QUEUES SERVED IN CYCLIC ORDER

We study two models of a system of queues served in cyclic order by a single server. In each model, the ith queue is characterized by general service time distribution junction Hi(·) and Poisson input with parameter λi. In the exhaustive service model, the server continues to serve a particular queue until the server becomes idle and there are no units waiting in that queue; at this time the server advances to and immediately starts service on the next nonempty queue in the cyclic order. The gating model differs from the exhaustive service model in that when the server advances to a nonempty queue, a gate closes behind the waiting units. Only those units waiting in front of the gate are served during this cycle, with the service of subsequent arrivals deferred to the next cycle. We find expressions for the mean number of units in a queue at the instant it starts service, the mean cycle time, and the Laplace‐Stieltjes transform of the cycle time distribution function. © 1969 The Bell System Technical Journal