Geometric Distributions in the Theory of Queues

Abstract

SUMMARY First a new explanation in probability terms is given for the occurrence of geometric or conditional geometric distributions in some queueing problems. The methods used allow some simple but useful generalizations to be obtained. In §§2 and 3, these results are used to find the equilibrium distribution for a queueing system for which customers can arrive late, and for which the service time has a negative exponential distribution. The effects of different assumptions about the distribution of lateness on the queue distribution are investigated. In §4, a generalization of a result in the theory of Markov chains given in §1 is derived.