Abstract:
A method and apparatus for measuring network performance. A stream of packets of encoded data, sent by a transmitter across a network, are received. The stream of packets includes (n+1) packets having transmittal timestamps from a clock local to the transmitter, where n is an integer greater than or equal to one. An (n+1) th  transmittal timestamp and an n th  transmittal timestamp are determined. A value is calculated based on the (n+1) th  and the n th  transmittal timestamps. The value corresponds to the size of a virtual buffer needed to store the packets during a measurement interval. The value is used to determine a performance measure for the network.

Description:
BACKGROUND 
       [0001]    Digital multimedia content (e.g. video and/or audio data) must be transported across communication networks in a reliable and timely manner to the end user. Streaming video services (e.g. Internet Protocol television (IPTV), video conferencing, video-on-demand, etc.) are especially sensitive to delay, jitter, or data loss, which can all negatively impact the quality of the end user&#39;s experience. Typically, digital multimedia content is encoded prior to transmission across the network. Part  1  (Systems) of the Moving Pictures Expert Group (MPEG-2) standard defines a Transport Stream (TS) for encoding and transporting multimedia content across somewhat unreliable mediums such as broadcast channels, internet protocol networks, etc. The Transport Stream consists of packets that carry video or audio data in their payload. The TS packets are received and decoded to reconstruct the original multimedia content. The Transport Stream protocol is also specified in International Standard ISO/IEC13818-1. 
         [0002]    Determining the performance of a network that carries digital multimedia content is an important element to the successful design and operation of such a network. One measure of a network&#39;s performance is known as the Media Delivery Index (MDI). The MDI has two components: the delay factor (DF) and the media loss rate (MLR). The MDI is expressed as two numbers separated by a colon: DF:MLR. 
         [0003]    The DF component of the MDI is the maximum difference, observed at the end of each network packet, between the arrival of media data and the drain of media data. DF is indicative of the packet jitter. A high value for DF indicates that a larger buffer depth is required to minimize the effects of packet jitter. To calculate DF, consider a virtual buffer VB used to buffer received packets of a stream. Each time a packet P i , where i&gt;0, arrives during a measurement interval, compute two VB values, VB(i,pre) and VB(i,post) as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     VB 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           i 
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         S 
                         j 
                       
                     
                     - 
                     
                       MR 
                       · 
                       
                         T 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     VB 
                      
                     
                       ( 
                       
                         i 
                         , 
                         post 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       VB 
                        
                       
                         ( 
                         
                           i 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     + 
                     
                       S 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where S j  is the media payload size of the j th  packet in the measurement interval, T i  is the arrival time relative to the last received packet in the previous measurement interval, or in the case of the first measurement interval, relative to the first packet. MR is the nominal media rate in bytes per second. VB(i,pre) is the virtual buffer size just before the arrival of P i , and VB(i,post) is the virtual buffer size just after the arrival of P i . This calculation is subject to the initial condition of VB(0,post)=VB(0,pre)=0 and VB(1,pre)=−MR·T 1  at the beginning of each measurement interval. A measurement interval is defined from just after the time of arrival of the last packet during a nominal period to the time just after the arrival of the last packet of the next nominal period. The length of the measurement interval is arbitrary and may vary from application to application, but is typically selected to be 1 second. 
         [0004]    The nominal media rate can be variable or constant. If there is a constant bit rate (CBR), the transmission of the media stream is defined to be constant at the bit level. If there is a variable bit rate (VBR), the rate can vary, but is defined to be piece-wise constant, as defined in the Detailed Description. The prior art DF is well defined for the CBR case only. 
         [0005]    The DF is calculated once every measurement interval as follows by finding the difference between the maximum and minimum values of VB: 
         [0000]    
       
         
           
             
               
                 
                   DF 
                   = 
                   
                     
                       
                         
                           max 
                           
                             i 
                             ≥ 
                             0 
                           
                         
                          
                         
                           ( 
                           
                             VB 
                              
                             
                               ( 
                               
                                 i 
                                 , 
                                 post 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           min 
                           
