Applied Probability and Queues

This book serves as an introduction to queuing theory and provides a thoroughtreatment of tools like Markov processes renewal theory random walks Levyprocesses ... » 

This book serves as an introduction to queuing theory and provides a thoroughtreatment of tools like Markov processes renewal theory random walks Levyprocesses matrixanalytic methods and change of measure. It also treats indetail basic structures like GIG1 and GIGs queues Markovmodulated modelsand queuing networks and gives an introduction to areas such as storageinventory and insurance risk. Exercises are included and a survey ofmathematical prerequisites is given in an appendix This much updated andexpanded second edition of the 1987 original contains an extended treatment ofqueuing networks and matrixanalytic methods as well as additional topics likePoissons equation the fundamental matrix insensitivity rare events andextreme values for regenerative processes Palm theory rate conservation Levyprocesses reflection Skorokhod problems Loynes lemma Siegmund dualitylight traffic heavy tails the Ross conjecture and ordering and finite bufferproblems. Students and researchers in statistics probability theoryoperations research and industrial engineering will find this book useful.TOCSimple Markovian Models. Markov Chains. Markov Jump Processes. QueueingTheory at the Markovian Level. Basic Mathematical Tools. Basic RenewalTheory. Regenerative Processes. Further Topics in Renewal Theory andRegenerative Processes. Random Walks. Special Models and Methods. SteadyState Properties of GIG1. Explicit Examples in the Theory of Random Walksand Single Server Queues. Multidimensional Methods. Manyserver Queues.Conjugate Processes. Insurance Risk DAM and Storage Models. Appendices. «