Tail Asymptotics of Queueing Networks with Subexponential Service Times

To myself and my parents... iii ACKNOWLEDGEMENTS Throughout my graduate studies, I am indebted to many people for their help and encouragement. First of all, I would like to thank my advisor Prof. Hayriye Ayhan. It is impossible for me to express in words my full appreciation. However, I would like to thank all of her advice and support during my graduate studies. I would not have completed this thesis without her infinite patience and understanding. I would also like to thank all of my committee members, Prof. comments for assisting me in teaching courses and looking for a job as well as her recommendation letters. I would like to thank all my friends who made my studies in USA enjoyable. I cannot list them all here, but I would like to especially mention my best friends, Finally, I would also like to thank my father Heedong Kim, my mother Heejung Goo, my brother Junghun Kim, and my sister-in-law Minam Goo for their love and support. 1 A closed feedforward fork and join queueing network with K = 7 stations. 15 2 Simulation results and the tail asymptotics of system times for Systems xi SUMMARY 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 …