FUNDAMENTAL BOUNDS AND APPROXIMATIONS FOR ATM MULTIPLEXERS WITH APPLICATIONS TO VIDEO TELECONFERENCING

The main contributions of this paper are two-fold. First, we prove fun damental, similarly behaving lower and upper bounds, and give an appro ximation based on the bounds, which is effective for analyzing ATM mul tiplexers, even when the traffic has many, possibly heterogeneous, sou rces and their models are of high dimension. Second, we apply our anal ytic approximation to statistical models of video teleconference traff ic, obtain the multiplexing system's capacity as determined by the num ber of admissible sources for given cell-loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulati ons, which are driven by actual data from coders. The results are surp risingly close. Our bounds are based on large deviations theory. The m ain assumption is that the sources are Markovian and time-reversible. Our approximation to the steady-state buffer distribution is called Ch ernoff-dominant eigenvalue since one parameter is obtained from Cherno ff's theorem and the other is the system's dominant eigenvalue. Fast, effective techniques are given for their computation. In our applicati on we process the output of variable bit rate coders to obtain DAR(1) source models which, while of high dimension, require only knowledge o f the mean, variance, and correlation. We require cell-loss probabilit y not to exceed 10(-6) trunk bandwidth ranges from 45 to 150 Mb/s, buf fer sizes are such that maximum delays range from 1 to 60 ms, and the number of coder-sources ranges from 15 to 150. Even for the largest sy stems, the time for analysis is a fraction of a second, while each sim ulation takes many hours. Thus, the real-time administration of admiss ion control based on our analytic techniques is feasible.