Unifying queueing model for ATM and its analysis

This paper considers a discrete-time single-server queueing system with infinite buffer size and a finite number of independent Markov-modulated Bernoulli processes (MMBPs). A simple analytical approach is presented to analyse the asymptotic behaviour of such a queueing system. An explicit expression for the tail distribution of the buffer contents is given, from which two upper bounds for the tail distribution are derived. These two upper bounds are good and even tight in many cases, as shown by the numerical results. Compared to a previously reported general solution technique, our approximate analytical approach is very easy to use and is not limited by the system size and the traffic parameters. The CPU time required to calculate the upper bounds of the tail distribution is quite acceptable for practical use; especially for a single traffic type, the calculation costs nearly no CPU time on a normal PC. This analytical method is also suitable for more general Markov-modulated arrival processes.