                             i 
                             ≥ 
                             0 
                           
                         
                          
                         
                           ( 
                           
                             VB 
                              
                             
                               ( 
                               
                                 i 
                                 , 
                                 pre 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     MR 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Note that the maximum and minimum include the zeros introduced by the initial conditions at i=0. 
         [0006]    The MLR is defined as the number of lost or out-of-order packets per second. 
         [0007]    For more information regarding the MDI, DF, and MLR measurements, please refer to the following publications: “A Proposed Media Delivery Index (MDI)”, by J. Welch and J. Clark, published in April 2006 by the Internet Engineering Task Force as IETF RFC 4445 and available at the following URL: http://www.rfc-editor.org/rfc/rfc4445.txt; and “IPTV QoE: Understanding and Interpreting MDI Values”, a white paper published by Agilent Technologies on Aug. 30, 2006 and available at the following URL: http://cp.literature.agilent.com/litweb/pdf/5989-5088EN. pdf 
         [0008]    An obstacle in calculating the DF is determining the media rate MR. One value to use is the embedded media rate (also referred to as the “elementary stream rate”), which is encoded at a lower level in the program elementary stream (PES) from which the TS packets are created by an MPEG-2 encoder. The embedded media rate is the number of bits per unit time needed to represent the video or audio data only. However, significant processing is required to extract the embedded media rate from these lower level encodings—the received TS packets must first be decoded by the decoder to reconstruct the PES, before the media rate can be extracted from the PES. This process is complex and requires significant hardware and software resources. Furthermore, to perform it in a scalable fashion, the test equipment must parse the PES stream over hundreds of simultaneous video channels, which is typical in an IPTV network. In addition, the embedded media rate is not an accurate representation of the true media rate, because it does not include the necessary MPEG transport overhead required to transmit the payloads. 
         [0009]    Therefore, there remains a need for an improved method and apparatus for determining DF. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  shows a block diagram of a system for sending a transport packet stream across a network. 
           [0011]      FIG. 2  shows an exploded view of an exemplary transport packet stream having N transport stream packets. 
           [0012]      FIG. 3  shows a plot of an exemplary transport packet stream against a timeline as it arrives at the receiver. 
           [0013]      FIG. 4  is a block diagram of a system for calculating a delay factor for a network. 
           [0014]      FIG. 5  shows a flow chart for a method for calculating the delay factor. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]      FIG. 1  shows a block diagram of a system for sending a transport packet stream  21  across a network  22 . The transport packet stream consists of Transport Stream (TS) packets, encoded according to the ISO/IEC 13818-1 MPEG-2 standard. A transmitter  24  inserts Program Clock Reference (PCR) timestamps into selected TS packets according to the ISO/IEC 13818-1 MPEG-2 standard, and transmits the transport packet stream  21  across the network  22  to a receiver  26 . For a variable bit rate (VBR) transmission, the stream rate is defined to be constant between successive PCRs. As will be described below, the calculation for DF can be simplified by using these PCR timestamps that are already included within the TS packets. 
         [0016]      FIG. 2  shows an exploded view of the transport packet stream  21 , having N TS packets. (It should be noted that if network  22  is an internet protocol (IP) network, seven TS packets  23  are normally grouped together into an Ethernet frame for transmission). Each TS packet  23  has a header  25  and a payload  27 . The header  25  in  FIG. 2  contains an adaptation field  29 , although this field is optional. Within the adaptation field  29  is the Program Clock Reference  31  (PCR), which is a timestamp from a system clock within an MPEG-2 encoder in the transmitter  24  that is inserted at the time the packet is transmitted. The PCR  31  is 48 bits long and consists of 2 sections. The first section is 33 bits wide, and includes a 90 kHz clock. The second section is 9 bits wide, and is a 27 MHz clock. The remaining 6 bits are reserved. 
         [0017]    The PCR  31  is recovered by the receiver  26  and used as a reference for two other timestamps within the transport stream layer: the decoding timestamp (DTS) and the presentation timestamp (PTS). The DTS and PTS specify the time instants at which the packet should be decoded and presented, respectively. The PCR  31  is a necessary field because the DTS and PTS use it as a reference base—without the PCR  31 , the TS packets  23  could not be decoded at the proper time. The MPEG-2 standard requires that the PCR  31  be provided at least once every 100 milliseconds (although the PCR  31  could be included more often), but not every TS packet  23  needs to include a PCR  31 . The standard also requires that the value of the PCR be accurate to within 500 nanoseconds of the actual scheduled transmission time. 
         [0018]      FIG. 3  shows a plot of an exemplary transport packet stream  33  against a timeline  35  as it arrives at the receiver  26 . The figure shows the arrival at time T i  of the packet bearing the n th  PCR, and the subsequent packets, k n  in total, until the arrival of a TS packet containing the next PCR, where i, k and n are integers greater than or equal to one. As previously mentioned, seven TS packets  23  are normally grouped together into an Ethernet frame for transmission across an internet protocol network, so the TS packets would normally arrive bunched up in groups of seven packets at a time. However, for the sake of generalization beyond one specific implementation, the TS packets are illustrated in  FIG. 3  as arriving in a continuous stream without their Ethernet frames. 
         [0019]    Define the functions X(i,pre) and X(i,post) for each packet i as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       VB 
                        
