This paper studies the interdeparture process in a mathematical model of an ATM multiplexer. The technique is based on a discrete‐time queueing model of k input queues feeding one output queue, a situation commonly arising in ATM switches. The process between input queues and output queue is analysed in detail.
For a service rate of one cell per time slot (s = 1) the exact solution of the interdeparture process is given based on the binomial distribution. For a service rate greater than one cell per time slot (s > 1) a solution is derived using the state probabilities of the input queues. The probability density function of the interdeparture process is then obtained by summing a combination of the multinomial joint distribution function of s random variables. If the state probabilities are referred to as the distribution of buffer contents after arrival, the formula returns exact results. © 1998 John Wiley & Sons, Ltd.