On mean-field \(GI/GI/1\) queueing model: existence, uniqueness

TL;DR

This paper develops a mean-field model for the GI/GI/1 queueing system, proving existence and uniqueness of solutions using martingale problem techniques, thus advancing theoretical understanding of such stochastic processes.

Contribution

It introduces a mean-field extension of the GI/GI/1 queue and establishes existence and uniqueness of solutions under new assumptions on intensities.

Findings

Existence of a mean-field GI/GI/1 queueing process.

Uniqueness in distribution of the process.

Application of martingale problem framework.

Abstract

A mean-field extension of the queueing system \(GI/GI/1\) is considered. The process is constructed as a Markov solution of a martingale problem. Uniqueness in distribution is established under a bit different sets of assumptions on intensities.