                       
                         ( 
                         
                           i 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     MR 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         post 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       VB 
                        
                       
                         ( 
                         
                           i 
                           , 
                           post 
                         
                         ) 
                       
                     
                     MR 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Then DF can be expressed as 
         [0000]        DF =max i≧0  ( X ( i,  post))−min i≧0 ( X ( i,  pre))   (6) 
         [0020]    Now consider the interval between the n th  and n+1 st  PCR-bearing packets. Let k n  be the number of packets in this interval, as shown in  FIG. 3 . For i&gt;1, define Δt i  to be the time between the arrival of the i th  and (i−1) st  packets, then X(i,pre) satisfies the recurrence: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       X 
                        
                       
                         ( 
                         
                           i 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     - 
                     
                       X 
                        
                       
                         ( 
                         
                           
                             i 
                             - 
                             1 
                           
                           , 
                           pre 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           PCR 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           PCR 
                           n 
                         
                       
                       
                         k 
                         n 
                       
                     
                     - 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         t 
                         i 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Note 
                      
                     
                         
                     
                      
                     that 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       X 
                        
                       
                         ( 
                         
                           1 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     = 
                     
                       - 
                       
                         T 
                         1 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Also 
                     , 
                     then 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         post 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       X 
                        
                       
                         ( 
                         
                           i 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           PCR 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           PCR 
                           n 
                         
                       
                       
                         k 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0021]    When the data stream is CBR, the following derivation can be used to show that equation (7) is an accurate calculation for DF. First, equation (4) is repeated below for the convenience of the reader: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         . 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       VB 
                        
                       
                         ( 
                         
                           i 
                           , 
                           pre 
                         
                         ) 
                       
                     
                     MR 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0022]    After substituting in equation (1) for the term VB(i,pre), 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           i 
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           S 
                           j 
                         
                         MR 
                       
                     
                     - 
                     
                       T 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0023]    Then, the summation term on the right side of equation (9) is expanded to pull out the case where j=i−1: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             
                               i 
                               - 
                               2 
                             
                           
                            
                           
                               
                           
                            
                           
                             
                               S 
                               j 
                             
                             MR 
                           
                         
                         - 
                         
                           T 
                           
                             i 
                             - 
                             1 
                           
                         
                       
                       ] 
                     
                     + 
                     
                       
                         S 
                         
                           i 
                           - 
                           1 
                         
                       
                       MR 
                     
                     - 
                     
                       ( 
                       
                         
                           T 
                           i 
                         
                         - 
                         
                           T 
                           
                             i 
                             - 
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       X 
                        
                       
                         ( 
                         
                           
                             i 
                             - 
                             1 
                           
                           , 
                           pre 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         S 
                         
