytes   5   480   93.2%   96.4%   0.21 ms           97   1236 bytes   5   485   92.2%   96.3%   0.21 ms           98   1224 bytes   5   490   91.3%   96.3%   0.20 ms           99   1212 bytes   5   495   90.4%   96.3%   0.20 ms           100   1201 bytes   5   500   89.5%   96.2%   0.20 ms       EC-1   92   1491 bytes   6   552   93.9%   97.0%   0.22 ms       (STS-1)   93   1476 bytes   6   558   92.9%   96.9%   0.22 ms       51.840 Mbps   94   1461 bytes   6   564   91.9%   96.9%   0.21 ms           95   1447 bytes   6   570   90.9%   96.9%   0.21 ms           96   1433 bytes   6   576   90.0%   96.8%   0.21 ms           97   1419 bytes   6   582   89.1%   96.8%   0.21 ms           98   1405 bytes   6   588   88.2%   96.8%   0.20 ms           99   1392 bytes   6   594   87.3%   96.7%   0.20 ms           100   1379 bytes   6   600   86.4%   96.7%   0.20 ms           101   1366 bytes   6   606   85.5%   96.7%   0.20 ms           102   1353 bytes   6   612   84.7%   96.7%   0.20 ms           103   1341 bytes   6   618   83.9%   96.6%   0.19 ms           104   1329 bytes   6   624   83.1%   96.6%   0.19 ms           105   1317 bytes   6   630   82.3%   96.6%   0.19 ms           106   1305 bytes   6   636   81.5%   96.5%   0.19 ms           107   1294 bytes   6   642   80.7%   96.5%   0.19 ms           108   1283 bytes   6   648   80.0%   96.5%   0.19 ms           109   1272 bytes   6   654   79.3%   96.4%   0.18 ms           110   1261 bytes   6   660   78.5%   96.4%   0.18 ms           111   1250 bytes   5   555   93.4%   96.4%   0.18 ms           112   1240 bytes   5   560   92.6%   96.3%   0.18 ms       OC-3/STM-1   275   1497 bytes   6   1650   94.3%   97.0%   0.07 ms       155.520 Mbps   276   1491 bytes   6   1656   93.9%   97.0%   0.07 ms           277   1486 bytes   6   1662   93.6%   97.0%   0.07 ms           278   1481 bytes   6   1668   93.2%   96.9%   0.07 ms           279   1476 bytes   6   1674   92.9%   96.9%   0.07 ms           280   1471 bytes   6   1680   92.6%   96.9%   0.07 ms           281   1466 bytes   6   1686   92.2%   96.9%   0.07 ms           282   1461 bytes   6   1692   91.9%   96.9%   0.07 ms           283   1457 bytes   6   1698   91.6%   96.9%   0.07 ms           330   1261 bytes   6   1980   78.5%   96.4%   0.06 ms           331   1257 bytes   6   1986   78.3%   96.4%   0.06 ms           332   1254 bytes   6   1992   78.1%   96.4%   0.06 ms           333   1250 bytes   5   1665   93.4%   96.4%   0.06 ms           334   1247 bytes   5   1670   93.1%   96.4%   0.06 ms           335   1243 bytes   5   1675   92.8%   96.3%   0.06 ms                  
 
         [0121]    Those skilled in the art now have enough information to determine the minimum required number of appointments for a TDM circuit. The steps of a general process are shown in FIG. 2 for the asynchronous method.  
         [0122]    First, the accuracy of the TDM circuit and accuracy of the Accumulator clock is determined 30. Next, the maximum packet payload size is determined 32. The minimum number of packets per schedule interval (Kmin) is then calculated 34 using equation (10). The following parameters are then calculated 36 for Kmin: maximum expected packet size, number of appointments required per packet, total number of appointments required per itinerary, schedule efficiency, bandwidth efficiency and packetization delay. The value of K is then incremented and these six parameters are recalculated 38 until the number of appointments per packet equals 1.  
         [0123]    Packetization delay is then considered 40. If packetization delay is an issue at this bit rate, then a value for the number of appointments required (A) is chosen 42 with the best combination of schedule efficiency, bandwidth efficiency and packetization delay.  
         [0124]    If packetization delay is not an issue at this bit rate, then a value for the number of appointments required (A) is chosen 44 with the best combination of schedule efficiency and bandwidth efficiency.  
         [0125]    II. General Illustrative Embodiments of the Invention  
         [0126]    While the previous section described specific illustrative embodiments of synchronous and asynchronous methods according to the invention, the following generally describes the method according to the invention to calculate the requisite descriptors of a scheduled IP itinerary for an emulated TDM circuit, given any TDM bit rate. After the following description of the general case for both synchronous and asynchronous systems and methodology, illustrative embodiments are derived (all subject to the assumptions hereinafter). The first derived embodiment for each of synchronous and asynchronous systems and methodology described hereinafter relates to a 20 ms schedule interval and 250 byte appointment size (which is the same as presented in Sections IA and IB hereinbefore). The second derived embodiment for each of synchronous and asynchronous systems and methodology described hereinafter relates to a 120 ms schedule interval and 50 byte appointment size. While there is some redundancy, the illustrative embodiments described hereinafter are demonstrative of the general and specific applicability of the systems and methods according to the invention.  
         [0127]    Again, TDM circuits can be generally mapped across scheduled networks using one of the following methods:  
         [0128]    1. Synchronous Method.  
         [0129]    In the Synchronous Method, all TDM circuits are synchronized to the scheduled network. For each TDM circuit, a specified number of TDM circuit bytes that occur in an integer number of periods, such as 125 microsecond (μs), are mapped into each scheduled packet.  
         [0130]    2. Asynchronous Method.  
         [0131]    In the Asynchronous Method, each TDM circuit is allowed to be asynchronous relative to the scheduled network. Each TDM circuit is accumulated into a buffer for a provisionable amount of time (the Accumulation Interval), and the number of accumulated bits (truncated to an integer number of bytes) are placed into each scheduled packet. The time of the Accumulation Interval is referenced to the scheduled network clock. Since the TDM circuits are not synchronized to the scheduled network, the number of bytes per scheduled packet is expected to vary by a small amount.  
         [0132]    TDM circuits can be categorized into five categories:  
         [0133]    1. The 24-channel Plesiochronous Digital Hierarchy, named because the primary interface, DS1, includes 24 individual 64 kbit/s payload channels.  
         [0134]    2. The 30-channel Plesiochronous Digital Hierarchy, named because the primary interface, E1, usually includes 30 individual 64 kbit/s payload channels.  
         [0135]    3. Synchronous Optical Network (SONET).  
         [0136]    4. Synchronous Digital Hierarchy (SDH).  
         [0137]    5. All other serial or parallel bit streams.  
         [0138]    Table 12 and Table 13 list examples of these PDH, SONET, and SDH circuits, their interface rates, and examples of some payloads that each can transport. Many of these interfaces can have several different payload options, and all are candidates for the present invention.  
                                               TABLE 12                           PDH Circuit Interfaces            PDH Interface   TDM Interface Rate   Channelized Payload                    DS1   1.544   Mbps   24 channels @ 64 kbps       DS1c   3.152   Mbps   2 DS1s       DS2   6.312   Mbps   4 DS1s       DS3   44.736   Mbps   7 DS2s       DS4NA   139.264   Mbps   3 DS3s       DS4   274.176   Mbps   6 DS3s       E1   2.048   Mbps   30 channels @ 64 kpbs       E2   8.448   Mbps   4 E1s       E3   34.368   Mbps   4 E2s       E4   139.264   Mbps   4 E3s       E5   565.148   Mbps   4 E4s                  
 
