Performance of Statistical Multiplexers with Finite Number of Inputs and Train Arrivals

A slotted statistical multiplexer with a finite number of input links is considered in this paper. Messages arriving on each input link contain a fixed number of fixed??-??length packets and are carried to the multiplexer in the form of a packet ?>train ?> at the rate of one packet per slot. Several messages may arrive contiguously on an input link; idle periods are geometrically distributed. The multiplexer buffer is modeled as a discrete??-??time single??-??server queueing system with train arrivals. By means of a generating function approach, a technique to derive the moments of the buffer occupancy is developed and an explicit expression for the mean buffer occupancy is given. Furthermore, an approximate method is presented to get a tight upper bound for the tail distribution of the buffer occupancy, especially for large traffic load.