THE PERIODIC MARKOV MODULATED BATCH BERNOULLI PROCESS AND ITS APPLICATION TO MPEG VIDEO TRAFFIC

The Markov modulated batch Bernoulli process (MMBBP) is widely used fo r modeling a superposition of multiple voices and data at multiplexers in asynchronous transfer mode (ATM) networks, because the MMBBP has t he time correlation property and its autocorrelation function is expon entially decaying. However, experimental studies on the MPEG (Motion P ictures Expert Group) video traffic show that its autocorrelation func tion is periodic as well as exponentially decaying, So, the MMBBP is n ot adequate to describe the MPEG video traffic. In this paper, we prop ose a new stochastic process which we call the periodic Markov modulat ed batch Bernoulli process (P-MMBBP) to describe the MPEG video traffi c adequately. We derive the autocorrelation function of the P-MMBBP an d 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 cons ider the P-MMBBP/D/1 queue and derive the queue length distribution an alytically. From numerical results, we show that periodicity gives a s ignificant effect on the tail behavior of the queue length distributio n. We also compare tail probabilities obtained by using the P-MMBBP wi th those obtained by using the 2-state MMBBP. Our comparison shows tha t the use of the 2-state MMBBP underestimates tail probabilities. (C) 1998 Elsevier Science B.V.