Queueing Systems, Volume I, Volume 1Queueing 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. |
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Page 61
Leonard Kleinrock. said to constitute a Poisson process . Let us study the Poisson process more carefully and show its relationship to the exponential distribution . The Poisson process is central to much of elementary and intermediate ...
Leonard Kleinrock. said to constitute a Poisson process . Let us study the Poisson process more carefully and show its relationship to the exponential distribution . The Poisson process is central to much of elementary and intermediate ...
Page 65
... Poisson process , then the joint distribution of the instants when these arrivals occurred is the same as the distribution of k points uniformly distributed over the same interval . Furthermore , it is easy to show from the properties ...
... Poisson process , then the joint distribution of the instants when these arrivals occurred is the same as the distribution of k points uniformly distributed over the same interval . Furthermore , it is easy to show from the properties ...
Page 149
... Poisson process driving an exponential server generates a Poisson process for de- partures . This startling result is usually referred to as Burke's theorem [ BURK 56 ] ; a number of others also studied the problem ( see , for example ...
... Poisson process driving an exponential server generates a Poisson process for de- partures . This startling result is usually referred to as Burke's theorem [ BURK 56 ] ; a number of others also studied the problem ( see , for example ...
Contents
PRELIMINARIES | 1 |
Distribution of Attained Service | 2 |
The Batch Processing Algorithm | 3 |
Copyright | |
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arrival occurs arriving customer assume average number behavior birth birth-death process busy period C₁ calculate Chapman-Kolmogorov equation Chapter coefficients condition consider continuous-time Markov chain customers arrive define definition denote density function departure equal equilibrium probability ergodic Erlangian example exponentially distributed expression finite flow Fx(x given in Eq gives hippie imbedded Markov chain independent instants interarrival interval invert k₁ Laplace transform last equation limit 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 population probability vector queueing system queueing theory random process random variables random walk reader referred result semi-Markov processes sequence server service facility service-time shown in Figure solution solve state-transition-rate diagram stochastic processes sub-busy period theorem transition probabilities waiting X₁ z-transform zero