Browsing by Subject "Matrix geometric distribution"

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    Fitting matrix geometric distributions by model reduction
    (Taylor and Francis Inc., 2015) Akar, N.
    A novel algorithmic method is proposed to fit matrix geometric distributions of desired order to empirical data or arbitrary discrete distributions. The proposed method effectively combines two existing approaches from two different disciplines: well-established model reduction methods used in system theory and moment matching methods of applied probability that employ second-order discrete phase-type distributions. The proposed approach is validated with exhaustive numerical examples including well-known statistical data. Copyright
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    A matrix analytical method for the discrete time Lindley equation using the generalized Schur decomposition
    (ACM, 2006) Akar, Nail
    In this paper, we study the discrete time Lindley equation governing an infinite size GI/GI/1 queue. In this queuing system, the arrivals and services are independent and identically distributed but they obey a discrete time matrix geometric distribution not necessarily with finite support. Our GI/GI/1 model allows geometric batch arrivals and also treats late, early, and hybrid arrival models in a unified manner. We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair (E, A) where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach taken in this paper is purely matrix analytical and we obtain a matrix geometric representation for the related quantities (queue lengths or waiting times) for the discrete time GI/GI/1 queue using this approach.