         [0139]    [0139]                                                                                                               TABLE 13                       SONET and SDH Circuit Interfaces                                SONET   Full TDM Interface   Synchronous           Interface   Rate   Payload Envelope   Payload Capacity                    OC-1   51.840   Mpbs   50.112   Mpbs   49.536   Mpbs       OC-3   155.520   Mpbs   150.336   Mpbs   149.760   Mpbs       OC-12   622.080   Mpbs   601.344   Mpbs   599.040   Mpbs       OC-48   2488.320   Mpbs   2405.376   Mpbs   2396.160   Mpbs       OC-192   9953.280   Mpbs   9621.504   Mpbs   9584.640   Mpbs       OC-768   39813.120   Mpbs   38486.016   Mpbs   38338.560   Mpbs                    SDH   Full TDM Interface   Synchronous           Interface   Rate   Payload Envelope   Payload Capacity                    STM-1   155.520   Mpbs   150.336   Mpbs   149.760   Mpbs       STM-4   622.080   Mpbs   601.344   Mpbs   599.040   Mpbs       STM-16   2488.320   Mpbs   2405.376   Mpbs   2396.160   Mpbs       STM-64   9953.280   Mpbs   9621.504   Mpbs   9584.640   Mpbs       STM-256   39813.120   Mpbs   38486.016   Mpbs   38338.560   Mpbs                    
         [0140]    The descriptors for a TDM circuit schedule itinerary include the following:  
         [0141]    Total number of appointments required for the TDM circuit.  
         [0142]    Number of appointments for each scheduled IP packet.  
         [0143]    Synchronous Method only—The number of 125 microsecond (μs) TDM frames per scheduled IP packet (or the number of TDM payload bytes per scheduled IP packet).  
         [0144]    Asynchronous Method only—The Accumulation Interval, which is the time to accumulate an integer number of TDM circuit bytes into each scheduled packet.  
         [0145]    Schedule efficiency across the scheduled IP network, which is the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network.  
         [0146]    Bandwidth efficiency across the scheduled IP network, which is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet, including IP and higher layer (e.g., UDP) overhead.  
         [0147]    Packetization delay. This is the time required to accumulate TDM circuit bits into a packet.  
         [0148]    It will be shown that for any TDM circuit, the formulas in the present invention offer several choices of scheduled packet sizes. If the formulas produce more than one choice, a choice is made by balancing schedule efficiency, bandwidth efficiency and packetization delay.  
         [0149]    The distribution of the scheduled IP packets onto itineraries also affects the delay of the converted TDM signal; this phenomenon is examined in the final section. The two boundary cases—an even distribution for minimum delay, and a buffered block with maximum delay—are described. The large number of possibilities in between, and their effect on the network, is beyond the scope of this document.  
         [0150]    Assumptions  
         [0151]    There are several variables to be considered for mapping TDM circuits into scheduled IP packets, including the packet protocols, the size of the packet, and the boundaries between packets. The assumptions for the formulas for the second illustrative embodiment described herein are as follows:  
         [0152]    1. It is assumed that TDM circuits are converted to scheduled IP packets. The packets can then be transported over Ethernet, SONET, or any other type of network media formats. Since Ethernet has more frame overhead than Packet-over-SONET and other Optical mappings, it represents the worst case. The calculations shown in accordance with the present invention assume that Ethernet transport is an illustrative media for the scheduled packets, and the maximum payload is adjusted accordingly for this worst case. It is straightforward to adjust this maximum payload by using media other than Ethernet.  
         [0153]    2. Correlation between TDM frames and packet payloads.  
         [0154]    a. For the synchronous method, each scheduled IP packet should contain an integer number of 125 μs TDM frames for TDM circuits less than about 91 Mbps. DS3 TDM frames are unique in that they do not repeat every 125 μs, but a DS3 does represent an integer number of bytes every 125 μs. Individual DS0s do not have a frame; they represent a single byte every 125 μs. DS1s have a 193-bit frame every 125 μs, which is not an integer number of bytes; therefore, an optimal DS1 solution should convert every N×8 frames into a scheduled IP packet. As later assumptions will show, a 1500-byte Ethernet packet will contain 1418 bytes of payload, with the rest of the packet being overhead. The 1418 byte payload data representing a single 125 μs TDM frame, translates to a TDM circuit rate of 1418*8/125 μs=90.8 Megabits per second (Mbps). For TDM circuit speeds higher than about 91 Mbps, each scheduled IP packet should contain a fraction of a 125 μs TDM frame. This is intended to simplify the packetization design and timing recovery; other TDM sample times can also be used.  
         [0155]    b. For the asynchronous method, each scheduled IP packet can contain any number of bytes, subject to the maximum packet size in Assumption 5, below.  
         [0156]    3. The formulas for both the synchronous and asynchronous methods depend on two scheduling parameters: the schedule interval (cycle time of appointments) and the appointment size. Both methods will be described in detail with the following sets of schedule parameters:  
         [0157]    a. First, the schedule interval (SI) is assumed to be 20 milliseconds (ms), and the appointment size (Appt_Size) is assumed to be 2000 bits (250 bytes).  
         [0158]    b. Next, the schedule interval (SI) is assumed to be 120 milliseconds (ms), and the appointment size (Appt_Size) is assumed to be 400 bits (50 bytes).  
         [0159]    4. The maximum IP packet size is assumed to be constrained such that this packet on standard Ethernet can be fully contained in an integer number of appointments. This constraint helps to keep schedule efficiency high for TDM circuits over IP. Note that the largest standard IP/Ethernet packet is 1538 bytes, including 1500 bytes for the IP packet, 24 bytes for Ethernet overhead, and 12 bytes for the minimum interframe gap. (Although, Ethernet VLAN packets have a maximum size of 1542 bytes, which include a 4-byte VLAN tag, the illustrative examples assume that the VLAN tag is not present, although the present method also applies to Ethernet VLANs.) The maximum number of appointments per scheduled packet is therefore:  
         G   max     =       Integer   (       Maximum_Packet      _Size     Appt_Size     )     =     Integer   (     1538   Appt_Size     )                             
 
         [0160]    where G max  is the maximum contiguous group of appointments per scheduled packet.  
         [0161]    Consider the following illustrative examples:  
         [0162]    a. An appointment size of 250 bytes. A maximum sized IP/Ethernet frame would span 1538/250=6.152 appointments. Therefore, a maximum sized emulated TDM/Scheduled_IP/Ethernet packet is constrained to span exactly 6 appointments, or 1500 bytes. The emulated TDM/Scheduled_IP packet (without Ethernet overhead) should be no larger than 1500−38=1462 bytes.  
         [0163]    b. An appointment size of 50 bytes. A maximum sized IP/Ethernet frame would span 1538/50=30.76 appointments. Therefore, a maximum sized TDM/Scheduled_IP/Ethernet packet is constrained to span exactly 30 appointments, or 1500 bytes. The emulated TDM/Scheduled_IP packet (without Ethernet overhead) should be no larger than 1500−38=1462 bytes.  
         [0164]    c. In general, other appointment sizes will lead to different maximum packet sizes.  
         [0165]    5. High-layer packet overhead (overhead for layers above the IP layer) is assumed to include UDP, RTP, and a 4-byte TDM-specific control header, for a total of 24 bytes:  
         [0166]    a. [LDP 8 ] represents the 8 bytes of User Datagram Protocol (UDP) overhead. UDP is assumed to be used instead of Transmission Control Protocol (TCP) because of its better efficiency and lack of packet retransmissions.  
         [0167]    b. [RTP12] represents the 12 bytes of Real Time Protocol (RTP) overhead. RTP provides time stamping and sequencing. RTP might benefit the performance through a Scheduled IP network, or it could be chosen for compatibility with mappings over non-scheduled packet networks.  
         [0168]    c. [TDMC 4 ] represents the 4 bytes of TDM Control overhead. This field can indicate conventional circuit conditions such as Loss of Signal, Remote Defect, or Alarm Indication Signal (AIS), but the details of this field are outside the scope of the present invention. Other values can be chosen for TDM Control, including the absence altogether of this overhead.  
         [0169]    d. The above packet overhead is in addition to the 20-byte IP overhead, and the 38-byte Ethernet overhead (including 12 bytes for the minimum Ethernet gap). Therefore, each packet is assumed to have as much as 82 bytes of overhead.  
         [0170]    e. The 4-byte Ethernet VLAN header is assumed NOT to be present. Those skilled in the art can adjust the packet overhead by 4 bytes to include VLAN overhead [VLAN 4 ] on Ethernet interfaces, or choose other packet overhead combinations.  
         [0171]    It should be appreciated by those skilled in the art that other assumptions may be made in using the formulas as a function of the application. More specifically, other assumptions may be made based on different network configurations (i.e. other than Ethernet), and timing considerations. For example, the appointment size could be other than 50 or 250 bytes; that affects the method by changing the values for the maximum payload in a scheduled packet.  
         [0172]    IIA. Synchronous Method—General Case  
         [0173]    The key starting formula for the Synchronous Method is found by matching the number of TDM circuit bytes in a schedule interval with the number of payload bytes in a scheduled itinerary in the same schedule interval.  
                         F   T     ×   SI     T     =              A   ×   P     G                     F   ×   SI     0.125     =              A   ×   P     G                   (   15   )                               
 
         [0174]    F T  is the number of TDM bytes per time interval T.  
         [0175]    F is the number of TDM bytes in a 125 microsecond (0.125 millisecond) frame. For other TDM frame intervals, substitute the length of the TDM frame interval, in milliseconds, for 0.125. F should then represent the number of bytes in this TDM frame interval.  
         [0176]    SI is the schedule interval in milliseconds (ms).  
         [0177]    A is the total number of appointments per schedule interval for the emulated TDM circuit.  
         [0178]    P is the size of each scheduled IP packet payload, in bytes. The IP packet payload does not include any overhead bytes for RTP, UDP, IP, or Ethernet.  
         [0179]    G is the group of appointments that each packet requires.  
         [0180]    Solving for A, we get:  
             A   =       F   ×   G   ×   SI       P   ×   0.125               (   16   )                               
 
         [0181]    It is known from Assumption 2a that the size of each scheduled IP packet payload (P) is a multiple (N) of the bytes in a 125 μs TDM frame (F).  
             P   =     N   ×   F             (   17   )                               
 
         [0182]    N is the number of 125 μs TDM frames in each scheduled IP packet.  
         [0183]    Substituting Equation (17) into Equation (16) results in:  
             A   =         G   ×   SI         N   T     ×   T       =       G   ×   SI       N   ×   0.125                 (   18   )                               
 
         [0184]    wherein N T  is the number of TDM frames in time interval T.  
         [0185]    There are three additional constraints that can be placed on Equation (18) to converge on a solution:  
         [0186]    1. A must be an integer.  
         [0187]    2. It is desired that N also be an integer for most TDM circuits (N can be an integer fraction for TDM circuits above about 91 Mbps). Integer factors and a lookup function can be used to determine the number of appointments (A) per Schedule Interval, and a corresponding number of TDM frames per packet (N), for each value of G.  
         [0188]    3. There is a minimum number of appointments per schedule interval (A′) required, based on the number of TDM frames to be mapped and packet size. A′ must be at least the number of appointments for a single packet (G), and it must also satisfy Equation (16) for the largest packet size. This can be expressed as the following, for each value of G:  
                 A   ′     =     max        (     G        ,                  F   ×   G   ×   SI         P   max     ×   0.125           )                            (   19   )                               
 
         [0189]    A′ is one constraint that sets the minimum number of appointments required per Schedule Interval, for each possible value of G.  
         [0190]    The maximum packet payload size (P max ) depends on the appointment size and number group of appointments per packet:  
               P   max     =         (     Appt_Size   ×   G     )     -   Max_Overhead     =       (     Appt_Size   ×   G     )     -   82               (   20   )                               
 
