Queueing Systems: TheoryQueueing 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 18
... factor . The utilization factor is in a fundamental sense really the ratio R / C , which we introduced in Chapter 1. It is the ratio of the rate at which " work " enters the system to the maximum rate ( capacity ) at which the system ...
... factor . The utilization factor is in a fundamental sense really the ratio R / C , which we introduced in Chapter 1. It is the ratio of the rate at which " work " enters the system to the maximum rate ( capacity ) at which the system ...
Page 38
... factor each time n increases by 1. This shrinkage factor for any Markov process can be shown to be equal to the absolute value of the product of the characteristic values of its transition probability matrix ; in our example we have ...
... factor each time n increases by 1. This shrinkage factor for any Markov process can be shown to be equal to the absolute value of the product of the characteristic values of its transition probability matrix ; in our example we have ...
Page 335
... factor out two powers of z ( we are required to factor out only one power of z in order to bring the numerator degree below that of the denomina- tor , but obviously in this case we may as well factor out both and simplify our ...
... factor out two powers of z ( we are required to factor out only one power of z in order to bring the numerator degree below that of the denomina- tor , but obviously in this case we may as well factor out both and simplify our ...
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 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 linear Markov chain Markov processes Markovian 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 shown in Figure solution solve stages state-transition-rate diagram stochastic processes theorem transition probabilities waiting X₁ z-transform zero