Markov modulated periodic arrival process offered to an ATM multiplexer

When a superposition of on/off sources is offered to a deterministic server, we are faced with a particular queueing system, the analysis of which has a significant role in ATM networks. Periodic cell generation during active times is a major feature of these sources. We provide an analytical approach to solve for this queueing system via an approximation to the transient behavior of the nD/D/1 queue. The solution to the queue length distribution is given in terms of a solution to a linear differential equation with variable coefficients. The technique proposed here has close similarities with the fluid flow approximation and is amenable to extension for more complicated queueing systems with such correlated arrival processes. A numerical example for a packetized voice multiplexer is finally given to demonstrate our results.