           P   max =( Appt _Size× G )− Max _Overhead=( Appt _Size× G )−82   (20)  
         [0191]    Max_Overhead is the maximum number of overhead bytes per packet, which is 82 bytes (see Assumption 5d).  
         [0192]    The possible Appointments per Schedule Interval are now determined by choosing the lowest integer that satisfies both equations (18) and (19) for each value of G.  
         [0193]    For most TDM circuits, this will still leave several choices for possible mappings; up to one minimum value of A for each value of G. The final selection is made by choosing a balance between Packetization Delay, Schedule Efficiency, and Bandwidth Efficiency. Each of these three parameters is described below.  
         [0194]    Packetization Delay  
         [0195]    Packetization delay is proportional to the number of 125 μs TDM frames in each scheduled IP packet:  
             Packetization_Delay   =         N   T     ×   T     =     N   ×   125                 µs               (   21   )                               
 
         Packetization_Delay= N   T   ×T=N= 33   125  μs    (21)  
         [0196]    wherein N T  is the number of TDM frames in time interval T.  
         [0197]    Schedule Efficiency  
         [0198]    The schedule efficiency (Sched_Eff) of an emulated TDM circuit refers to the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network. This also equates to the number of TDM circuit bytes in a schedule interval divided by the number of reserved appointment bytes in that schedule interval. The TDM circuit bit rate is represented by the number of bytes per 125 μs TDM frame (F).  
             Sched_Eff   =           F   T     T         A   ×   Appt_Size     SI       =       F   ×   SI       A   ×   Appt_Size   ×   0.125                 (   22   )                               
 
         [0199]    wherein F T  is the number of TDM bytes per time interval T.  
         [0200]    Bandwidth Efficiency  
         [0201]    The Bandwidth Efficiency across the scheduled IP network is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet flow, including IP and higher layer (e.g., UDP) overhead. Alternatively, the Bandwidth Efficiency is the ratio of packet payload to overall packet size (including IP and higher overhead). The Bandwidth Efficiency (BW_Eff) can be calculated by the following equation:  
             BW_Eff   =           N   T     ×     F   T             N   T     ×     F   T       +     Max_IP      _Overhead         =       N   ×   F         N   ×   F     +   44                 (   23   )                               
 
         [0202]    Max_IP_Overhead represents the maximum total number of packet overhead bytes at or above the IP layer. According to Assumption 5, this includes IP overhead (20 bytes), UDP (8 bytes), RTP (12 bytes), and TDM Control (4 bytes) which equals 44 in the present illustrative embodiment. This does not include overhead specific to a physical interface layer, such as Ethernet.  
         [0203]    The Synchronous Method is described in detail in the following sections for two different sets of scheduling parameters. As mentioned previously, those skilled in the art can readily determine the formulas for other values of scheduling parameters in view hereof.  
         [0204]    IIB. The Synchronous Method with 20 ms Schedule Intervals and 250-byte Appointments as Derived From the General Methodology.  
         [0205]    Substituting a Schedule Interval (SI) of 20 ms into Equation 18 results in:  
             A   =       160   ×   G     N             (   24   )                               
 
         [0206]    As noted in Assumption 4a, the maximum sized TDM/Scheduled_IP packet is constrained to occupy a maximum of six (6) 250-byte appointments. Therefore, the group of appointments per packet (G) is in the range [1:6]. Equation (24) can now be specified for the six possible instances of G, which is summarized by Equation (25):  
                   G   =              1   :     A   1       =     160     N   1                     G   =              2   :     A   2       =     320     N   2                     G   =              3   :     A   3       =     480     N   3                     G   =              4   :     A   4       =     640     N   4                     G   =              5   :     A   5       =     800     N   5                     G   =              6   :     A   6       =     960     N   6                       (   25   )                               
 
         [0207]    Since A and N are generally both integers, the possible number of appointments become an integer factor of the values 160, 320, 480, 640, 800, and 960. There are only a finite number of integers that can satisfy the set of equations in (25) above. Table 14 shows the possible values for {A 1 :A 6 }.  
                                                                                                                                             TABLE 14                           Possible Integer Values of A and N            G = 1   G = 2   G = 3   G = 4   G = 5   G = 6            A 1     N 1     A 2     N 2     A 3     N 3     A 4     N 4     A 5     N 5     A 6     N 6                      1   160   1   320   1   480   1   640   1   800   1   960       2   80   2   160   2   240   2   320   2   400   2   480       4   40   4   80   3   160   4   160   4   200   3   320       5   32   5   64   4   120   5   128   5   160   4   240       8   20   8   40   5   96   8   80   8   100   5   192       10   16   10   32   6   80   10   64   10   80   6   160       16   10   16   20   8   60   16   40   16   50   8   120       20   8   20   16   10   48   20   32   20   40   10   96       32   5   32   10   12   40   32   20   25   32   12   80       40   4   40   8   15   32   40   16   32   25   15   64       80   2   64   5   16   30   64   10   40   20   16   60       160   1   80   4   20   24   80   8   50   16   20   48               160   2   24   20   128   5   80   10   24   40               320   1   30   16   160   4   100   8   30   32                       32   15   320   2   160   5   32   30                       40   12   640   1   200   4   40   24                       48   10           400   2   48   20                       60   8           800   1   60   16                       80   6                   64   15                       96   5                   80   12                       120   4                   96   10                       160   3                   120   8                       240   2                   160   6                       480   1                   192   5                                               240   4                                               320   3                                               480   2                                               960   1                  
 
         [0208]    However, two conditions set the minimum number of appointments required:  
         [0209]    1. There must be at least the number of appointments taken up by a packet (group size, G). In other words, the total number of appointments must be at least the number of appointments required for a single packet.  
         [0210]    2. For each group size (G) there is a maximum packet payload size (P max ) that also sets a minimum number of appointments, A′.  
                 For                 i     =         {     1   :   6     }     ,                A   i   ′       =     max        (       G   i     ,                  F   ×     G   i     ×   160       P     max                 i           )                
          or                 specifically   ,                                       A   1   ′     =            max        (     1   ,                  F   ×   160       P     max                 i           )                     A   2   ′     =            max        (     2   ,                  F   ×   320       P     max                 i           )                     A   3   ′     =            max        (     3   ,                  F   ×   480       P     max                 i           )                     A   4   ′     =            max        (     4   ,                  F   ×   640       P     max                 i           )                     A   5   ′     =            max        (     5   ,                  F   ×   800       P     max                 i           )                     A   6   ′     =            max        (     6   ,                  F   ×   960       P     max                 i           )                       (   26   )                               
 
         [0211]    The maximum packet payload size (P max ) for each of the 6 group sizes of appointments is limited by the number of payload bytes that the packet can support. Table 15 shows the maximum capacity of TDM payload per scheduled packet (P max ) for each of the appointment group sizes. The number 82 represents the maximum number of overhead bytes per packet.  
                         TABLE 15                           Maximum Packet Payloads (P max ) vs.       Appointment Groups per Packet (G)            G   P max  (in Bytes)               1   P max1  = (250 − 82) = 168       2   P max2  = P max1  + 250 = 418       3   P max3  = P max2  + 250 = 668       4   P max4  = P max3  + 250 = 918       5   P max5  = P max4  + 250 = 1168       6   P max6  = P max5  + 250 = 1418                  
 
         [0212]    Delay and Efficiency Considerations  
         [0213]    Equations (24) through (26) in the previous section may result in up to 6 possible values of the total minimum number of appointments per schedule interval (A), the number of TDM frames per IP packet (F), and Appointments per packet (G). The final selection is made by choosing a balance between Packetization Delay, Schedule Efficiency, and Bandwidth Efficiency.  
         [0214]    Equations (19) and (21) can be used to determine the Packetization Delay and Bandwidth Efficiency. Equation (20) can be simplified by substituting the schedule parameters assumed in this section, namely a Schedule Interval (SI) of 20 ms, and an Appointment Size (Appt_Size) of 250 bytes. The schedule efficiency (Sched_Eff) can then be calculated by substituting Appointment Size and Schedule Interval values into equation (22), which results in:  
             Sched_Eff   =         F   ×   SI       A   ×   Appt_Size   ×   0.125       =         F   ×   20       A   ×   250   ×   0.125       =       0.64   ×   F     A                 (   27   )                               
 
         [0215]    TDM Circuit Example  
         [0216]    Consider the E1 circuit, which is used extensively outside of the U.S. The E1 bit rate, including overhead, is 2.048 Mbps. Therefore F=32 bytes every 125 μs.  
         [0217]    Equations (21), (23), (24), (26), and (27) and Table 15 are then used to calculate the values shown in Table 16 below.  
         [0218]    Although there are two resulting configurations in Table 16 that have the highest Schedule Efficiency (G=3 and G=6, each with 24 appointments), the former has a lower bandwidth efficiency but much less packetization delay. The choice can be made depending upon overall efficiency and delay requirements. If packetization delay needs to be even lower, G=1 or G=2 (24 appointments each), may be preferable.  
         [0219]    More examples of common TDM circuits are shown in Table 17 below. Note that the high speed of OC-3/STM-1 limits the conversion to ½ of the bytes in each TDM frame. Cells in the table containing “—” indicate no solution for that packet size.  
                                                                                   TABLE 16                           Example: E1 Circuit - Synchronous Method with Schedule Interval =       20 ms and Appointment Size = 250 bytes                                Schedule   Bandwidth   Packetization       G   A′   A × N   A   N   Efficiency   Efficiency   Delay                    1   30.48   160   32   5   64.0%   78.4%   0.6 ms       2   24.50   320   32   10   64.0%   87.9%   1.3 ms       3   22.99   480   24   20   85.3%   93.6%   2.5 ms       4   22.31   640   32   20   64.0%   93.6%   2.5 ms       5   21.92   800   25   32   81.9%   95.9%   4.0 ms       6   21.66   960   24   40   85.3%   96.7%   5.0 ms                  
 
