A cyclic service tandem queueing model with parallel queues in the first stage

This paper presents an analysis for the steady state of a two-stage tandem queueing model served by a single server, in which the first stage has two queues in parallel. Generating functions are obtained for two joint queue length distributions, one at the instant just after service completion and the other at an arbitrary instant, using a solution of a functional equation with two variables and the rate conservation principle in the theory of piecewise Markov process. The Laplace-Stieltjes transforms are also derived for some sojourn time distributions. Some numerical results for mean waitng times and mean total sojourn times are presented.