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. |
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Page 75
Leonard Kleinrock. differential * equation . Use the conservation relationship , Eq . ( 2.122 ) , to eliminate the last unknown term . † 6. Invert the solution to get an explicit solution in terms of k . 7. If step 6 cannot be carried ...
Leonard Kleinrock. differential * equation . Use the conservation relationship , Eq . ( 2.122 ) , to eliminate the last unknown term . † 6. Invert the solution to get an explicit solution in terms of k . 7. If step 6 cannot be carried ...
Page 193
... last as Qn + 1 ( 2 ) . Similarly , we may write the right - hand side of this equation as the expecta- tion of the product of two factors , giving us Qn + 1 ( 2 ) = E [ zn¬A¶n z ° n + 1 ] ( 5.79 ) We now observe , as earlier , that the ...
... last as Qn + 1 ( 2 ) . Similarly , we may write the right - hand side of this equation as the expecta- tion of the product of two factors , giving us Qn + 1 ( 2 ) = E [ zn¬A¶n z ° n + 1 ] ( 5.79 ) We now observe , as earlier , that the ...
Page 307
... last and from Eq . ( 8.102 ) , we obtain immediately W * ( s ) C * ( s ) = a。l * ( −s ) + W * ( s ) — a 。 where as in the past C * ( s ) is the Laplace transform for the density describing the random variable ũ . This last equation ...
... last and from Eq . ( 8.102 ) , we obtain immediately W * ( s ) C * ( s ) = a。l * ( −s ) + W * ( s ) — a 。 where as in the past C * ( s ) is the Laplace transform for the density describing the random variable ũ . This last equation ...
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