On the Transient, Busy and Idle Period Analysis of Statistical Multiplexers with N Input Links and Train Arrivals

In this paper, we present an exact transient (discrete-time) queuing analysis of a statistical multiplexer with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets. The functional equation describing this queuing model is manipulated and transformed into a mathematical tractable form. This allows us to derive the transient probability generating function (pgf) of the buffer occupancy. From this transient pgf, time-dependent performance measures such as transient probability of empty buffer, transient mean of buffer occupancy and instantaneous packet overflow probabilities can be derived. The transient analysis provides useful insights into the derivation of the busy period distribution function, which will be illustrated for the simpler GI/D/1 case. We also present closed-form expressions for the idle period distribution of the queuing model under consideration. The paper presents significant new results on the transient and busy-period analysis of statistical multiplexers with N input links and train arrivals. Key-Words: ATM multiplexers, Transient analysis, Train arrivals, busy-period, idle-period, Discrete-time queues.