Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Jan 2008 
Place of Publication  Haifa 
Publisher  
Publication status  Published  2008 
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On the control of queueing networks and the asymptotic variance rate of outputs. / Nazarathy, J.
Haifa : University of Haifa, 2008. 132 p.Research output: Thesis › Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
TY  THES
T1  On the control of queueing networks and the asymptotic variance rate of outputs
AU  Nazarathy, J.
PY  2008
Y1  2008
N2  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 multiclass 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 pushpull 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 pushpull 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 birthdeath 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 PushPull system, we obtain expressions for the asymptotic variance rate, by means of a diffusion limit whose proof relies on our positive Harris recurrence result.
AB  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 multiclass 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 pushpull 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 pushpull 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 birthdeath 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 PushPull system, we obtain expressions for the asymptotic variance rate, by means of a diffusion limit whose proof relies on our positive Harris recurrence result.
M3  Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
PB  University of Haifa
CY  Haifa
ER 