Matrix-geometric Solutions in Stochastic Models: An Algorithmic ApproachTopics include matrix-geometric invariant vectors, buffer models, queues in a random environment and more. |
Contents
MatrixGeometric Invariant Vectors | 1 |
Probability Distributions of Phase Type | 41 |
QuasiBirthandDeath Processes | 81 |
Copyright | |
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Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach Marcel F. Neuts Limited preview - 1994 |
Common terms and phrases
A₁ A₂ algorithmic am+1 arrival process arrival rate B₁ behavior blocks buffer busy period clearly column computation conditional probability consider corresponding defined denote density diagonal differential equations eigenvalue elements embedded Markov chain Erlang distributions evaluate example exponential servers finite follows formula GI/PH/1 queue given interarrival invariant probability vector invariant vector irreducible iterative J₁ K₁ Laplace-Stieltjes transform left eigenvector left transitions Lemma M. F. Neuts m₁ Markov chain Markov process Markov renewal process matrix Q minimal nonnegative solution nonnegative matrix nonsingular number of customers obtained parameters partitioned PH-distribution phase type Poisson Poisson process positive recurrent probability distributions process Q Proof QBD process queueing models queueing theory random readily representation satisfies service rate service time distribution spectral radius stationary probability vector stochastic matrix stochastic models structure T₁ theorem transition probability matrix Unit values waiting time distributions zero λι μ₁ μι Σ Σ