Title:
Tail asymptotics of queueing networks with subexponential service times

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Authors
Kim, Jung-Kyung
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Ayhan, Hayriye
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Abstract
This dissertation is concerned with the tail asymptotics of queueing networks with subexponential service time distributions. Our objective is to investigate the tail characteristics of key performance measures such as cycle times and waiting times on a variety of queueing models which may arise in many applications such as communication and manufacturing systems. First, we focus on a general class of closed feedforward fork and join queueing networks under the assumption that the service time distribution of at least one station is subexponential. Our goal is to derive the tail asymptotics of transient cycle times and waiting times. Furthermore, we argue that under certain conditions the asymptotic tail distributions remain the same for stationary cycle times and waiting times. Finally, we provide numerical experiments in order to understand how fast the convergence of tail probabilities of cycle times and waiting times is to their asymptotic counter parts. Next, we consider closed tandem queues with finite buffers between stations. We assume that at least one station has a subexponential service time distribution. We analyze this system under communication blocking and manufacturing blocking rules. We are interested in the tail asymptotics of transient cycle times and waiting times. Furthermore, we study under which conditions on system parameters a stationary regime exists and the transient results can be generalized to stationary counter parts. Finally, we provide numerical examples to understand the convergence behavior of the tail asymptotics of transient cycle times and waiting times. Finally, we study open tandem queueing networks with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.
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Date Issued
2009-07-06
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Dissertation
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