IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v9y2007i3d10.1007_s11009-007-9032-8.html
   My bibliography  Save this article

Stability Criteria for Multi-class Queueing Networks with Re-entrant Lines

Author

Listed:
  • I. M. MacPhee

    (Durham University)

  • L. J. Müller

    (Institut für Kreislaufwirtschaft)

Abstract

In this paper we show how the stability criteria for the model proposed in MacPhee and Müller (Queueing Syst 52(3):215–229, 2006) can be applied to queueing networks with re-entrant lines. The model considered has Poisson arrival streams, servers that can be configured in various ways, exponential service times and Markov feedback of completed jobs. The stability criteria are expressed in terms of the mean drifts of the process under the various server configurations. For models with re-entrant lines we impose here a boundary sojourn condition to ensure adequate control of the process when one or more queues are empty. We show with some examples, including the generalised Lu–Kumar network discussed in Niño-Mora and Glazebrook (J Appl Probab 37(3):890–899, 2000), how our results can be applied.

Suggested Citation

  • I. M. MacPhee & L. J. Müller, 2007. "Stability Criteria for Multi-class Queueing Networks with Re-entrant Lines," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 377-388, September.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9032-8
    DOI: 10.1007/s11009-007-9032-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-007-9032-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-007-9032-8?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. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    2. Kevin D. Glazebrook & José Niño-Mora, 1997. "Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network," Economics Working Papers 429, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2000.
    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. Allahviranloo, Mahdieh & Recker, Will, 2013. "Daily activity pattern recognition by using support vector machines with multiple classes," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 16-43.
    2. Alexander Zadorojniy & Guy Even & Adam Shwartz, 2009. "A Strongly Polynomial Algorithm for Controlled Queues," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 992-1007, November.
    3. Xiuli Chao & Frank Y. Chen, 2005. "An Optimal Production and Shutdown Strategy when a Supplier Offers an Incentive Program," Manufacturing & Service Operations Management, INFORMS, vol. 7(2), pages 130-143, March.
    4. Dwi Ertiningsih & Sandjai Bhulai & Flora Spieksma, 2018. "A novel use of value iteration for deriving bounds for threshold and switching curve optimal policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 638-659, December.
    5. Hui Zhao & Vinayak Deshpande & Jennifer K. Ryan, 2006. "Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 547-567, September.
    6. Waal, P.R. & Dijk, N.M. van, 1988. "Monotonicity of performance measures in a processor sharing queue," Serie Research Memoranda 0051, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. Nicole Leder & Bernd Heidergott & Arie Hordijk, 2010. "An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory," Operations Research, INFORMS, vol. 58(4-part-1), pages 918-932, August.
    8. Sobel, Matthew J. & Szmerekovsky, Joseph G. & Tilson, Vera, 2009. "Scheduling projects with stochastic activity duration to maximize expected net present value," European Journal of Operational Research, Elsevier, vol. 198(3), pages 697-705, November.
    9. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    10. Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos, 2005. "Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 97-118, March.
    11. Rob Shone & Vincent A. Knight & Paul R. Harper, 2020. "A conservative index heuristic for routing problems with multiple heterogeneous service facilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 511-543, December.
    12. Dinard van der Laan, 2015. "Assigning Multiple Job Types to Parallel Specialized Servers," Tinbergen Institute Discussion Papers 15-102/III, Tinbergen Institute.
    13. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
    14. Economou, Antonis, 2003. "On the control of a compound immigration process through total catastrophes," European Journal of Operational Research, Elsevier, vol. 147(3), pages 522-529, June.
    15. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    16. Ping Cao & Jingui Xie, 2016. "Optimal control of a multiclass queueing system when customers can change types," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 285-313, April.
    17. Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    18. Alexey Piunovskiy & Yi Zhang, 2012. "The Transformation Method for Continuous-Time Markov Decision Processes," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 691-712, August.
    19. Guy Even & Alexander Zadorojniy, 2012. "Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks," Annals of Operations Research, Springer, vol. 201(1), pages 159-167, December.
    20. Peter Buchholz & Dimitri Scheftelowitsch, 2019. "Computation of weighted sums of rewards for concurrent MDPs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 1-42, February.

    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:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9032-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.