Nonintersecting Paths and Applications in Queueing Theory

Abstract

In this paper, some applications of nonintersecting lattice paths to queueing problems are presented. In particular, we derive a determinant formula for non-coincidence probabilities of non-identically distributed Poisson processes from which, in an almost elementary way, zero-avoiding transition probabilities in a Markovian tandem queue can be found. Finally, we present a result about D/M/l queues, where the arrival instances are not equally spaced.