## 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. |

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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 - 1999 |

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algorithm Ao(I argument assume birth-and-death process blocks Chapter columns compute condition consider converges define denote density diagonal eigenvalue epochs equal equation Erlang distribution expected number expected sojourn exponentially distributed finite follows function geometric distribution given homogeneous infinite infinitesimal interval iterations Jackson network Jordan normal form Latouche Lemma linear M/M/1 queue Markov chain Markov process Markov property Markovian point process matrix G node number of customers number of visits obtain parameter passage probabilities PH renewal process phase phase-type 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 Stochastic Models subset substochastic taboo Theorem tion transient transition matrix transition probabilities