Statistical multiplexing of correlated variable-length packet trains: an analytic performance study

We consider a statistical multiplexer which is modeled as a discrete-time s ingle-server queueing system. Messages consisting of a variable number of f ixed-length packets arrive to the muliplexer at the rate of one packet per slot ('train arrivals'), which results in what we call a primary correlatio n in the packet arrival process. The distribution of the message lengths ti n terms of packets) is general. Additionally, the arrival process exhibits a secondary correlation, which results from the fact that the distribution of the number of leading packet arrivals in a slot depends on some environm ent variable. We assume this environment to have two possible states, each with geometric sojourn times. By using generating functions and an infinite -dimensional state description, we derive closed-form expressions for the m ean, the variance and the tail distribution of the buffer contents in the s teady state. Some numerical examples illustrate the effect of both primary and secondary correlation on the multiplexer performance.