Samenvatting
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.
Originele taal2  Engels 

Kwalificatie  Doctor in de Filosofie 
Toekennende instantie 

Begeleider(s)/adviseur 

Datum van toekenning  1 jan 2008 
Plaats van publicatie  Haifa 
Uitgever  
Status  Gepubliceerd  2008 
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Citeer dit
Nazarathy, J. (2008). On the control of queueing networks and the asymptotic variance rate of outputs. University of Haifa.