Queueing Analysis: Finite systemsQueueing 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. |
Contents
Preface | 7 |
Number of Messages Served in a Busy Period | 75 |
TimeDependent Process | 125 |
Copyright | |
6 other sections not shown
Common terms and phrases
A(V_ A(X_ arbitrary message arriving message B₂ blocking probability busy period process busy period started carried load dB(x defined denote elapsed service exhaustive service FCFS system following set G-limited idle period initial condition joint distribution Joint probability k messages Laplace transform LCFS limited service system M/G/1/K system Markov chain mean length mean number mean waiting messages arrive messages served messages that arrive msisk multiple vacation model number of messages obtain P₁ Pk(x Po(t Prob Prob[A(V_ Prob[L pushout queue size distribution remaining service remaining vacation semi-Markov process server is busy server vacations service completion service facility service period set of equations setup single vacation model steady-state Substituting successive Markov points system is given throughput time-dependent process Κλ λ λ λ Σ λη πλ Πο Πρ Σ ακ Σ π Σ Σ Σπ