Queueing Systems, Volume IQueueing systems. Some important random processes. Elementary queueing theory. Birth-death queueing systems in equilibrium. Markovian queues in equilibrium. Intermediate queueing theory. The queue M/G/I. The Queue G/M/m. The method of collective marks. Advanced material. The queue G/G/I. Appendices. Glossary. A queueing theory primer; Bounds, inequalities and approximations. Priority queueing. Computer time-sharing and multiacces systems. Computer-communication networks: analysis and design. Computer-communication networks: measurement, flow control, and ARPANET traps; Glossary. v. 2 . Computer applications - ISBN - 0-471-49111-X. |
Contents
PRELIMINARIES | 1 |
General Results | 2 |
Markov BirthDeath and Poisson Processes | 3 |
Copyright | |
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arrival rate arriving customer assume average number behavior birth-death process busy period calculate Chapman-Kolmogorov equation Chapter coefficients condition consider constant convolution customers arrive define definition denote density function departure derivative discrete-time equal equilibrium probability ergodic Erlangian example exponentially distributed expression factor finite flow given in Eq gives hippie imbedded Markov chain independent instants integral interarrival interval invert k₁ Laplace transform last equation limit linear M/M/1 system Markov chain Markov process matrix memoryless method node notation number of arrivals number of customers o(At obtain P₁ parameter permit Poisson arrival Poisson process probability vector queueing system queueing theory random variables random walk reader referred renewal theory result semi-Markov processes sequence server service facility service-time shown in Figure solution solve state-transition-rate diagram stochastic processes theorem transition probabilities vector waiting X₁ z-transform zero