The periodic Markov modulated batch Bernoulli process and its application to MPEG video traffic

The Markov modulated batch Bernoulli process (MMBBP) is widely used for modeling a superposition of multiple voices and data at multiplexers in asynchronous transfer mode (ATM) networks, because the MMBBP has the time correlation property and its autocorrelation function is exponentially decaying. However, experimental studies on the MPEG (Motion Pictures Expert Group) video traffic show that its autocorrelation function is periodic as well as exponentially decaying. So, the MMBBP is not adequate to describe the MPEG video traffic.

In this paper, we propose a new stochastic process which we call the periodic Markov modulated batch Bernoulli process (P-MMBBP) to describe the MPEG video traffic adequately. We derive the autocorrelation function of the P-MMBBP and show that the autocorrelation functions of the P-MMBBP and the MPEG video traffic are of the same pattern. We also propose a simple way to match parameters of the P-MMBBP from real MPEG video traffic. We consider the P-MMBBP/D/1 queue and derive the queue length distribution analytically. From numerical results, we show that periodicity gives a significant effect on the tail behavior of the queue length distribution. We also compare tail probabilities obtained by using the P-MMBBP with those obtained by using the 2-state MMBBP. Our comparison shows that the use of the 2-state MMBBP underestimates tail probabilities.