IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v258y2017i1p207-215.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716307834
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.09.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Shih-Pin, 2004. "Parametric nonlinear programming for analyzing fuzzy queues with finite capacity," European Journal of Operational Research, Elsevier, vol. 157(2), pages 429-438, September.
    2. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    3. Mohammadi Bidhandi, Hadi & Patrick, Jonathan & Noghani, Pedram & Varshoei, Peyman, 2019. "Capacity planning for a network of community health services," European Journal of Operational Research, Elsevier, vol. 275(1), pages 266-279.
    4. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    5. Sagron, Ruth & Pugatch, Rami, 2021. "Universal distribution of batch completion times and time-cost tradeoff in a production line with arbitrary buffer size," European Journal of Operational Research, Elsevier, vol. 293(3), pages 980-989.
    6. Nha-Nghi Cruz & Hans Daduna, 2019. "Optimal capacity allocation in a production–inventory system with base stock," Annals of Operations Research, Springer, vol. 277(2), pages 329-344, June.
    7. Osorio, Carolina & Nanduri, Kanchana, 2015. "Urban transportation emissions mitigation: Coupling high-resolution vehicular emissions and traffic models for traffic signal optimization," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 520-538.
    8. Xuanzhu Fan & Jiafu Tang & Chongjun Yan, 2020. "Appointment scheduling optimization with two stages diagnosis for clinic outpatient," Computational Statistics, Springer, vol. 35(2), pages 469-490, June.
    9. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
    10. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    11. de Palma, André & Fosgerau, Mogens, 2013. "Random queues and risk averse users," European Journal of Operational Research, Elsevier, vol. 230(2), pages 313-320.
    12. Cruz, F.R.B. & Van Woensel, T. & Smith, J. MacGregor, 2010. "Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach," International Journal of Production Economics, Elsevier, vol. 125(2), pages 224-234, June.
    13. Chen, Jung-Tai, 2008. "Queueing models of certain manufacturing cells under product-mix sequencing rules," European Journal of Operational Research, Elsevier, vol. 188(3), pages 826-837, August.
    14. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović & Izack Cohen, 2020. "Bed Blocking in Hospitals Due to Scarce Capacity in Geriatric Institutions—Cost Minimization via Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 396-411, March.
    15. Carolina Osorio & Jana Yamani, 2017. "Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks," Transportation Science, INFORMS, vol. 51(3), pages 823-840, August.
    16. Conlon, Thomas & Cotter, John & Gençay, Ramazan, 2018. "Long-run wavelet-based correlation for financial time series," European Journal of Operational Research, Elsevier, vol. 271(2), pages 676-696.
    17. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    18. J. P. van der Gaast & M. B. M. de Koster & I. J. B. F. Adan, 2018. "Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model," Service Science, INFORMS, vol. 52(6), pages 1428-1443, December.
    19. Carolina Osorio & Kanchana Nanduri, 2015. "Energy-Efficient Urban Traffic Management: A Microscopic Simulation-Based Approach," Transportation Science, INFORMS, vol. 49(3), pages 637-651, August.
    20. Palmer, Geraint I. & Harper, Paul R. & Knight, Vincent A., 2018. "Modelling deadlock in open restricted queueing networks," European Journal of Operational Research, Elsevier, vol. 266(2), pages 609-621.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:207-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.