On deviation matrices for birth-death processes (Q5890264)
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scientific article; zbMATH DE number 1625784
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On deviation matrices for birth-death processes |
scientific article; zbMATH DE number 1625784 |
Statements
15 November 2002
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multidimensional queueing systems
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deviation matrices
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birth-death processes
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\(M/M/s/N\)
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\(M/M/s/\infty\)
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On deviation matrices for birth-death processes (English)
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Consider an irreducible, aperiodic, time-homogeneous and positive recurrent Markov chain with \(n\)-step transition probability \(\{p_{ij}^{(n)}\}\) and stationary distribution \(\{\pi_j\}\). Then the deviation matrix is defined by \(D_{ij}= \lim_{\alpha \uparrow 1} \sum_{n=0}^{\infty}(p_{ij}^{(n)}-\pi_j)\alpha^n\). This concept is useful in the control of multidimensional queueing systems. The authors give an algorithm for computing deviation matrices for birth-death processes. As an application, they obtain explicitly for the \(M/M/s/N\) and \(M/M/s/\infty\) queues.
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