Infinite-server M|G|$\infty$ queueing models with catastrophes

TL;DR

This paper analyzes infinite-server queueing models with both arrivals and catastrophes, deriving probability generating functions and transforms for key system metrics, enhancing understanding of such stochastic processes.

Contribution

It provides explicit probability generating functions and transforms for joint distributions and busy periods in infinite-server queues with catastrophes, a novel extension.

Findings

Derived PGFs for joint distributions of busy servers and served customers

Obtained Laplace-Stieltjes Transforms for busy period and cycle distributions

Enhanced analytical tools for queueing systems with catastrophes

Abstract

The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as well as the Laplace-Stieltjes Transforms of distribution of busy period and distribution of busy cycle for the models are found.