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Diffusion parameters of flows in stable multi-class queueing networks

Author

Listed:
  • Sarat Babu Moka

    (Macquarie University)

  • Yoni Nazarathy

    (The University of Queensland)

  • Werner Scheinhardt

    (University of Twente)

Abstract

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

Suggested Citation

  • Sarat Babu Moka & Yoni Nazarathy & Werner Scheinhardt, 2023. "Diffusion parameters of flows in stable multi-class queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 313-346, April.
    • Handle: RePEc:spr:queues:v:103:y:2023:i:3:d:10.1007_s11134-022-09869-1
    DOI: 10.1007/s11134-022-09869-1
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    References listed on IDEAS

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    1. Paul J. Burke, 1956. "The Output of a Queuing System," Operations Research, INFORMS, vol. 4(6), pages 699-704, December.
    2. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    3. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    4. 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.
    5. Hautphenne, Sophie & Kerner, Yoav & Nazarathy, Yoni & Taylor, Peter, 2015. "The intercept term of the asymptotic variance curve for some queueing output processes," European Journal of Operational Research, Elsevier, vol. 242(2), pages 455-464.
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