On the limiting characteristics for an inhomogeneous $M_t|M_t|S$ queue with catastrophes

TL;DR

This paper investigates the long-term behavior, convergence rates, and limiting characteristics of an inhomogeneous $M_t|M_t|S$ queueing model that includes the possibility of catastrophic events.

Contribution

It provides new insights into the ergodic properties and convergence bounds of inhomogeneous queueing systems with catastrophes.

Findings

Established conditions for weak ergodicity.

Derived bounds on the rate of convergence.

Analyzed the impact of catastrophes on queue stability.

Abstract

We study weak ergodicity, bounds on the rate of convergence, and problems of computing of the limiting characteristics for an inhomogeneous $M_t|M_t|S$ queueing model with possible catastrophes.