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      A matrix analytical method for the discrete time Lindley equation using the generalized Schur decomposition

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      Author
      Akar, N.
      Date
      2006
      Journal Title
      SMCtools'06: Proceeding from the 2006 Workshop on Tools for Solving Structured Markov Chains
      Volume
      201
      Language
      English
      Type
      Conference Paper
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      Please cite this item using this persistent URL
      http://hdl.handle.net/11693/27167
      Abstract
      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. Copyright 2006 ACM.
      Published as
      http://dx.doi.org/10.1145/1190366.1190377
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