         [0220]    [0220]                                                                                                           TABLE 17                           Examples of TDM Circuit Mappings - Synchronous Method with 20 ms       Schedule Interval, 50-byte Appointments                                            Schedule   Bandwidth   Packetization       Circuit   TDM Bit Rate   F   G   A′   A × N   A   N   Efficiency   Efficiency   Delay                    DS1    1.544 Mbps   24.125 Bytes   1   22.44   160   32   5   48.3%   73.3%   0.6 ms                   2   18.29   320   20   16   77.2%   89.8%   2.0 ms                   3   17.23   480   20   24   77.2%   92.9%   3.0 ms                   4   16.75   640   20   32   77.2%   94.6%   4.0 ms                   5   16.47   800   20   40   77.2%   95.6%   5.0 ms                   6   16.29   960   20   48   77.2%   96.3%   6.0 ms       E1    2.048 Mbps   32 Bytes   1   29.77   160   32   5   64.0%   78.4%   0.6 ms                   2   24.27   320   32   10   64.0%   87.9%   1.3 ms                   3   22.86   480   24   20   85.3%   93.6%   2.5 ms                   4   22.21   640   32   20   64.0%   93.6%   2.5 ms                   5   21.84   800   25   32   81.9%   95.9%   4.0 ms                   6   21.60   960   24   40   85.3%   96.7%   5.0 ms       E3   34.368 Mbps   537 Bytes   1   499.53   160   —   —   —   —   —                   2   407.20   320   —   —   —   —   —                   3   383.57   480   480   1   71.6%   92.4%   0.1 ms                   4   372.75   640   640   1   53.7%   92.4%   0.1 ms                   5   366.55   800   400   2   85.9%   96.1%   0.3 ms                   6   362.53   960   480   2   71.6%   96.1%   0.3 ms       DS3   44.736 Mbps   699 Bytes   1   650.23   160   —   —   —   —   —                   2   530.05   320   —   —   —   —   —                   3   499.29   480   —   —   —   —   —                   4   485.21   640   640   1   69.9%   94.1%   0.1 ms                   5   477.13   800   800   1   55.9%   94.1%   0.1 ms                   6   471.90   960   480   2   93.2%   96.9%   0.3 ms       EC-1   51.840 Mbps   810 Bytes   1   753.49   160   —   —   —   —   —       (STS-1)           2   614.22   320   —   —   —   —   —                   3   578.57   480   —   —   —   —   —                   4   562.26   640   640   1   81.0%   94.8%   0.1 ms                   5   552.90   800   800   1   64.8%   94.8%   0.1 ms                   6   546.84   960   960   1   54.0%   94.8%   0.1 ms       OC-3/   155.520 Mbps    2430 Bytes   1   2260.47   160   —   —   —   —   —       STM-1           2   1842.65   320   —   —   —   —   —                   3   1735.71   480   —   —   —   —   —                   4   1686.77   640   —   —   —   —   —                   5   1658.70   800   —   —   —   —   —                   6   1640.51   960   1920   0.5   81.0%   96.5%   0.1 ms                    
         [0221]    IIC. The Synchronous Method with 120 ms Schedule Intervals and 50-byte Appointments as Derived From the General Methodology  
         [0222]    Substituting a Schedule Interval (SI) of 120 ms into Equation 18, results in:  
             A   =       960   ×   G     N             (   28   )                               
 
         [0223]    As noted in Assumption 4b, the maximum sized TDM/Scheduled_IP packet is constrained to occupy thirty (30) 50-byte appointments. Therefore, the group of appointments per packet (G) is in the range [1:30]. Equation (28) can now be specified for the thirty possible instances of G, which is summarized by:  
               G   =       1   :     A   1       =     960     N   1                
          G   =       2   :     A   2       =     1920     N   2                
          G   =       3   :     A   3       =     2880     N   3                
        ⋯        
          G   =       29   :     A   5       =     27840     N   5                
          G   =       30   :     A   6       =     28800     N   6                   (   29   )                               
 
         [0224]    Since A and N are generally both integers, the possible number of appointments become an integer factor of the values 960, 1920, 2880, . . . , 27840, and 28800 in equation (29). There are only a finite number of integers that can satisfy the set of equations in (29) above. Table 18 (which spans multiple pages) shows the possible values of A and N for {G 1 :G 30 }.  
                                           TABLE 18                           Integer Factors for G = {1:30}            G   AxN   Integer Factors (Possible Values of A and N)                    1    960   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120,               160, 192, 240, 320, 480, 960       2    1920   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120,               128, 160, 192, 240, 320, 384, 480, 640, 960, 1920       3    2880   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64               72, 80, 90, 96, 120, 144, 160, 180, 192, 240, 288, 320, 360, 480, 576, 720,               960, 1440, 2880       4    3840   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120,               128, 160, 192, 240, 256, 320, 384, 480, 640, 768, 960, 1280, 1920, 3840       5    4800   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75,               80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800,               960, 1200, 1600, 2400, 4800       6    5760   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64,               72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480,               576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760       7    6720   1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48,               56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240,               280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240,               3360, 6720       8    7680   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120,               128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536,               1920, 2560, 3840, 7680       9    8640   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54,               60, 64, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 192, 216, 240, 270,               288, 320, 360, 432, 480, 540, 576, 720, 864, 960, 1080, 1440, 1728, 2160,               2880, 4320, 8640       10    9600   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75,               80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480,               600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600       11   10560   1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55,               60, 64, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 192, 220, 240, 264,               320, 330, 352, 440, 480, 528, 660, 704, 880, 960, 1056, 1320, 1760, 2112,               2640, 3520, 5280, 10560       12   11520   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64,               72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384,               480, 576, 640, 720, 768, 960, 1152, 1280, 1440, 1920, 2304, 2880, 3840,               5760, 11520       13   12480   1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60,               64, 65, 78, 80, 96, 104, 120, 130, 156, 160, 192, 195, 208, 240, 260, 312,               320, 390, 416, 480, 520, 624, 780, 832, 960, 1040, 1248, 1560, 2080, 2496,               3120, 4160, 6240, 12480       14   13440   1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48,               56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224,               240, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 840, 896, 960, 1120,               1344, 1680, 1920, 2240, 2688, 3360, 4480, 6720, 13440       15   14400   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50,               60, 64, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 192, 200, 225, 240,               288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200,               1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200, 14400       16   15360   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120,               128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280,               1536, 1920, 2560, 3072, 3840, 5120, 7680, 15360       17   16320   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64,               68, 80, 85, 96, 102, 120, 136, 160, 170, 192, 204, 240, 255, 272, 320, 340,               408, 480, 510, 544, 680, 816, 960, 1020, 1088, 1360, 1632, 2040, 2720,               3264, 4080, 5440, 8160, 16320       18   17280   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54,               60, 64, 72, 80, 90, 96, 108, 120, 128, 135, 144, 160, 180, 192, 216, 240,               270, 288, 320, 360, 384, 432, 480, 540, 576, 640, 720, 864, 960, 1080,               1152, 1440, 1728, 1920, 2160, 2880, 3456, 4320, 5760, 8640 17280       19   18240   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 64,               76, 80, 95, 96, 114, 120, 152, 160, 190, 192, 228, 240, 285, 304, 320, 380,               456, 480, 570, 608, 760, 912, 960, 1140, 1216, 1520, 1824, 2280, 3040,               3648, 4560, 6080, 9120, 18240       20   19200   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75,               80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400,               480, 600, 640, 768, 800, 960, 1200, 1280, 1600, 1920, 2400, 3200, 3840,               4800, 6400, 9600, 19200       21   20160   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36,               40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126,               140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336,               360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120,               1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720,               10080, 20160       22   21120   1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55               60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240,               264, 320, 330, 352, 384, 440, 480, 528, 640, 660, 704, 880, 960, 1056,               1320, 1408, 1760, 1920, 2112, 2640, 3520, 4224, 5280, 7040, 10560, 21120       23   22080   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 23, 24, 30, 32, 40, 46, 48, 60, 64, 69,               80, 92, 96, 115, 120, 138, 160, 184, 192, 230, 240, 276, 320, 345, 368, 460,               480, 552, 690, 736, 920, 960, 1104, 1380, 1472, 1840, 2208, 2760, 3680,               4416, 5520, 7360, 11040, 22080       24   23040   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64,               72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384,               480, 512, 576, 640, 720, 768, 960, 1152, 1280, 1440, 1536, 1920, 2304,               2560, 2880, 3840, 4608, 5760, 7680, 11520, 23040       25   24000   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75,               80, 96, 100, 120, 125, 150, 160, 192, 200, 240, 250, 300, 320, 375, 400,               480, 500, 600, 750, 800, 960, 1000, 1200, 1500, 1600, 2000, 2400, 3000,               4000, 4800, 6000, 8000, 12000, 24000       26   24960   1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60,               64, 65, 78, 80, 96, 104, 120, 128, 130, 156, 160, 192, 195, 208, 240, 260,               312, 320, 384, 390, 416, 480, 520, 624, 640, 780, 832, 960, 1040, 1248,               1560, 1664, 1920, 2080, 2496, 3120, 4160, 4992, 6240, 8320, 12480, 24960       27   25920   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54,               60, 64, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 192, 216, 240,               270, 288, 320, 324, 360, 405, 432, 480, 540, 576, 648, 720, 810, 864, 960,               1080, 1296, 1440, 1620, 1728, 2160, 2592, 2880, 3240, 4320, 5184, 6480,               8640, 12960, 25920       28   26880   1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48,               56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224,               240, 256, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 768, 840, 896,               960, 1120, 1280, 1344, 1680, 1792, 1920, 2240, 2688, 3360, 3840, 4480,               5376, 6720, 8960, 13440, 26880       29   27840   1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80,               87, 96, 116, 120, 145, 160, 174, 192, 232, 240, 290, 320, 348, 435, 464,               480, 580, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 2320, 2784, 3480,               4640, 5568, 6960, 9280, 13920, 27840       30   28800   1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50,               60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225               240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900,               960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800,               5760, 7200, 9600, 14400, 28800                  
 
