A multi-orthogonal polynomials' approach to bulk queueing theory

2021/07/10 by Fidalgo, Ulises
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2107.04892

openalex publication_date 2021/07/10 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28

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.

Citations

• Calculation of Gauss quadrature rules

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