Markovian polling systems with an application to wireless random-access networks

Research output: Book/ReportReportAcademic

89 Downloads (Pure)

Abstract

Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating function of) the joint queue length distribution conditioned on a point in time when the server visits a certain queue. From this functional equation, expressions for the (cross-)moments of the queue lengths follow. We also derive a pseudo-conservation law for this class of polling systems. Using these results, we compute expressions for certain system parameters that minimise the total expected amount of work in systems that arise from the wireless random-access network setting. In addition, we derive approximations for those same parameters that minimise a weighted sum of mean waiting times in these systems. Based on these expressions, we also present an adaptive control algorithm for finding the optimal parameter values in a distributed fashion, which is particularly relevant in the context of wireless random-access networks. Keywords: queue lengths, binomial service disciplines, Markovian routing, random routing, wireless random-access networks
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages21
Publication statusPublished - 2014

Publication series

NameReport Eurandom
Volume2014001
ISSN (Print)1389-2355

Fingerprint

Servers
Markov processes
Conservation

Cite this

@book{2e5a58c1c0604be69d03d32d12beb69e,
title = "Markovian polling systems with an application to wireless random-access networks",
abstract = "Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating function of) the joint queue length distribution conditioned on a point in time when the server visits a certain queue. From this functional equation, expressions for the (cross-)moments of the queue lengths follow. We also derive a pseudo-conservation law for this class of polling systems. Using these results, we compute expressions for certain system parameters that minimise the total expected amount of work in systems that arise from the wireless random-access network setting. In addition, we derive approximations for those same parameters that minimise a weighted sum of mean waiting times in these systems. Based on these expressions, we also present an adaptive control algorithm for finding the optimal parameter values in a distributed fashion, which is particularly relevant in the context of wireless random-access networks. Keywords: queue lengths, binomial service disciplines, Markovian routing, random routing, wireless random-access networks",
author = "J.L. Dorsman and S.C. Borst and O.J. Boxma and M. Vlasiou",
year = "2014",
language = "English",
series = "Report Eurandom",
publisher = "Eurandom",

}

Markovian polling systems with an application to wireless random-access networks. / Dorsman, J.L.; Borst, S.C.; Boxma, O.J.; Vlasiou, M.

Eindhoven : Eurandom, 2014. 21 p. (Report Eurandom; Vol. 2014001).

Research output: Book/ReportReportAcademic

TY - BOOK

T1 - Markovian polling systems with an application to wireless random-access networks

AU - Dorsman, J.L.

AU - Borst, S.C.

AU - Boxma, O.J.

AU - Vlasiou, M.

PY - 2014

Y1 - 2014

N2 - Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating function of) the joint queue length distribution conditioned on a point in time when the server visits a certain queue. From this functional equation, expressions for the (cross-)moments of the queue lengths follow. We also derive a pseudo-conservation law for this class of polling systems. Using these results, we compute expressions for certain system parameters that minimise the total expected amount of work in systems that arise from the wireless random-access network setting. In addition, we derive approximations for those same parameters that minimise a weighted sum of mean waiting times in these systems. Based on these expressions, we also present an adaptive control algorithm for finding the optimal parameter values in a distributed fashion, which is particularly relevant in the context of wireless random-access networks. Keywords: queue lengths, binomial service disciplines, Markovian routing, random routing, wireless random-access networks

AB - Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating function of) the joint queue length distribution conditioned on a point in time when the server visits a certain queue. From this functional equation, expressions for the (cross-)moments of the queue lengths follow. We also derive a pseudo-conservation law for this class of polling systems. Using these results, we compute expressions for certain system parameters that minimise the total expected amount of work in systems that arise from the wireless random-access network setting. In addition, we derive approximations for those same parameters that minimise a weighted sum of mean waiting times in these systems. Based on these expressions, we also present an adaptive control algorithm for finding the optimal parameter values in a distributed fashion, which is particularly relevant in the context of wireless random-access networks. Keywords: queue lengths, binomial service disciplines, Markovian routing, random routing, wireless random-access networks

M3 - Report

T3 - Report Eurandom

BT - Markovian polling systems with an application to wireless random-access networks

PB - Eurandom

CY - Eindhoven

ER -