         [0225]    However, two conditions set the minimum number of appointments required:  
         [0226]    1. There must be at least the number of appointments taken up by a packet (group size, G). In other words, the total number of appointments must be at least the number of appointments required for a single packet.  
         [0227]    2. For each group size (G) there is a maximum packet payload size, P max  that also sets a minimum number of appointments, A′. (The term A′ is used because this is an interim value which is used to determine the actual minimum number of appointments required.)  
                 For                 i     =         {     1   :   30     }     ,                A   i   ′       =       max        (       G   i     ,                  F   ×     G   i     ×   SI         P     max                 i       ×   0.125         )       =     max        (       G   i     ,                  F   ×     G   i     ×   960       P     max                 i           )                  
          or                 specifically   ,                      A   1   ′     =     max        (     1   ,                  F   ×   960       P     max                 1           )              
            A   2   ′     =     max        (     2   ,                  F   ×   1920       P     max                 2           )              
            A   3   ′     =     max        (     3   ,                  F   ×   2880       P     max                 3           )              
        ⋯        
            A   29   ′     =     max        (     29   ,                  F   ×   27840       P     max                 5           )              
            A   30   ′     =     max        (     30   ,                  F   ×   28800       P     max                 6           )                 (   30   )                               
 
         [0228]    The maximum packet payload size (P max ) for each of the 30 group sizes of appointments is limited by the number of payload bytes that the packet can support. Table 19 shows the maximum capacity of TDM payload per scheduled packet (P max ) for each of the appointment group sizes. A group size (G) of 1 appointment, consisting of just 50 bytes, is not large enough to transport 82 bytes of overhead (Assumption 5) and some payload; therefore, only group sizes of 2 through 30 are considered in the following table.  
                                           TABLE 19                           Maximum Packet Payloads (P max ) vs.       Appointment Groups per Packet (G)            G   P max  (in Bytes)   Minimum Appts (A&#39;)                    2   P max2  = (100 − 82) = 18   A&#39; 2  = max(2, F*1920/18)       3   P max3  = P max2  + 50 = 68   A&#39; 3  = max(3, F*2880/68)       4   P max4  = P max3  + 50 = 118   A&#39; 4  = max(4, F*3840/118)       5   P max5  = 168   A&#39; 5  = max(5, F*4800/168)       6   P max6  = 218   A&#39; 6  = max(6, F*5760/218)       7   P max7  = 268   A&#39; 7  = max(7, F*6720/268)       8   P max8  = 318   A&#39; 8  = max(8, F*7680/318)       9   P max9  = 368   A&#39; 9  = max(9, F*8640/368)       10   P max10  = 418   A&#39; 10  = max(10, F*9600/418)       11   P max11  = 468   A&#39; 11  = max(11, F*10560/468)       12   P max12  = 5l8   A&#39; 12  = max(12, F*11520/518)       13   P max13  = 568   A&#39; 13  = max(13, F*12480/568)       14   P max14  = 6l8   A&#39; 14  = max(14, F*13440/618)       15   P max15  = 668   A&#39; 15  = max(15, F*1440/668)       16   P max16  = 718   A&#39; 16  = max(16, F*15360/718)       17   P max17  = 768   A&#39; 17  = max(17, F*1632O/768)       18   P max18  = 818   A&#39; 18  = max(18, F*17280/818)       19   P max19  = 868   A&#39; 19  = max(19, F*18240/868)       20   P max20  = 918   A&#39; 20  = max(20, F*19200/918)       21   P max21  = 968   A&#39; 21  = max(21, F*20160/968)       22   P max22  = 1018   A&#39; 22  = max(22, F*21120/1018)       23   P max23  = 1068   A&#39; 23  = max(23, F*22080/1068)       24   P max24  = 1118   A&#39; 24  = max(24, F*23040/1118)       25   P max25  = 1168   A&#39; 25  = max(25, F*24000/1168)       26   P max26  = 1218   A&#39; 26  = max(26, F*24960/1218)       27   P max27  = 1268   A&#39; 27  = max(27, F*25920/1268)       28   P max28  = 1318   A&#39; 28  = max(28, F*26880/1318)       29   P max29  = 1368   A&#39; 29  = max(29, F*27840/1368)       30   P max30  = 1418   A&#39; 39  = max(30, F*28800/1418)                  
 
         [0229]    Delay and Efficiency Considerations  
         [0230]    Equations (28) through (30) in the previous section may result in up to 29 possible values of the total minimum number of appointments per schedule interval (A), the number of TDM frames per IP packet (F), and Appointments per packet (G). The final selection is made by choosing a balance between Packetization Delay, Schedule Efficiency, and Bandwidth Efficiency.  
         [0231]    Equations (21) and (23) can be used to determine the Packetization Delay and Bandwidth Efficiency. Equation (22) can be simplified by substituting the schedule parameters assumed in this section, namely a Schedule Interval (SI) of 120 ms, and an Appointment Size (Appt_Size) of 50 bytes. The schedule efficiency (Sched_Eff) can then be calculated by Equation (31):  
             Sched_Eff   =         F   ×   SI       A   ×   Appt_Size   ×   0.125       =         F   ×   120       A   ×   50   ×   0.125       =       19.2   ×   F     A                 (   31   )                               
 
         [0232]    TDM Circuit Example  
         [0233]    Again, consider the E1 circuit, which is used extensively outside of the U.S. The E1 bit rate, including overhead, is 2.048 Mbps. Therefore F=32 bytes every 125 μs. Equations (21), (23), (29), (30), and (31) and Table 19 are then used to calculate the values shown in Table 20 below.  
         [0234]    Although there are two resulting configurations in Table 20 that have the highest Schedule Efficiency (G=21 and G=28, each with 672 appointments), the former has lower bandwidth efficiency but less packetization delay. The choice can be made depending upon overall efficiency and delay requirements. If packetization delay needs to be even lower, other choices, such as G=12 (720 appointments) or G=17 (680 appointments) may be preferable.  
                                                                                           TABLE 20                           Example: E1 Circuit - Synchronous Method with Schedule Interval = 120 ms       and Appointment Size = 50 bytes                                    Schedule   Bandwidth   Packetization       G   A × N   P max     A′   A   N   Efficiency   Efficiency   Delay                    2    1920   18   3413.33   —   —   —   —   —       3    2880   68   1355.29   1440    2   42.7%   59.3%   0.25 ms       4    3840   118   1041.36   1280    3   48.0%   68.6%   0.38 ms       5    4800   168   914.29   960   5   64.0%   78.4%   0.63 ms       6    5760   218   845.50   960   6   64.0%   81.4%   0.75 ms       7    6720   268   802.39   840   8   73.1%   85.3%   1.00 ms       8    7680   318   772.83   960   8   64.0%   85.3%   1.00 ms       9    8640   368   751.30   864   10   71.1%   87.9%   1.25 ms       10    9600   418   734.93   800   12   76.8%   89.7%   1.50 ms       11   10560   468   722.05   880   12   69.8%   89.7%   1.50 ms       12   11520   518   711.66   720   16   85.3%   92.1%   2.00 ms       13   12480   568   793.10   780   16   78.8%   92.1%   2.00 ms       14   13440   618   695.92   840   16   73.1%   92.1%   2.00 ms       15   14400   668   689.82   720   20   85.3%   93.6%   2.50 ms       16   15360   718   684.57   768   20   80.0%   93.6%   2.50 ms       17   16320   768   680.00   680   24   90.4%   94.6%   3.00 ms       18   17280   818   675.99   720   24   85.3%   94.6%   3.00 ms       19   18240   868   672.44   760   24   80.8%   94.6%   3.00 ms       20   19200   918   669.28   768   25   80.0%   94.8%   3.13 ms       21   20160   968   666.45   672   30   91.4%   95.6%   3.75 ms       22   21120   1018   663.89   704   30   87.3%   95.6%   3.75 ms       23   22080   1068   661.57   690   32   89.0%   95.9%   4.00 ms       24   23040   1118   659.46   720   32   85.3%   95.9%   4.00 ms       25   24000   1168   657.53   750   32   81.9%   95.9%   4.00 ms       26   24960   1218   655.76   780   32   78.8%   95.9%   4.00 ms       27   25920   1268   654.13   720   36   85.3%   96.3%   4.50 ms       28   26880   1318   652.63   672   40   91.4%   96.7%   5.00 ms       29   27840   1368   651.23   696   40   88.3%   96.7%   5.00 ms       30   28800   1418   649.93   720   40   85.3%   96.7%   5.00 ms                  
 
         [0235]    Those skilled in the art can readily determine the formulas for other values of scheduling parameters in view hereof. Those skilled in the art now have enough information to determine the minimum required number of appointments for a TDM circuit. The steps to the process for determining the minimum number of required appointments are shown in FIG. 3 for the synchronous method.  
         [0236]    First, the number of bytes per 125 μs frame is determined 50. Next, schedule interval (SI) and appointment size is chosen 52. The range of possible values of group appointments per packet (packet size) is determined based on the chosen schedule interval and appointment size. The value of the maximum payload of a packet (Pmax) for each possible packet size is determined 54. The minimum number of appointments required per schedule interval (A) is then determined for each packet size 56. The packetization delay, schedule efficiency and bandwidth efficiency for each value of A is then determined 58.  
         [0237]    Packetization delay is then considered 60. If packetization delay is an issue at this bit rate 62, then a value for the number of appointments required (A) is chosen with the best combination of schedule efficiency, bandwidth efficiency and packetization delay.  
         [0238]    If packetization delay is not an issue at this bit rate, then a value for the number of appointments required (A) is chosen 64 with the best combination of schedule efficiency and bandwidth efficiency.  
         [0239]    IID. Asynchronous Method—General Case  
         [0240]    In the Asynchronous Method, TDM circuits are no longer synchronized to the 2 0 scheduled network. One can theoretically choose any Accumulation Interval to accumulate bytes from TDM circuits into scheduled packets; the only restrictions are:  
         [0241]    1. The number of accumulated bytes in the Accumulation Interval must be less than or equal to the payload of a maximum-sized packet; practical considerations of schedule efficiency can restrict this somewhat further, according to Assumption 4.  
         [0242]    2. The resulting number of appointments must be within the capacity of the scheduled network. This restricts TDM circuits to bit rates that are lower than the interface speeds that they traverse on the scheduled network.  
         [0243]    There is a more practical method than having an infinitely adjustable Accumulation Interval. For constant bit rate flows such as emulated TDM circuits, there are a constant number of packets per schedule interval. The Asynchronous Method calculates the minimum number of packets per schedule interval, which is limited by the maximum TDM circuit bit rate (relative to the scheduled network) and the maximum scheduled packet size.  
         [0244]    Although TDM circuits have a constant bit rate, the Asynchronous Method assumes that the TDM circuit is not synchronized to the scheduled network. Therefore, the maximum TDM circuit bit rate relative to the scheduled network is calculated by using the following formula:  
               TDM_BR   max     =       TDM_BR   nom     ×     [     1   -     (         Δ                   TDM_Clock   max       +     Δ                   Accum_Clock   max         1000000     )       ]               (   32   )                               
 
