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Layered Queueing Networks – Performance Modelling, Analysis and Optimisation Layered queueing networks : performance modelling, analysis and optimisation Citation for published version (APA): Dorsman, J. L. (2015). Layered queueing networks : performance modelling, analysis and optimisation. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR784295 DOI: 10.6100/IR784295 Document status and date: Published: 01/01/2015 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 29. Sep. 2021 Layered Queueing Networks Performance Modelling, Analysis and Optimisation A catalogue record is available from the Eindhoven University of Technology Library. ISBN: 978-90-386-3763-1 Printed by Ipskamp Drukkers, Enschede, the Netherlands. Cover design by Bas Ruhé. Layered Queueing Networks Performance Modelling, Analysis and Optimisation PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties, in het openbaar te verdedigen op dinsdag 17 februari 2015 om 14:00 uur door Jan-Pieter Lodewijk Dorsman geboren te Amstelveen Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecommissie is als volgt: voorzitter: prof.dr. E.H.L. Aarts 1e promotor: prof.dr.ir. O.J. Boxma 2e promotor: prof.dr. R.D. van der Mei (VUA en CWI) copromotor: dr. M. Vlasiou leden: prof.dr. R.J. Boucherie (UT) prof.dr.ir. R. Dekker (EUR) prof.dr. A.G. de Kok prof.dr.ir. J. Walraevens (Universiteit Gent) DANKWOORD (ACKNOWLEDGEMENTS) Dit proefschrift is het resultaat van enkele jaren onderzoek verricht als promovendus aan de Technische Universiteit Eindhoven (TU/e) en het Centrum Wiskunde & Informatica (CWI) te Amsterdam. Tijdens deze periode heb ik mij gesteund geweten door velen, die op een directe dan wel indirecte wijze een essentiële bijdrage hebben geleverd aan de totstandkoming van deze dissertatie. Het is niet meer dan gepast aan hen in dit welge- meende dankwoord mijn dank te betuigen. Allereerst ben ik zowel mijn copromotor Maria Vlasiou als mijn promotoren Onno Boxma en Rob van der Mei zeer erkentelijk voor de uitmuntende begeleiding, die zij mij op complementaire wijze geboden hebben. Maria, jouw kritische blik heeft mij dikwijls verder doen kijken dan ik in eerste instantie deed. Ik heb veel van jou geleerd en die wijze lessen zullen ongetwijfeld in de toekomst nog vele malen hun dienst bewijzen. Onno, ik heb een voorbeeld mogen nemen aan jouw manier van en jouw visie op het verrichten van onderzoek, en wat dat betreft beschouw ik mijzelf als bevoorrecht. Ook de uitzonderlijk intensieve maar niettemin buitengewoon prettige samenwerking bij vele onderwijstaken zal mij nog lang heugen. Rob, jouw tomeloze enthousiasme heeft ervoor gezorgd dat ik het plezier in mijn werkzaamheden heb behouden. Ik heb veelvuldig van jouw ijzersterke relativeringsvermogen kunnen profiteren, hetgeen bij tijd en wijle van groot belang is geweest. Naast de hierboven genoemde personen heb ik in mijn promotietijd onderzoek mogen verrichten met vele anderen. In het bijzonder ben ik René Bekker, Sandjai Bhulai, Sem Borst, Nir Perel, Petra Vis, Erik Winands en Bert Zwart dankbaar voor ettelijke prettige samenwerkingsverbanden. Deze hebben geleid tot verscheidene onderzoeksresultaten, waarvan enkele in dit proefschrift zijn opgenomen. Voorts ben ik dank verschuldigd aan Richard Boucherie, Rommert Dekker, Ton de Kok en Joris Walraevens voor het zitting nemen in de promotiecommissie en de grondige beoordeling van het manuscript. Bij het schrijven van dit proefschrift heb ik veel technische hulp genoten van Marko Boon en de omslag van deze dissertatie is ontworpen door Bas Ruhé. De Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) ben ik erkentelijk voor de financiële ondersteu- ning in het kader van een project van het stochastiekcluster STAR. Om op succesvolle wijze werk te verzetten in het wetenschappelijke metier is een prettige werkomgeving vereist. Mijn collega’s op het