Discrete-time analysis of the busy and idle period distributions of a finite-capacity ATM multiplexer with periodic input

In this paper we present an exact solution for the distribution of the busy and idle periods of a finite-capacity ATM multiplexer. The multiplexer input lines and also the output line is considered as discretized into time slots of cell-duration length. The input traffic is the superposition of a number of independent and periodic sources. For different load situations we present recursive algorithms whose complexity is of polynomial order and which are efficient in terms of computing time and memory requirements. By special parameter choice we are able to compute the exact busy and idle period distributions also for the infinite-capacity multiplexer. Numerical examples show that the mean value and especially the coefficient of variation of the busy period depend strongly on the traffic intensity. By the numerical results we get some insight into the changes of the traffic characteristics when one ATM multiplexer stage is passed.