         [0245]    TDM_BR max  is the maximum bit rate of the TDM circuit, in bits/sec, relative to the scheduled network.  
         [0246]    TDM_BR nom  is the nominal bit rate of the TDM circuit, in bits/sec.  
         [0247]    ATDM_Clock max  is the maximum frequency drift of the TDM circuit clock, in parts per million (ppm). For example, if the accuracy of the TDM clock is ±50 ppm, then ATDM_Clock max =50.  
         [0248]    ΔAccum_Clock max  is the maximum frequency drift of the Accumulator clock, in parts per million (ppm). For example, if the accuracy of the Accumulator clock is ±50 ppm, then ΔAccum_Clock max =50.  
         [0249]    The minimum number of packets per schedule interval is calculated by using the following formula:  
               K   min     =     Roundup              [         TDM_BR   max     ×   SI         P   max     ×   8       ]             (   33   )                               
 
         [0250]    SI is the Schedule Interval, in seconds.  
         [0251]    P max  is the maximum payload per scheduled packet (in bytes). P max  depends on the maximum packet size on the scheduled network, which is calculated using Assumption 4, and the number of overhead bytes per packet (see Assumption 5).  
         [0252]    Roundup is a function f(x) that rounds up the value “x” to the next highest integer that is greater than or equal to x.  
         [0253]    K min  is the minimum number of packets per Schedule Interval.  
         [0254]    Once K min  is calculated, larger integer values of K (the number of packets per schedule interval) are analyzed by incrementing K by 1, and calculating the following parameters:  
         [0255]    Maximum Expected Packet Size (MEPS)  
         [0256]    Required Number of appointments per schedule interval (A)  
         [0257]    Group of appointments (G) per scheduled packet  
         [0258]    Schedule Efficiency  
         [0259]    Bandwidth Efficiency  
         [0260]    Packetization Delay (also equal to the Accumulation Interval)  
         [0261]    As with the Synchronous Method, the selection of parameters for the Asynchronous Method is made by choosing a balance between Packetization Delay, Schedule Efficiency, and Bandwidth Efficiency.  
         [0262]    The Maximum Expected Packet Size (MEPS), in bytes, is calculated by the following equation:  
             MEPS   =       Roundup              [         TDM_BR   max     ×   SI       8   ×   K       ]     +   78             (   34   )                               
 
         [0263]    In the above equation, the roundup function Roundup(x) rounds up the value x to the smallest integer that is greater than or equal to x.  
         [0264]    The number 82 represents the total number of overhead bytes per packet, as stated by Assumption 5. This includes the 4-byte TDM Control field, and overhead for: RTP (12 bytes); UDP (8 bytes); IP (20 bytes); and Ethernet (38 bytes, including Ethernet&#39;s 12-byte minimum interframe gap).  
         [0265]    The total number of appointments required (A) per Schedule Interval is calculated by the following equation:  
             A   =     K   ×     Roundup              [     MEPS   Appt_Size     ]               (   35   )                               
 
         [0266]    In the above equation, the roundup function Roundup(x) rounds up the value x to the smallest integer that is greater than or equal to x. Appt_Size is the appointment size of scheduled network, in bytes.  
         [0267]    The group of appointments (G) per scheduled packet is simply the total number of appointments required per Schedule Interval divided by the number of packets per Schedule Interval, or G=A/K.  
         [0268]    The Schedule Efficiency is the ratio of the original TDM circuit bit rate to the amount of bandwidth reserved by the total number of appointments in its itinerary over a scheduled packet network. The Schedule Efficiency (Sched_Eff) can be calculated by the following equation:  
             Sched_Eff   =         TDM_BR   nom     ×   SI       Appt_Size   ×   A               (   36   )                               
 
         [0269]    The Bandwidth Efficiency across the scheduled IP network is the ratio of the original TDM circuit bit rate to the bit rate of the scheduled packet, including IP and higher layer (e.g., UDP) overhead. The Bandwidth Efficiency (BW_Eff) can be calculated by the following equation:  
                   BW_Eff   =           TDM_BR   nom     ×   SI           TDM_BR   nom     ×   SI     +     (     Max_IP      _Overhead   ×   8   ×   K     )         =                     TDM_BR   nom     ×   SI         TDM_BR   nom     ×   SI   ×     (     44   ×   8   ×   K     )                     (   37   )                               
 
         [0270]    The number 44 represents the maximum total number of packet overhead bytes at or above the IP layer. According to Assumption 5, this includes IP overhead (20 bytes), UDP (8 bytes), RTP (12 bytes), and TDM Control (4 bytes). This does not include overhead specific to a physical interface layer, such as Ethernet.  
         [0271]    The Packetization Delay is the same as the Accumulation Interval, and can be calculated using the number of packets per schedule interval:  
             Packetization_Delay   =     Accumulation_Interval   =     SI   K               (   38   )                               
 
         [0272]    Two illustrative examples of the Synchronous Method are described in detail in the following sections for two different sets of scheduling parameters. As mentioned previously, those skilled in the art can readily determine the formulas for other values of scheduling parameters.  
         [0273]    IIE. The Asynchronous Method with 20 ms Schedule Intervals and 250-Byte Appointments as Derived From the General Methodolgy.  
         [0274]    According to Assumption 4a, the maximum IP packet size with a 20 ms (0.02 seconds) Schedule Interval and 250-byte Appointments is assumed to be 1462 bytes. According to Assumption 5, there is assumed to be 44 overhead bytes at or above the IP layer, per packet. This includes IP overhead (20 bytes), UDP (8 bytes), RTP (12 bytes), and TDM Control (4 bytes). Therefore, the maximum payload per scheduled packet (P max ) is 1462−44=1418 bytes.  
         [0275]    Equations (33-38) can now be simplified in order to calculate the following parameters:  
         [0276]    K min  (the minimum number of packets per Schedule Interval)  
         [0277]    Maximum Expected Packet Size (MEPS)  
         [0278]    Required Number of appointments per schedule interval (A)  
         [0279]    Group of appointments (G) per scheduled packet  
         [0280]    Schedule Efficiency (Sched_Eff)  
         [0281]    Bandwidth Efficiency (BW_Eff)  
         [0282]    Packetization Delay (also equal to the Accumulation Interval)  
               K   min     =       Roundup              [         TDM_BR   max     ×   0.02       1418   ×   8       ]     =     Roundup              [       TDM_BR   max     567200     ]               (   39   )                               
 
             MEPS   =       Roundup              [         TDM_BR   max     ×   0.02       8   ×   K       ]     +   82             (   40   )               A   =     K   ×     Roundup              [     MEPS   250     ]               (   41   )               Sched_Eff   =       TDM_BR   nom       100000   ×   A               (   42   )               BW_Eff   =           TDM_BR   nom     ×   0.02           TDM_BR   nom     ×   0.02     +     (     352   ×   K     )         =       TDM_BR   nom         TDM_BR   nom     +     (     17600   ×   K     )                   (   43   )               Packetization_Delay   =     Accumulation_Interval   =       20                 ms     K               (   44   )                               
 
         [0283]    Consider the E1 circuit, 2.048 Mbps, where the entire E1 bit rate, including TDM overhead, is mapped into scheduled packets. A table of possible system parameters can be created, once the clock accuracies are known. The following assumption will be made to proceed with the example; however, the present method can be used with any clock accuracies:  
         Assume Δ TDM _Clock max   +ΔAccum _Clock max =150  ppm    
         [0284]    The clock accuracies can be substituted into Equation (32) to determine the maximum TDM circuit bit rate relative to the scheduled network:  
               TDM_BR                max       =       2048000   ×     [     1   +     (     150   1000000     )       ]       =     2048307.2                 bps               (   45   )                               
 
         [0285]    This resulting TDM_BR max  is substituted into Equation (25) to determine K min  (the minimum number of packets per Schedule Interval):  
               K   min     =       Roundup   [     2048307.2   567200     ]     =       Roundup        [   3.61   ]       =   4               (   46   )                               
 
