A tight upper bound for the tail distribution of the buffer contents in statistical multiplexers with heterogeneous MMBP traffic sources

An ATM statistical multiplexer with infinite buffer capacity and a number of independent (not necessarily identical) 2-state MMBP (Markov modulated Bernoulli process) traffic sources is considered in this paper, which is modeled as a discrete-time single-server queueing system with correlated arrivals. A simple analytic approach is presented to obtain an upper bound for the tail distribution of the buffer contents. This upper bound is good and even tight in many cases, as shown by the numerical results. Compared to a previously reported general solution technique, our approximate analytic approach is very easy to use and not limited by the system size, and costs nearly no CPU-time. So it is useful in practice. This analytic method can also be easily extended to general m-state Markov modulated arrival processes (e.g., m-state MMBPs)