CWI, inclusief de masterstudenten die in de voorbije jaren bij het CWI stage hebben gelopen, hebben in niet geringe mate ervoor gezorgd dat aan deze voorwaarde is voldaan. Het spijt mij oprecht dat ik niet ieder van hen apart bij naam kan noemen, daar dit een oeverloze stroom van namen zou genereren. Wel kan ik zonder enige twijfel stellen dat de collegiale sfeer in de stochas- tiekgroep onontbeerlijk is gebleken bij de voltooiing van dit proefschrift. De reuring en vi DANKWOORD (ACKNOWLEDGEMENTS) de vele karakteristieke curiositeiten die aan de orde van een doorsnee werkdag op het CWI zijn geweest, hebben de onderzoeks- en onderwijsbeslommeringen aanzienlijk ver- aangenaamd. In het licht van een prettige werkomgeving dien ik ook de collega’s van EURANDOM en de stochastieksectie bij de TU/e, inclusief het secretariaat, te noemen. Ongeacht de duur van elke periode waarin ik verzuimde de rivieren over te steken, heb ik mij bij elk daaropvolgend rentree in Eindhoven weer welkom en thuis gevoeld. Dit is niet zonder meer vanzelfsprekend en ik ben hun hiervoor dankbaar. Ik ben de afgelopen jaren op deze wijze onderdeel geweest van twee relatief grote onderzoeksgroepen, elk met zijn eigen populatie en karakteristieken. Ik beschouw dit als een verrijking. In het laatste jaar van mijn promotietijd heb ik enkele maanden de onderzoeksgroep Stochastic Modelling and Analysis of Communication Systems (SMACS) mogen bezoeken, die onderdeel is van de vakgroep Telecommunicatie en Informatieverwerking (TELIN) van de Universiteit Gent in België. Dit verblijf was uiterst leerzaam in meerdere opzichten en bovenal zeer naar mijn goesting. Ik dank Dieter Claeys en Joris Walraevens voor de hoffelijke Vlaamse gastvrijheid en de mij geboden mogelijkheid mee te draaien in het Gentse onderzoeksleven. Naast hen heb ik tijdens mijn verblijf in West-Vlaanderen ook op een zeer prettige wijze onderzoek verricht met Dieter Fiems, Wouter Rogiest en Jasper Vanlerberghe. Ten laatste, maar beslist niet ten minste, wens ik een woord van dank te richten aan familie en vrienden voor het verlenen van het constante besef dat er meer bestaat dan onderzoek. Voor een directe bijdrage aan de totstandkoming van dit proefschrift kan en zal ik hen dan ook zeer zeker niet bedanken. Ondanks dit, of liever gezegd dankzij dit, is de succesvolle completering van deze dissertatie wellicht nog het meest aan hen toe te schrijven. Jan-Pieter Dorsman Amsterdam, november 2014 CONTENTS Dankwoord (Acknowledgements)v 1 Introduction1 1.1 Motivation.......................................1 1.2 Literature review of layered queueing networks................3 1.2.1 Computer science literature........................3 1.2.2 Queueing literature.............................7 1.3 Model descriptions..................................8 1.3.1 The extended machine repair model...................8 1.3.2 The Markovian polling model....................... 11 1.3.3 The carousel storage model........................ 13 1.4 Contributions and overview of the thesis..................... 15 I The extended machine repair model 19 2 Numerical computation and light-traffic asymptotics 21 2.1 Introduction...................................... 21 2.2 Model description and notation.......................... 22 2.3 Application of the power-series algorithm.................... 23 2.3.1 Preliminaries................................. 23 2.3.2 Computational scheme........................... 25 2.4 Light-traffic behaviour................................ 29 2.4.1 Marginal queue length........................... 30 2.4.2 Joint queue length.............................. 32 3 Heavy-traffic asymptotics 35 3.1 Introduction...................................... 35 3.2 Notation and preliminaries............................. 38 3.3 Heavy-traffic asymptotics of the workload.................... 41 3.4 Extension to waiting times
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