Packet Delay and Queue Length for Statistical Multiplexers with Low-Speed Access Lines

Abstract A slotted statistical multiplexer is considered to which variable-length messages arrive via low-speed access lines. More specifically, messages are assumed to consist of multiple packets and to enter the multiplexer buffer at a rate of one packet per slot, which results in a correlated packet arrival stream into the multiplexer. Assuming a geometric distribution for the message lengths, the system is analyzed by using a two-dimensional state description, and a functional equation characterizing the queue-length behavior of the multiplexer buffer is found. An (implicit) expression for the probability generating function of the packet delay is also obtained. A technique is then developed to derive from these results closed-form expressions for the moments of the queue-length and the packet-delay distributions. Explicit formulas are given for the mean and the variance of both distributions. The results are illustrated by means of a practical example and the influence of the correlation in the packet arrival stream is investigated.