Queueing Analysis: Finite systems
Queueing models have been used very effectively for the performance of evaluation of many computer and communication systems. As a continuation of Volume 1: Vacation and Priority Systems, which dealt with M/G/1-type systems, this volume explores systems with a finite population (M/G/1/N) and those with a finite capacity (M/G/1/K). The methods of imbedded Markov chains and semi-Markov processes, the delay cycle analysis, and the method of supplementary variables are extensively used. In order to maximise the reader's understanding, multiple approaches have been employed, including the derivation of the results by several techniques. This elaborate presentation of new and important research results applicable to emerging technologies is aimed at engineers and mathematicians alike, with a basic understanding or a comprehensive knowledge of queueing systems. It will be of particular interest to researchers and graduate students of applied probability, operations research, computer science and electrical engineering and to researchers and engineers of performance of computers and communication networks. Volume 3: Discrete Time Systems will follow this volume to complete the set.
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arriving message assume batch busy period process busy period started carried load defined denote distribution Pk elapsed service exceptional service exhaustive service exponentially distributed FCFS system G-limited identical idle period imbedded Markov points initial condition initial delay joint distribution joint probability Kronecker's delta Laplace transform LCFS LST W(s M/G/l/K system marginal distribution Markov chain mean length mean number mean response mean waiting message of class messages arrive messages served messages that arrive method of supplementary multiple vacation model normalization condition Note number of messages NXP0 obtain performance measures Pk(x Prob Prob[L probability density function probability distribution pushout quasirandom queue size distribution remaining service remaining vacation Section semi-Markov process server is busy server vacations service completion service facility service period set of equations single vacation model steady-state Substituting time-dependent process unfinished virtual waiting