On the control of queueing networks and the asymptotic variance rate of outputs

J. Nazarathy

    Research output: ThesisPhd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)

    Abstract

    In this thesis we study several topics related to the control of queueing networks and analysis of the asymptotic variance rate of output processes. We first address the problem of optimal control of a multi-class queueing network over a finite time horizon with linear holding costs. Our method for control and its analysis was published in Nazarathy and Weiss (2008b). We then analyze the stability properties of an example network with infinite virtual queues which we call the push-pull network. This network can be controlled in a way such that the servers operate all of the time while the queues remain stochastically bounded as in Kopzon et al. (2008). Our analysis generalizes the memoryless processing time results of that paper to the case of general processing durations. We utilize the fluid stability framework for showing positive Harris recurrence of Markov processes associated with queueing networks. These results were published in Nazarathy andWeiss (2008c). The sample path behavior of the push-pull network has motivated us to analyze the variability of its output processes. A first measure for such variability is the asymptotic variance rate: the linear increase of the variance function of a counting process over time. Experimenting with this performance measure, we observe an interesting phenomena that occurs in simple finite capacity birth-death queues and obtain a closed formula for the asymptotic variance rate for such systems. These results have been published in Nazarathy and Weiss (2008a). Returning to the Push-Pull system, we obtain expressions for the asymptotic variance rate, by means of a diffusion limit whose proof relies on our positive Harris recurrence result.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • University of Haifa
    Supervisors/Advisors
    • Weiss, Gideon, Promotor, External person
    Award date1 Jan 2008
    Place of PublicationHaifa
    Publisher
    Publication statusPublished - 2008

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