Introduction to Matrix Analytic Methods in Stochastic Modeling
Matrix 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.
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Contents
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SA05_ch1
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3 |
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SA05_ch2
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33 |
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SA05_ch3
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61 |
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SA05_ch4
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83 |
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SA05_ch5
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107 |
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SA05_ch6
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129 |
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SA05_ch7
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147 |
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SA05_ch8
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165 |
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SA05_ch10
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221 |
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SA05_ch11
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239 |
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SA05_ch12
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259 |
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SA05_ch13
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267 |
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SA05_ch14
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281 |
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SA05_ch15
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295 |
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SA05_ch16
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305 |
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SA05_backmatter
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313 |
Other editions - View all
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Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche,V. Ramaswami Limited preview - 1999 |
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Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche,V. Ramaswami No preview available - 1999 |
Common terms and phrases
algorithm apply argument arrival assume blocks called Chapter clearly columns completes compute condition consider continuous converges corresponding customers define denote density determine discrete discussed distribution eigenvalue epochs equal equation event example exists expected Figure finite follows function give given holds homogeneous immediately independent infinite initial interest interval irreducible iterations Latouche Lemma linear Markov chain Markov process methods Models moves Neuts node nonnegative number of visits observe obtain occur passage PH distributions phase Poisson positive recurrent present probability Proof prove queue Ramaswami random reach records remains Remark renewal renewal process representation respectively restricted satisfy sequence server similar simple sojourn solution solve space spent starting stationary distribution step stochastic structure subset term Theorem tion transient transition matrix values vector visits write