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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16 230 Exercise 6
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1st slot arbitrary message arbitrary slot boundary boundary is given busy period process busy period started defined delay cycle denotes the number discrete-time early arrival model elapsed service exhaustive service system FCFS system FDMA Geo^/G/l system Hence idle period initial condition joint distribution joint PGF Kronecker's delta late arrival model LCFS least one message length Markov chain mean waiting measured in slots message of class messages arrive messages present messages that arrive multiple vacation model Note number of messages obtain the PGF packet model period is given PGF P(z PGF W(u priority queues Prob[L probability queue size immediately recurrence relation remaining service ROS system semi-Markov process service completion service cycle service period service time immediately set of equations steady-state Substituting supermessage of class system immediately system is empty system is given system with multiple system without vacations TDMA th slot time-dependent process vacation period wA(z