Queues Served in Cyclic Order: Waiting Times

Abstract

This paper extends the results of a previous paper in which two models of a system of queues served in cyclic order were studied. One model is an exhaustive service model, in which the server waits on all customers in a queue before proceeding to the next queue in cyclic order. The other is a gating model, in which a gate closes behind the waiting units when the server arrives, and the server waits on only those customers in front of the gate, deferring service of later arrivals until the next cycle. In the present paper, the Laplace-Stieltjes transforms of the order-of-arrival waiting time distribution functions and, for the exhaustive service model, the mean waiting time for a unit arriving at a queue, are obtained.