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arXiv · 2107.04892

A multi-orthogonal polynomials' approach to bulk queueing theory

Ulises Fidalgo
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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.

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Ulises Fidalgo. 2021-07-10. A multi-orthogonal polynomials' approach to bulk queueing theory. https://arxiv.org/abs/2107.04892

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