                           i 
                           - 
                           1 
                         
                       
                       MR 
                     
                     - 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         t 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Δt i  is the time between the arrival of the i th  and (i−1) th  packets. The term S i−1 /MR is the amount of time expected for the transmitter to send the (i−1) th  TS packet, which is equal to the ratio of the difference between consecutive PCR timestamps, and the number of packets transmitted between the PCR timestamps. Therefore: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       S 
                       
                         i 
                         - 
                         1 
                       
                     
                     MR 
                   
                   = 
                   
                     
                       
                         PCR 
                         
                           n 
                           + 
                           1 
                         
                       
                       - 
                       
                         PCR 
                         n 
                       
                     
                     
                       k 
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0024]    Replacing the equivalent term for S i−1 /MR in equation (12) back into equation (11), equation (7) is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         i 
                         , 
                         pre 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       X 
                        
                       
                         ( 
                         
                           
                             i 
                             - 
                             1 
                           
                           , 
                           pre 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           PCR 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           PCR 
                           n 
                         
                       
                       
                         k 
                         n 
                       
                     
                     - 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         t 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0025]    Note that equation (7) generalizes to data streams that are VBR, in a well-defined and naturally-defined manner, since VBR is piece-wise CBR. Unlike the derivation for the CBR case, this generalization cannot be derived from the original definition of DF in RFC 4445. 
         [0026]    In essence, the packet size S j  and media rate MR in the prior art formulation of DF can be expressed using the expected time between packet arrivals, which can be computed from the expression: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       PCR 
                       
                         n 
                         + 
                         1 
                       
                     
                     - 
                     
                       PCR 
                       n 
                     
                   
                   
                     k 
                     n 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0027]    The value k n  can be obtained by counting packets, assuming there is no loss, or by comparing sequence numbers of the packets, which are available under some encapsulations. Since the MLR component of the MDI measurement would indicate when a packet loss occurred, MLR should be taken into consideration to determine the accuracy and validity of the DF measure. 
         [0028]    Equations (7) and (8) are calculated using only the difference between two PCR timestamps, the packet counts k n , and the time elapsed Δt i  between the packet arrivals. No determinations need to be made as to the size of the packets at all, as required by the prior art equations for calculating DF. The PCR values, k n , and Δt i  are also relatively easy to extract from a TS packet stream, compared to the difficulties involved in reconstructing the PES to extract the embedded media rate. Thus, equations (7) and (8) are a simpler alternative to the prior art method. 
         [0029]    Furthermore, using equations (7) and (8) results in a more accurate gauge of the network performance, since this method includes the overhead for protocol requirements and reflects the true transport rate of the multimedia data. Also, since these calculations rely on the actual media rate rather than a pre-defined fixed media rate (e.g. the embedded media rate), equations (7) and (8) are valid for both constant bit rate and variable bit rate transmissions. 
         [0030]    The disclosed embodiments can be extended for Multiple Program Transport Stream (MPTS) if all elementary streams(ES) within the stream share a common reference time. 
         [0031]      FIG. 4  is a block diagram of a system  41  for calculating a DF for a network. The system  41  is part of the receiver  26  shown in  FIG. 1 . The system  41  includes a TS packet parser  43 , a local clock  45 , a stream identifier  47 , a processor  49 , and a memory  51 . 
         [0032]    The TS packet parser  43  parses the incoming TS packet stream  33  to identify the TS packets containing PCRs, and to extract the PCRs. The TS packet parser  43  also counts the incoming TS packets, for example, by using an internal counter or by comparing sequence numbers of the packets, which are available under some encapsulations. The processor  49  receives the extracted PCRs and the packet count from the TS packet parser  43 . The local clock  45  determines the local time of arrival for the TS packets and associates an arrival timestamp with each TS packet. The stream identifier  47  identifies which video stream the TS packets belong to, which is necessary in multi-stream applications such as IPTV. The processor  49  receives the arrival timestamps from the local clock  45  and stores them. The processor  49  receives the identified video stream from stream identifier  47  to determine which video stream the PCRs and arrival timestamps correspond to. Local memory  51  is used store the arrival timestamps and PCRs. 
         [0033]    The processor  49  calculates X(i,pre) according to equation (7) and X(i,post) according to equation (8) for each arrived packet i, and stores the result in the memory  51 . The processor  49  also determines the maximum X(i,post) and minimum X(i,pre) during each measurement interval and then calculates DF according to equation (6). 
         [0034]      FIG. 5  shows a flow chart for a method for calculating the delay factor. In step  63  the measurement interval begins. In step  65  packet i is received and its arrival timestamp is stored. In step  67  the packet is examined for a PCR. If one is not present, the next packet is processed. If a PCR is present, the PCR is extracted and stored in memory in step  69 . In step  71 , a check is made as to whether this is the first PCR that has been received. (At least two PCRs must have been received in order to calculate the term 
         [0000]    
       
