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 27
... transition probabilities , then we can uniquely find the probability of being in various states at time n [ see Eqs . ( 2.55 ) and ( 2.56 ) below ] . - If it turns out that the transition probabilities are independent of n , then we ...
... transition probabilities , then we can uniquely find the probability of being in various states at time n [ see Eqs . ( 2.55 ) and ( 2.56 ) below ] . - If it turns out that the transition probabilities are independent of n , then we ...
Page 39
... transition probabilities are independent of time . Among the quantities we were able to calculate was the m - step transition probability pm ) , which gave the probability of passing from state E , to state E , in m steps ; the ...
... transition probabilities are independent of time . Among the quantities we were able to calculate was the m - step transition probability pm ) , which gave the probability of passing from state E , to state E , in m steps ; the ...
Page 178
... transition probabilities describe our Markov chain ; thus we define the one - step transition probabilities L Pij = P [ qn + 1 = j | 9n = i ] ( 5.25 ) - Since these transitions are observed only at departures , it is clear that 9n + 1 ...
... transition probabilities describe our Markov chain ; thus we define the one - step transition probabilities L Pij = P [ qn + 1 = j | 9n = i ] ( 5.25 ) - Since these transitions are observed only at departures , it is clear that 9n + 1 ...
Contents
PRELIMINARIES | 1 |
General Results | 2 |
Markov BirthDeath and Poisson Processes | 3 |
Copyright | |
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arrival occurs arrival rate arriving customer assume average number behavior birth birth-death process busy period C₁ calculate Chapman-Kolmogorov equation Chapter coefficients condition consider constant continuous-time Markov chain convolution customers arrive define definition denote density function derivative equilibrium probability ergodic example exponentially distributed expression factor finite flow Fx(x given in Eq gives hippie independent instants integral interarrival interval inversion Laplace transform last equation limit Markov chain Markov processes Markovian matrix memoryless method node notation number of arrivals number of customers o(At obtain p₁ parameter Poisson arrival Poisson process population probability vector Px(t queueing system queueing theory random process random variables random walk reader referred result semi-Markov processes sequence server service facility shown in Figure solution solve stages state-transition-rate diagram stochastic processes theorem transition probabilities waiting X₁ z-transform zero