         [0286]    A table of parameters can now be created using various values of K (K≧K min ) using Equations (26-30); an illustrative example is shown in Table 21. It is now a simple matter of choosing the value of K with the best Schedule Efficiency and Bandwidth Efficiency,that meets the customer&#39;s packetization delay requirements.  
         [0287]    Several more examples are shown in Table 22 for other common TDM circuits. The Asynchronous Method is in no way limited to the values shown in Tables 21 and 22. Many more combinations are possible.  
                                                                   TABLE 21                           Example Schedule Parameters for E1 Circuits, Asynchronous Method,       with 20 ms Schedule Intervals       and 250-byte Appointments            Packets per                           Schedule   Maximum   Total       Interval   Expected   Appts.   Schedule   Bandwidth   Packetization       (K)   Packet Size   (A)   Efficiency   Efficiency   Delay                    4   1363 bytes    24   85.3%   96.7%   5.00 ms       5   1107 bytes    25   81.9%   95.9%   4.00 ms       6   936 bytes   24   85.3%   95.1%   3.33 ms       7   814 bytes   28   73.1%   94.3%   2.86 ms       8   723 bytes   24   85.3%   93.6%   2.50 ms       9   651 bytes   27   75.9%   92.8%   2.22 ms       10   595 bytes   30   68.3%   92.1%   2.00 ms       11   548 bytes   33   62.1%   91.4%   1.82 ms       12   509 bytes   36   56.9%   90.7%   1.67 ms       13   476 bytes   26   78.8%   90.0%   1.54 ms       14   448 bytes   28   73.1%   89.3%   1.43 ms       15   424 bytes   30   68.3%   88.6%   1.33 ms       16   403 bytes   32   64.0%   87.9%   1.25 ms       17   384 bytes   34   60.2%   87.3%   1.18 ms       18   367 bytes   36   56.9%   86.6%   1.11 ms       19   352 bytes   38   53.9%   86.0%   1.05 ms       20   339 bytes   40   51.2%   85.3%   1.00 ms       21   326 bytes   42   48.8%   84.7%   0.95 ms       22   315 bytes   44   46.5%   84.1%   0.91 ms       23   305 bytes   46   44.5%   83.5%   0.87 ms       24   296 bytes   48   42.7%   82.9%   0.83 ms       25   287 bytes   50   41.0%   82.3%   0.80 ms       26   279 bytes   52   39.4%   81.7%   0.77 ms       27   272 bytes   54   37.9%   81.2%   0.74 ms       28   265 bytes   56   36.6%   80.6%   0.71 ms       29   259 bytes   58   35.3%   80.1%   0.69 ms       30   253 bytes   60   34.1%   79.5%   0.67 ms       31   248 bytes   31   66.1%   79.0%   0.65 ms       32   243 bytes   32   64.0%   78.4%   0.63 ms       33   238 bytes   33   62.1%   77.9%   0.61 ms       34   233 bytes   34   60.2%   77.4%   0.59 ms       35   229 bytes   35   58.5%   76.9%   0.57 ms                  
 
         [0288]    [0288]                                                                                       TABLE 22                           Examples of TDM Circuit Mappings - Asynchronous Method with 20 ms       Schedule Interval, 50-byte Appointments                Packets   Maximum                           TDM Circuit   per   Expected   Appts.       Bit Rate to   Schedule   Packet   per   Total   Schedule   Bandwidth   Packetization       be Scheduled   Interval   Size   Packet   Ap-   Efficiency   Efficiency   Delay                    DS-1   3   1369   bytes   pts. 6   18   85.8%   96.7%   6.67 ms       1.544 Mbps   4   1048   bytes   5   20   77.2%   95.6%   5.00 ms           5   855   bytes   4   20   77.2%   94.6%   4.00 ms           6   726   bytes   3   18   85.8%   93.6%   3.33 ms           7   634   bytes   3   21   73.5%   92.6%   2.86 ms           8   565   bytes   3   24   64.3%   91.6%   2.50 ms           9   511   bytes   3   27   57.2%   90.7%   2.22 ms           10   469   bytes   2   20   77.2%   89.8%   2.00 ms           11   433   bytes   2   22   70.2%   88.9%   1.82 ms           12   404   bytes   2   24   64.3%   88.0%   1.67 ms           13   379   bytes   2   26   59.4%   87.1%   1.54 ms           14   358   bytes   2   28   55.1%   86.2%   1.43 ms           15   340   bytes   2   30   51.5%   85.4%   1.33 ms           16   324   bytes   2   32   48.3%   84.6%   1.25 ms           17   310   bytes   2   34   45.4%   83.8%   1.18 ms           18   297   bytes   2   36   42.9%   83.0%   1.11 ms           19   286   bytes   2   38   40.6%   82.2%   1.05 ms           20   276   bytes   2   40   38.6%   81.4%   1.00 ms           21   266   bytes   2   42   36.8%   80.7%   0.95 ms           22   258   bytes   2   44   35.1%   80.0%   0.91 ms           23   250   bytes   1   23   67.1%   79.2%   0.87 ms           24   243   bytes   1   24   64.3%   78.5%   0.83 ms           25   237   bytes   1   25   61.8%   77.8%   0.80 ms       E3   61   1491   bytes   6   366   93.9%   97.0%   0.33 ms       34.368 Mbps   62   1469   bytes   6   372   92.4%   96.9%   0.32 ms           63   1447   bytes   6   378   90.9%   96.9%   0.32 ms           64   1425   bytes   6   384   89.5%   96.8%   0.31 ms           65   1405   bytes   6   390   88.1%   96.8%   0.31 ms           66   1385   bytes   6   396   86.8%   96.7%   0.30 ms           67   1365   bytes   6   402   85.5%   96.7%   0.30 ms           68   1346   bytes   6   408   84.2%   96.6%   0.29 ms           69   1328   bytes   6   414   83.0%   96.6%   0.29 ms           70   1310   bytes   6   420   81.8%   96.5%   0.29 ms           71   1293   bytes   6   426   80.7%   96.5%   0.28 ms           72   1276   bytes   6   432   79.6%   96.4%   0.28 ms           73   1260   bytes   6   438   78.5%   96.4%   0.27 ms           74   1244   bytes   5   370   92.9%   96.3%   0.27 ms           75   1228   bytes   5   375   91.6%   96.3%   0.27 ms       DS-3   79   1498   bytes   6   474   94.4%   97.0%   0.25 ms       44.736 Mbps   80   1481   bytes   6   480   93.2%   96.9%   0.25 ms           81   1463   bytes   6   486   92.0%   96.9%   0.25 ms           82   1447   bytes   6   492   90.9%   96.9%   0.24 ms           83   1430   bytes   6   498   89.8%   96.8%   0.24 ms           84   1414   bytes   6   504   88.8%   96.8%   0.24 ms           85   1398   bytes   6   510   87.7%   96.8%   0.24 ms           86   1383   bytes   6   516   86.7%   96.7%   0.23 ms           87   1368   bytes   6   522   85.7%   96.7%   0.23 ms           88   1354   bytes   6   528   84.7%   96.7%   0.23 ms           89   1339   bytes   6   534   83.8%   96.6%   0.22 ms           90   1325   bytes   6   540   82.8%   96.6%   0.22 ms           91   1312   bytes   6   546   81.9%   96.5%   0.22 ms           92   1298   bytes   6   552   81.0%   96.5%   0.22 ms           93   1285   bytes   6   558   80.2%   96.5%   0.22 ms           94   1272   bytes   6   564   79.3%   96.4%   0.21 ms           95   1260   bytes   6   570   78.5%   96.4%   0.21 ms           96   1248   bytes   5   480   93.2%   96.4%   0.21 ms           97   1236   bytes   5   485   92.2%   96.3%   0.21 ms           98   1224   bytes   5   490   91.3%   96.3%   0.20 ms           99   1212   bytes   5   495   90.4%   96.3%   0.20 ms           100   1201   bytes   5   500   89.5%   96.2%   0.20 ms       EC-1   92   1491   bytes   6   552   93.9%   97.0%   0.22 ms       (STS-1)   93   1476   bytes   6   558   92.9%   96.9%   0.22 ms       51.840 Mbps   94   1461   bytes   6   564   91.9%   96.9%   0.21 ms           95   1447   bytes   6   570   90.9%   96.9%   0.21 ms           96   1433   bytes   6   576   90.0%   96.8%   0.21 ms           97   1419   bytes   6   582   89.1%   96.8%   0.21 ms           98   1405   bytes   6   588   88.2%   96.8%   0.20 ms           99   1392   bytes   6   594   87.3%   96.7%   0.20 ms           100   1379   bytes   6   600   86.4%   96.7%   0.20 ms           101   1366   bytes   6   606   85.5%   96.7%   0.20 ms           102   1353   bytes   6   612   84.7%   96.7%   0.20 ms           103   1341   bytes   6   618   83.9%   96.6%   0.19 ms           104   1329   bytes   6   624   83.1%   96.6%   0.19 ms           105   1317   bytes   6   630   82.3%   96.6%   0.19 ms           106   1305   bytes   6   636   81.5%   96.5%   0.19 ms           107   1294   bytes   6   642   80.7%   96.5%   0.19 ms           108   1283   bytes   6   648   80.0%   96.5%   0.19 ms           109   1272   bytes   6   654   79.3%   96.4%   0.18 ms           110   1261   bytes   6   660   78.5%   96.4%   0.18 ms           111   1250   bytes   5   555   93.4%   96.4%   0.18 ms           112   1240   bytes   5   560   92.6%   96.3%   0.18 ms       OC-3/STM-1   275   1497   bytes   6   1650   94.3%   97.0%   0.07 ms       155.520 Mbps   276   1491   bytes   6   1656   93.9%   97.0%   0.07 ms           277   1486   bytes   6   1662   93.6%   97.0%   0.07 ms           278   1481   bytes   6   1668   93.2%   96.9%   0.07 ms           279   1476   bytes   6   1674   92.9%   96.9%   0.07 ms           280   1471   bytes   6   1680   92.6%   96.9%   0.07 ms           281   1466   bytes   6   1686   92.2%   96.9%   0.07 ms           282   1461   bytes   6   1692   91.9%   96.9%   0.07 ms           283   1457   bytes   6   1698   91.6%   96.9%   0.07 ms           330   1261   bytes   6   1980   78.5%   96.4%   0.06 ms           331   1257   bytes   6   1986   78.3%   96.4%   0.06 ms           332   1254   bytes   6   1992   78.1%   96.4%   0.06 ms           333   1250   bytes   5   1665   93.4%   96.4%   0.06 ms           334   1247   bytes   5   1670   93.1%   96.4%   0.06 ms           335   1243   bytes   5   1675   92.8%   96.3%   0.06 ms                    
         [0289]    IIF. The Asynchronous Method with 120 ms Schedule Intervals and 50-Byte Appointments as Derived From the General Methodology.  
         [0290]    According to Assumption 4b, the maximum IP packet size with a 120 ms (0.12 seconds) Schedule Interval and 50-byte Appointments is assumed to be 1462 bytes. According to Assumption 5, there is assumed to be 44 overhead bytes at or above the IP layer, per packet. This includes IP overhead (20 bytes), UDP (8 bytes), RTP (12 bytes), and TDM Control (4 bytes). Therefore, the maximum payload per scheduled packet (P max ) is 1462−44=1418 bytes.  
         [0291]    Equations (33-38) can now be simplified in order to calculate the following parameters:  
         [0292]    K min  (the minimum number of packets per Schedule Interval)  
         [0293]    Maximum Expected Packet Size (MEPS)  
         [0294]    Required Number of appointments per schedule interval (A)  
         [0295]    Group of appointments (G) per scheduled packet  
         [0296]    Schedule Efficiency (Sched_Eff)  
         [0297]    Bandwidth Efficiency (BW_Eff)  
         [0298]    Packetization Delay (also equal to the Accumulation Interval)  
               K   min     =       Roundup   [         TDM_BR   max     ×   0.12       1418   ×   8       ]     =     Roundup   [         TDM_BR   max     ×   0.12     11344     ]               (   47   )               MEPS   =       Roundup   [         TDM_BR   max     ×   0.12       8   ×   K       ]     +   82             (   48   )               A   =     K   ×     Roundup   [     MEPS   50     ]               (   49   )               Sched_Eff   =       TDM_BR   nom       100000   ×   A               (   50   )               BW_Eff   =         TDM_BR   nom     ×   0.12           TDM_BR   nom     ×   0.12     +     (     352   ×   K     )                 (   51   )               Packetization_Delay   =     Accumulation_Interval   =       120                 ms     K               (   52   )                               
 
