Queueing systems, Volume 2
Presents and develops methods from queueing theory in mathematical language and in sufficient depth so that the student may apply the methods to many modern engineering problems and conduct creative research. Step-by-step development of results with careful explanation, and lists of important results make it useful as a handbook and a text.
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The FB Scheduling Algorithm
The Multilevel Processor Sharing Scheduling Algorithm
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arriving customer assume average number behavior birth-death process busy period calculate Chapman-Kolmogorov equation Chapter Cn+1 coefficients condition consider convolution customers arrive define definition denote density function departure derive discrete-time equal equilibrium probability ergodic Erlangian example exponentially distributed expression factor finite flow geometric distribution given in Eq gives hippie idle period imbedded Markov chain independent instants integral interarrival interval invert Laplace transform last equation limit M/G/l queue M/M/l system Markov process matrix memoryless method node notation number of arrivals number of customers obtain parameter permit Pk(t Poisson arrivals Poisson process probability vector queueing system queueing theory random variables random walk reader renewal theory 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 vector waiting waiting-time z-transform zero