         
           
             
               
                 PCR 
                 
                   n 
                   + 
                   1 
                 
               
               - 
               
                 PCR 
                 n 
               
             
             
               k 
               n 
             
           
         
       
     
         [0000]    in equations (7) and (8).) If it is the first PCR, the next packet is processed. If this is not the first PCR, equation (13) is computed in step  73 . In step  75 , equations (7) and (8) are computed using the stored arrival timestamps to get values for X(i,pre) and X(i,post) In step  77 , the arrival timestamps are cleared. In step  79 , the minimum and maximum of the computations in step  75  are determined. If this is not the end of the measurement interval, the maximum X(i,post) and minimum X(i,pre) up to this point in the measurement interval are stored in step  85  and processing continues. Otherwise, the DF is calculated and reported in step  83 . 
         [0035]    In one embodiment, the term 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       PCR 
                       
                         n 
                         + 
                         1 
                       
                     
                     - 
                     
                       PCR 
                       n 
                     
                   
                   
                     k 
                     n 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    can be initially computed once and used as a constant throughout the measurement interval. This can be done when the data stream is CBR across the measurement interval, and simplifies the calculations even further. As each packet arrives, X(i,pre) and X(i,post) from equations (7) and (8) can be simply computed using the constant value above in equation (13) and the packet inter-arrival time Δt i . Any other PCR values in packets that arrive within the same measurement interval may be ignored. 
         [0036]    In one embodiment, equations (7) and (8) can also be used to define a coarse-grained version of the DF, denoted DF′, that is simpler to compute. Instead of examining the inter-arrival time for each packet, only inter-arrival times of the PCR-bearing packets are considered. Thus equations (7) and (8) simplify to: 
         [0000]        X ′( n,  pre)= X ′( n− 1, pre)+( PCR   n   −PCR   n−1 )−( T′   n   −T′   n−1 )   (14) 
         [0000]      and 
         [0000]        X ′( n,  post)= X ′( n,  pre)+( PCR   n+1   −PCR   n )   (15) 
         [0000]    where T′ n  is the arrival time of the packet bearing PCR n  relative to the last PCR-bearing packet in the previous measurement interval, or in the case of the first measurement interval, relative to the first PCR-bearing packet. Then 
         [0000]        X ′(0, pre)= X ′(0, post) 
         [0000]        X ′(1, pre)=− T′   1    
         [0000]    DF′ is then expressed as: 
         [0000]        DF′=max   n≧0  ( X ′( n,  post))−min n≧0  ( X ′( n,  pre))   (16) 
         [0000]    Note that the k n  and the associated division are not necessary for this measurement. These equations require only the difference between two PCR timestamps, and the time lapse between the receipt of the TS packets carrying those timestamps. While equations (14) and (15) do not return exactly the same results as a full DF calculation, they offer a good approximation. It should be noted that since the PCR  31  is only required to be inserted once every 100 milliseconds, the values X(n,pre) and X(n,post) have an error term of this magnitude. 
         [0037]    Although the present invention has been described in detail with reference to particular embodiments, persons possessing ordinary skill in the art to which this invention pertains will appreciate that various modifications and enhancements may be made without departing from the spirit and scope of the claims that follow.