Networks of infinite-server queues with multiplicative transitions

TL;DR

This paper develops a mathematical framework for analyzing infinite-server queue networks with multiplicative transitions, enabling the computation of moments and applicable to various systems like retrial queues and rerouting networks.

Contribution

It introduces a novel model of queue networks with multiplicative state changes and derives a PDE system for their probability generating functions.

Findings

Derived PDE system for joint PGF of the network

Applicable to retrial queues, rerouting networks, and storage systems

Numerical examples demonstrate practical utility

Abstract

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we characterize the joint probability generating function in terms of a system of partial differential equations; this system enables the evaluation of (transient as well as stationary) moments. We show that several relevant systems fit in the framework developed, such as networks of retrial queues, networks in which jobs can be rerouted when links fail, and storage systems. Numerical examples illustrate how our results can be used to support design problems.