Queueing Analysis: Discrete-time systems
Queueing models have been used very effectively for the performance evaluation of many computer and communication systems. This third volume of Queueing Analysis follows Volume 1: Vacation and Priority Systems , which considers M/G/1, M/G/1 with vacations and priority queues and Volume 2: Finite Systems , which analyzes M/G/1/N and M/G/1/K. It is devoted to discrete-time queueing systems which are finding new applications in emerging high-speed communication networks. It covers single-server systems with an independent batch arrival process and a general service time distribution, and with features such as the server vacation, priority scheduling, finite population, and finite capacity. Ambiguities related to the timings of events in the discrete-time setting are fully clarified. Many existing results have been arranged systematically with references and combined with new results in uniform notation. The volume includes a comprehensive bibliography on performance evaluation of computers and communication networks. In accordance with Volumes 1 and 2 of Queueing Analysis , this publication will be of specific 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.
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agrees analysis arbitrary message arbitrary slot boundary assume beginning boundary is given busy period busy period process called consider consists continuous-time corresponding defined delay cycle denotes derive determine elapsed service exhaustive service express FCFS system function Hence identical idle period initial condition joint distribution joint PGF LCFS length mean mean waiting measured in slots messages arrive messages that arrive Note nth slot number of messages observed obtain PGF W(u Po(w probability queue size immediately relation remaining service respectively response served server service completion service cycle service facility service period service system service time immediately set of equations setup single Sk SK Sk SK-1 Sk SN started steady-state Substituting supermessage system immediately system is given unfinished vacation period Volume WA(z waiting yields zero Σ Σ