Departure process in tandem queues

Abstract

In a system of single-server queues in series, a customer enters the first queue ; he waits till he is served, enters the second queue, and so on. A heuristic method of approximating the distribution function of the inter-departure time through erlangian distribution is presented in this paper. It is proved that if all the queues are in equilibrium, the expected value of the inter-departure time at each of the queues in tandem equals the expected value of the inter-arrival time in the first queue. For a queue not in equilibrium, the inter-departure time follows asymptotically the distribution of its service time. The output from an unstable queue equals the input into the next queue in tandem if the latter is in equilibrium. The approach given in this paper is supported though simulation experiments.