Exact tail asymptotics for fluid models driven by an $M/M/c$ queue

TL;DR

This paper derives exact tail asymptotics for the stationary distribution of a fluid model driven by an M/M/c queue, extending the kernel method to analyze tail behaviors in a two-dimensional queueing system.

Contribution

It introduces an extension of the kernel method to obtain three types of exact tail asymptotics for the fluid model driven by an M/M/c queue, a novel analytical approach.

Findings

Identified three types of exact tail asymptotics.

Extended kernel method for tail analysis.

Provided precise asymptotic formulas for the stationary distribution.

Abstract

In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the $M/M/c$ queue, which is a two-dimensional queueing system with a discrete phase and a continuous level. We extend the kernel method to study tail asymptotics of its stationary distribution, and a total of three types of exact tail asymptotics is identified from our study and reported in the paper.