An Approximate Method for Treating a Class of Multiqueue Problems

Abstract

The following problem is considered: N queues of unrestricted length are served in cyclic order by a single server. Input to each queue is Poisson, the service time distribution may be arbitrary, and a finite time is required by the server to go from one queue to the next. Supposing that at any queue the server serves all units which he finds when he arrives, what is the probability Pn that in a stationary state he finds exactly n units? The method for solving this problem is based on the notion of a "self-consistent" probability distribution and is actually applicable to a general class of multiqueue situations of which the one considered here is typical. 204

An Approximate Method for Calculating Delays for a Family of Cyclic-Type Queues

“…In these papers, the Laplace-Stieltjes transforms of the waiting time distributions were obtained. Attempts to obtain the distributions for similar models by approximate methods were made by Leibowitz 4 and Schay, Jr. 6 The method presented here approximately calculates the steadystate delays of an arriving customer. The approximation is carried out by modifying the model to achieve a manageable state space.…”

Multiqueue Systems with Nonexhaustive Cyclic Service

“…The approximate methods usually rest on some simplifying assumptions such as the "independence assumption" 12 under which the stochastic processes within a particular queue are considered more or less independent of the processes within the other queues.…”

Effect of Switchover Time in Cyclically Switched Systems

“…Since then, there has been an extensive research in this area, especially since the range of applications in which cyclic polling models can be used is very broad. Leibowitz (Leibowitz, 1961) was among the first to study an approximate solution for symmetrically loaded cyclic polling system with gated service and constant switchover time. Cooper and Murray (Coooper & Murray, 1969;Cooper, 1970) analyzed exhaustive and gated service systems using an imbedded Markov chain technique for zero switchover time.…”