Queueing analysis: a foundation of performance evaluation, vol. 1 : vacation and priority systems
Queueing models with the server's vacations and/or priority-based scheduling can be used for the performance evaluation of many computer and communication systems. This book provides a comprehensive and accessible analysis of these queueing models in the framework of M/G/1 systems. The method of imbedded Markov chains, the delay cycle analysis, and the method of supplementary variables are extensively used to study the M/G/1, M/G/1 with vacations, and M/G/1 with priorities. Only a basic understanding of queueing systems is assumed. A comprehensive bibliography of books on queues and teletraffic engineering completes the volume.
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2 Waiting time of a message that arrives during the m th generation
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analysis arbitrary message arrival process arrival rate busy period process Chapter consider defined delay cycle denotes elapsed service equation exceptional service exhaustive service system FCFS order FCFS system gated service system idle period initial condition initial delay interdeparture joint distribution joint probability Laplace transform LCFS length LST W(s M/G/l system Markov chain Markov point mean number mean waiting message arrives message of class message waiting messages served messages that arrive multiple vacation model Note number of messages Operations Research Poisson process preemptive resume priority priority class priority discipline priority messages priority queues Queueing Systems Queueing Theory remaining service resume priority system Section semi-Markov process server service completion service period single vacation model Stochastic Stochastic Processes Substituting system with multiple system with setup system without vacations T-cycle Takagi th message th service theorem unfinished vacation period Wp(s zero