On the relations among the distributions at different epochs for discrete-time GI/Geom/1 queues

Abstract

In this paper we discuss the discrete-time GI/Geom/1 queue and derive relations among prearrival and random epochs as well as the outside observer's distributions. Two variations of the model, namely late arrival system with delayed access and early arrival system, have been discussed along with the relations between prearrival-epoch probabilities for the two models.