Applied Probability and QueuesSpringer Science & Business Media, 2003. 5. 15. - 438페이지 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. |
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arrival Asmussen assume asymptotic birth-death process bounded Brownian motion Consider convergence Corollary corresponding cycle define denote density discrete distribution F equivalent ergodic example exists exponential exponential distribution F(dx finite follows formula function GI/G/1 queue given Hence implies independent intensity matrix interarrival distribution irreducible Jackson network jump ladder height Laplace transform Lemma Lévy process limit M/M/1 queue Markov chain Markov process Markov property Markovian martingale mean node nonlattice nonnegative phase phase-type Poisson process positive recurrent Problems Proof of Theorem Proposition queue length queueing system queueing theory random walk regenerative renewal equation renewal process renewal theorem resp Section server service time distribution Show solution stationary distribution steady-state stochastic transition matrix waiting workload Y₁ yields
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417 페이지 - Conditional limit theorems relating a random walk to its associate, with applications to risk reserve processes and the G//G/1 queue.