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A Recurrent Solution of Ph/M/c/N-like and Ph/M/c-like Queues

Abstract : We propose an efficient semi-numerical approach to compute the steady-state proba- bility distribution for the number of requests at arbitrary and at arrival time instants in Ph/M/c- like systems in which in the inter-arrival time distribution is represented by an acyclic set of memoryless phases. Our method is based on conditional probabilities and results in a simple computationally stable recurrence. It avoids the explicit manipulation of potentially large ma- trices and involves no iteration. Due to the use of conditional probabilities, it delays the onset of numerical issues related to floating-point underflow as the number of servers and/or phases increases. For generalized Coxian distributions, the computational complexity of the proposed approach grows linearly with the number of phases in the distribution.
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https://hal.inria.fr/inria-00492748
Contributor : Thomas Begin <>
Submitted on : Wednesday, June 16, 2010 - 6:04:40 PM
Last modification on : Friday, June 25, 2021 - 3:40:05 PM
Long-term archiving on: : Friday, September 17, 2010 - 1:56:57 PM

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Alexandre Brandwajn, Thomas Begin. A Recurrent Solution of Ph/M/c/N-like and Ph/M/c-like Queues. [Research Report] RR-7321, INRIA. 2010, pp.16. ⟨inria-00492748⟩

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