Strong asymptotic behavior of multi-orthogonal polynomials associated with a queueing model

TL;DR

This paper analyzes the strong asymptotic behavior of multi-orthogonal polynomials linked to a queueing model with bulk service, providing insights into their mathematical properties and implications for the model's transition probabilities.

Contribution

It presents new asymptotic results for type I and type II multiple orthogonal polynomials associated with a specific queueing model, advancing understanding of their behavior.

Findings

Derived strong asymptotics for multi-orthogonal polynomials

Connected polynomial behavior to queueing transition probabilities

Enhanced mathematical understanding of queueing models with bulk service

Abstract

We describe the strong asymptotic behavior of type I and type II multiple orthogonal polynomials which were used to give an integral expression for a transition probability function corresponding to a queueing models that has a bulk service admitting batches with a fixed size of customers.