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. 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 queuing 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 obtain a tight upper bound for the tail distribution of the buffer occupancy, especially for large traffic load