A multi-orthogonal polynomials' approach to bulk queueing theory

Abstract

We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal polynomials with respect to a system of distributions that contain measures supported on starlike subsets of the complex plane. We also study the corresponding steady state.

References in corpus (1)

• Nikishin systems on star-like sets: algebraic properties and weak asymptotics of the associated multiple orthogonal polynomials