An Accurate Analytical Model for MPEGCoded Video

Coded Video Tra c Hai Liu, Nirwan Ansari, and Yun-Qing Shi Abstract: Self-similar processes, modulated according to the MPEG frame structure, are proposed to capture both the SRD (short range dependency) and LRD (long range dependency) of MPEG video tra c. Introduction: Tra c generated by video applications is increasingly cramming existing networks, and it is thus essential to accurately characterize video tra c for e cient network management. Traditional models, however, fall short in describing video tra c which is strongly autocorrelated and bursty [1]. Hence, autocorrelations among data should be taken into consideration. The empirical data used here was MPEG-1 coded data of Star Wars1. The frames were organized as follows: IBBPBBPBBPBB IBBPBB. . . , i.e., 12 frames in a Group of Pictures (GOP). I, P, and B frames were compressed by di erent techniques. It is clear that the autocorrelation function (ACF) of the MPEG coded video, shown in Fig. 1, can hardly be captured by a simple random process. To Model MPEG Coded Data, we decompose the MPEG tra c into 10 subsequencesXI ;XP ;XB1 ;XB2 ; , andXB8 . XI consists of all I frames, XP all P frames,XB1 the rst B frames in all GOPs, XB2 the second B frames in all GOPs, and so on. We have used k , e k and e pk (k is the lag between frames, and is a constant), corresponding to the ACFs of a self-similar process [2], a Markov process, and anM=G=1 input process [3], respectively, to approximate ACFs of these subsequences. For illustrative purposes, approximations for P andB1, shown in Fig. 2 and 3, indicates that self-similar processes are better choices, and are thus used to model these subsequences. Using the least squares method, = 0:4663, 0:3546, 0:4468, 0:4779, 0:4294, 0:4656, 0:4380, 0:4682, 0:4465, and 0:4606 for XI ; XP ; XB1 ; XB2 ; , and XB8 , respectively. The corresponding Hurst parameters (H=1=2) for these processes are H = 0:7668, 0:8227, 0:7766, 0:7610, 0:7853, 0:7672, 0:7810, 0:7659, 0:7768, 0:7697, respectively. Marginal distributions of these subsequences are modeled by Beta distributions which have the following form of probability density function: f(x; ; ; 0; 1) = 8<: 1 1 0 ( + ) ( ) ( )( x 0 1 0 ) 1(1 x 0 1 0 ) 1 0 x 1; 0 < ; 0 < 0 otherwise (1) where and are the shape parameters, and [ 0; 1] is the domain where the distribution is de ned. Using the formulae introduced in [4], ̂ = 1:5237, 1:5699, 1:4172, 1:3016, 1:6858, 1:6329, 1:7276, 1:4218, 4:0585, 1:5402, and ̂ = 12:7263, 11:1939, 8:1089, 8:1604, 11:8499, 13:9278, 12:2180, 8:6536, 10:4233, 11:1768 are obtained forXI , XP , XB1 , XB2 , , and XB8 , respectively. By combining XI , XP , XB1 , XB2 , , and XB8 in a manner similar to the GOP pattern, a model for MPEG coded tra c is obtained. The ACF of the tra c generated by our model shown in Fig. 4 is very close to that of the 1The MPEG-I coded data were the courtesy of M.W.Garrett of Bellcore and M.Vetterli of UC Berkeley. real data trace for both small and large lag (k), implying that our model can capture both SRD and LRD. Acknowledgment: This work was carried out in part while N. Ansari was on leave at the Chinese Univ. of Hong Kong, and Y.Q. Shi on leave at the Nanyang Tech. Univ. of Singapore. H. Liu, N. Ansari, and Y.Q. Shi (NJ Center for Wireless Telecommunications, ECE Dept, New Jersey Inst. of Tech., Newark, NJ 07102, USA) References [1] PAXSON, V., and FLOYD, S.: `Wide-area tra c: The failure of poisson modeling'. Proc. SIGCOMM'94, 1994, pp. 257{268 [2] BERAN, J.: `Statistics for long-memory processes' (Chapman & Hall, 1994) [3] KRUNZ, M. and MAKOWSKI, A.M.: `Modeling video tra c using m=g=1 input processes: A compromise between Markovian and LRD models', IEEE J., 1998, JSAC-16, pp. 733{749 [4] HAHN G.J., and SHAPIRO S.S.: `Statistical models in engineering' (Wiley & Sons, 1967)