Decomposition results for stochastic storage processes and queues with alternating L\'evy inputs

TL;DR

This paper extends workload decomposition results for Lévy queues with various input types, using new martingale tools to analyze systems with alternating Lévy inputs, server vacations, and interruptions.

Contribution

It introduces generalized decomposition results for Lévy queues with complex input processes and server behaviors, utilizing novel martingale techniques.

Findings

Workload decompositions for Lévy queues with secondary jump inputs

Analysis of queues with server vacations or interruptions

Application to polling systems with Lévy inputs

Abstract

In this paper we generalize known workload decomposition results for L\'{e}vy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general L\'{e}vy inputs. Our main tools are new martingale results, which have been derived in a companion paper.