Lévy-driven polling systems and continuous-state branching processes

O.J. Boxma, J. Ivanovs, K.M. Kosinski, M.R.H. Mandjes

Research output: Book/ReportReportAcademic

Abstract

In this paper we study an N-queue polling model with switchover times. Each of the queues is fed by a non-decreasing Lévy process, which can be different during each of the consecutive periods within the server's cycle. The N-dimensional Lévy processes obtained in this fashion are described by their (joint) Laplace exponent, thus allowing for non-independent input streams. For such a system we derive the steady-state distribution of the joint workload at embedded epochs, i.e. polling and switching instants. Using the Kella-Whitt martingale, we also derive the steady-state distribution at an arbitrary epoch. Our analysis heavily relies on establishing a link between fl uid (Lévy input) polling systems and multitype Jirina processes (continuous-state discrete-time branching processes). This is done by properly defining the notion of the branching property for a discipline. This definition is broad enough to contain the most important service disciplines, like exhaustive and gated.
Original languageEnglish
Place of PublicationAmsterdam
PublisherCentrum voor Wiskunde en Informatica
Number of pages16
Publication statusPublished - 2009

Publication series

NameCWI Report
VolumePNA-E0909

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