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A method of approximate analysis of an open exponential queuing network with losses due to finite shared buffers in multi-queue nodes

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  • Vinarskiy, Miron

Abstract

We consider a model of an open exponential queuing network where each node comprises several multi-class MR/M/1 queues that share a common waiting space (a buffer) of limited capacity. A customer arriving to a node with fully occupied buffer is lost. An assumption is made that each class input traffic to a node, which is a superposition of the class external Poisson flow and the class flows coming from other nodes, is a Poisson process. Under this assumption a method of an approximate analysis is presented. It is based on solving iteratively a system of non-linear equations for the unknown nodal flow rates. It is shown that the gradient iterations solve the multi-class network equations. For the single-class model we use the direct substitution iterations. In the latter case existence and uniqueness of the solution, obtained by the iterative algorithm, is rigorously proven. It is demonstrated for a few network configurations that the network and node performance characteristics received by analytic approach are close to those obtained by simulation method. Our contribution is a performance evaluation methodology that could be usefully employed in queuing network design.

Suggested Citation

  • Vinarskiy, Miron, 2017. "A method of approximate analysis of an open exponential queuing network with losses due to finite shared buffers in multi-queue nodes," European Journal of Operational Research, Elsevier, vol. 258(1), pages 207-215.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:207-215
    DOI: 10.1016/j.ejor.2016.09.031
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    References listed on IDEAS

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    1. Shi, Leyuan, 1995. "Approximate analysis for queueing networks with finite capacity and customer loss," European Journal of Operational Research, Elsevier, vol. 85(1), pages 178-191, August.
    2. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    3. Sunkyo Kim, 2011. "Modeling Cross Correlation in Three-Moment Four-Parameter Decomposition Approximation of Queueing Networks," Operations Research, INFORMS, vol. 59(2), pages 480-497, April.
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