This book serves as an introduction to queuing theory and provides a
thorough treatment of tools like Markov processes, renewal theory,
random walks, Levy processes, matrix-analytic methods and change of
measure. It also treats in detail basic structures like GI/G/1 and
GI/G/s queues, Markov-modulated models and queuing networks, and gives
an introduction to areas such as storage, inventory, and insurance
risk. Exercises are included and a survey of mathematical
prerequisites is given in an appendix
This much updated and expanded second edition of the 1987 original
contains an extended treatment of queuing networks and matrix-analytic
methods as well as additional topics like Poisson's equation, the
fundamental matrix, insensitivity, rare events and extreme values for
regenerative processes, Palm theory, rate conservation, Levy
processes, reflection, Skorokhod problems, Loynes' lemma, Siegmund
duality, light traffic, heavy tails, the Ross conjecture and ordering,
and finite buffer problems.
Students and researchers in statistics, probability theory, operations
research, and industrial engineering will find this book useful. TOC:Simple Markovian Models.- Markov Chains.- Markov Jump Processes.- Queueing Theory at the Markovian Level.- Basic Mathematical Tools.- Basic Renewal Theory.- Regenerative Processes.- Further Topics in Renewal Theory and Regenerative Processes.- Random Walks.- Special Models and Methods.- Steady-State Properties of GI/G/1.- Explicit Examples in the Theory of Random Walks and Single Server Queues.- Multidimensional Methods.- Many-server Queues.- Conjugate Processes.- Insurance Risk, DAM and Storage Models.- Appendices.
