Introduction to Matrix Analytic Methods in Stochastic ModelingMatrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included. |
Contents
SA05_ch1 | 3 |
SA05_ch2 | 33 |
SA05_ch3 | 61 |
SA05_ch4 | 83 |
SA05_ch5 | 107 |
SA05_ch6 | 129 |
SA05_ch7 | 147 |
SA05_ch8 | 165 |
SA05_ch10 | 221 |
SA05_ch11 | 239 |
SA05_ch12 | 259 |
SA05_ch13 | 267 |
SA05_ch14 | 281 |
SA05_ch15 | 295 |
SA05_ch16 | 305 |
SA05_backmatter | 313 |
Other editions - View all
Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche,V. Ramaswami Limited preview - 1999 |
Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche,V. Ramaswami No preview available - 1987 |
Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche,V. Ramaswami No preview available - 1999 |
Common terms and phrases
A₁ algorithm argument assume birth-and-death process blocks Chapter column compute condition consider converges define denote density diagonal eigenvalue epochs equal equation Erlang distribution expected number expected sojourn exponentially distributed finite follows function given homogeneous infinite infinitesimal interval iterations Jackson network Laplace-Stieltjes transform Latouche Lemma level l(0 linear M/M/1 queue Markov chain Markov process Markov property Markovian point process matrix G matrix-geometric n₁ node number of customers number of visits obtain parameter passage probabilities PH renewal process phase Poisson process positive recurrent probabilistic probabilities recorded Proof prove QBD is irreducible QBD is positive QBD is recurrent Ramaswami random variables records the expected records the probability sequence server service rate sp(R starting stationary distribution stationary probability vector stochastic matrix subset substochastic taboo Theorem tion traffic coefficient transient transition matrix transition probabilities visit to l(n λ λ λι μι πη πο Χο Рмм