         [0299]    Consider the E1 circuit, 2.048 Mbps, where the entire E1 bit rate, including TDM overhead, is mapped into scheduled packets. A table of possible system parameters can be created, once the clock accuracies are known. The following assumption will be made to proceed with the example; however, the present method can be used with any clock accuracies:  
         Assume Δ TDM _Clock max   +ΔAccum _Clock max =150  ppm    
         [0300]    The clock accuracies can be substituted into Equation (32) to determine the maximum TDM circuit bit rate relative to the scheduled network:  
               TDM_BR   max     =       2048000   ×     [     1   +     (     150   1000000     )       ]       =     2048307.2                 bps               (   53   )                               
 
         [0301]    This resulting TDM_BR max  is substituted into Equation (47) to determine K min  (the minimum number of packets per Schedule Interval):  
               K   min     =       Roundup   [       2048307.2   ×   0.12       1418   ×   8       ]     =       Roundup        [   21.67   ]       =   22               (   54   )                               
 
         [0302]    A table of parameters can now be created using various values of K (K≧K min ) using equations (34-38); an illustrative example is shown in Table 23. It is now a simple matter of choosing the value of K with the best Schedule Efficiency and bandwidth efficiency that meets the customer&#39;s packetization delay requirements.  
                                         TABLE 23                           Example Schedule Parameters for E1 Circuits,       Asynchronous Method, with 120 ms Schedule Intervals       and 50-byte Appointments            Packets                           per   Maximum       Schedule   Expected   Total       Interval   Packet   Appts.   Schedule   Bandwidth   Packetization       (K)   Size   (A)   Efficiency   Efficiency   Delay               22   1479 bytes    660   93.1%   96.9%   5.45 ms       23   1418 bytes    667   92.1%   96.8%   5.22 ms       24   1363 bytes    672   91.4%   96.7%   5.00 ms       25   1311 bytes    675   91.0%   96.5%   4.80 ms       26   1264 bytes    676   90.9%   96.4%   4.62 ms       27   1220 bytes    675   91.0   96.3%   4.44 ms       28   1180 bytes    672   91.4%   96.1%   4.29 ms       29   1142 bytes    667   92.1%   96.0%   4.14 ms       30   1107 bytes    690   89.0%   95.9%   4.00 ms       31   1174 bytes    682   90.1%   95.7%   3.87 ms       32   1043 bytes    672   91.4%   95.6%   3.75 ms       33   1014 bytes    693   88.7%   95.5%   3.64 ms       34   986 bytes   680   90.4%   95.4%   3.53 ms       35   960 bytes   700   87.8%   95.2%   3.43 ms       36   936 bytes   684   89.8%   95.1%   3.33 ms       37   913 bytes   703   87.4%   95.0%   3.24 ms       38   891 bytes   684   89.8%   94.8%   3.16 ms       39   870 bytes   702   87.5%   94.7%   3.08 ms       40   851 bytes   720   85.3%   94.6%   3.00 ms       41   832 bytes   697   88.1%   94.5%   2.93 ms       42   814 bytes   714   86.1%   94.3%   2.86 ms       43   797 bytes   688   89.3%   94.2%   2.79 ms       44   781 bytes   704   87.3%   94.1%   2.73 ms       45   765 bytes   720   85.3%   93.9%   2.67 ms       46   750 bytes   690   89.0%   93.8%   2.61 ms       47   736 bytes   705   87.1%   93.7%   2.55 ms       48   723 bytes   720   85.3%   93.6%   2.50 ms       49   710 bytes   735   83.6%   93.4%   2.45 ms       50   697 bytes   700   87.8%   93.3%   2.40 ms       50   697 bytes   700   87.8%   93.3%   2.40 ms       51   685 bytes   714   86.1%   93.2%   2.35 ms       52   673 bytes   728   84.4%   93.1%   2.31 ms       53   662 bytes   742   82.8%   92.9%   2.26 ms       54   651 bytes   756   81.3%   92.8%   2.22 ms       55   641 bytes   715   85.9%   92.7%   2.18 ms       56   631 bytes   728   84.4%   92.6%   2.14 ms       57   622 bytes   741   82.9%   92.5%   2.11 ms       58   612 bytes   754   81.5%   92.3%   2.07 ms       59   603 bytes   767   80.1%   92.2%   2.03 ms       60   595 bytes   720   85.3%   92.1%   2.00 ms       61   586 bytes   732   83.9%   92.0%   1.97 ms       62   578 bytes   744   82.6%   91.8%   1.94 ms       63   570 bytes   756   81.3%   91.7%   1.90 ms       64   563 bytes   768   80.0%   91.6%   1.88 ms       65   555 bytes   780   78.8%   91.5%   1.85 ms       66   548 bytes   726   84.6%   91.4%   1.82 ms       67   541 bytes   737   83.4%   91.2%   1.79 ms       68   534 bytes   748   82.1%   91.1%   1.76 ms       69   528 bytes   759   80.9%   91.0%   1.74 ms       70   521 bytes   770   79.8%   90.9%   1.71 ms       71   515 bytes   781   78.7%   90.8%   1.69 ms       72   509 bytes   792   77.6%   90.7%   1.67 ms       73   503 bytes   803   76.5%   90.5%   1.64 ms       74   498 bytes   740   83.0%   90.4%   1.62 ms       75   492 bytes   750   81.9%   90.3%   1.60 ms       76   487 bytes   760   80.8%   90.2%   1.58 ms       77   482 bytes   770   79.8%   90.1%   1.56 ms       78   476 bytes   780   78.8%   90.0%   1.54 ms       79   471 bytes   790   77.8%   89.8%   1.52 ms       80   467 bytes   800   76.8%   89.7%   1.50 ms       81   462 bytes   810   75.9%   89.6%   1.48 ms       82   457 bytes   820   74.9%   89.5%   1.46 ms       83   453 bytes   830   74.0%   89.4%   1.45 ms       84   448 bytes   756   81.3%   89.3%   1.43 ms       85   444 bytes   765   80.3%   89.1%   1.41 ms       86   440 bytes   774   79.4%   89.0%   1.40 ms       87   436 bytes   783   78.5%   88.9%   1.38 ms       88   432 bytes   792   77.6%   88.8%   1.36 ms       89   428 bytes   801   76.7%   88.7%   1.35 ms       90   424 bytes   810   75.9%   88.6%   1.33 ms                  
 
         [0303]    Those skilled in the art now have enough information to determine the minimum required number of appointments for a TDM circuit. The steps to perform the asynchronous embodiments of the invention for any Schedule Interval and Appointment are shown in FIG. 4.  
         [0304]    First, the accuracy of the TDM circuit and accuracy of the Accumulator clock is determined 70. Next, the maximum bit rate of the TDM circuit relative to the scheduled network is calculated 72. The minimum number of packets per schedule interval (Kmin) is then calculated 74. The following parameters are then calculated 76 for Kmin: maximum expected packet size, total number of appointments required for this TDM circuit per schedule interval (A), schedule efficiency, bandwidth efficiency and packetization delay. The value of K is then incremented and these five parameters are recalculated 78 until a favorable packetization delay results.  
         [0305]    Packetization delay is then considered 80. If packetization delay is an issue at this bit rate 84, then a value for the number of appointments required (A) is chosen with the best combination of schedule efficiency, bandwidth efficiency and packetization delay.  
         [0306]    If packetization delay is not an issue at this bit rate, then a value for the number of appointments required (A) is chosen 88 with the best combination of schedule efficiency and bandwidth efficiency.  
         [0307]    Although the invention is described with respect to illustrative embodiments thereof, those skilled in the art should appreciate that the foregoing and various other changes, omissions and additions in the form and detail thereof may be made without departing from the spirit and scope of the invention.