Insensitivity in discrete time queues with a moving server

Abstract

Queues in which customers request service consisting of an integral number of segments and in which the server moves from service station to service station are of considerable interest to practitioners working on digital communications networks. In this paper, we present "insensitivity" theorems and thereby equilibrium distributions for two discrete time queueing models in which the server may change from one customer to another after completion of each segment of service. In the first model, exactly one segment of service is provided at each time point whether or not an arrival occurs, while in the second model, at most one arrival or service occurs at each time point. In each model, custo..