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Characterization and Optimization of Achievable Performance in General Queueing Systems

Author

Listed:
  • A. Federgruen

    (Columbia University, New York, New York)

  • H. Groenevelt

    (University of Rochester, Rochester, New York)

Abstract

This paper considers general (single facility) queueing systems with exponential service times, dealing with a finite number J of distinct customer classes. Performance of the system, as measured by the vector of steady state expected sojourn times of the customer classes (the performance vector ) may be controlled by adopting an appropriate preemptive priority discipline. We show that the performance space, the set of performance vectors which are achievable under some preemptive work conserving rule, is a polyhedron described by 2 J − 1 (in)equalities. The special structure of this polyhedron nevertheless allows for efficient procedures to minimize any separable convex function of the performance vector. Linear objectives are shown to be minimized by absolute priority rules, thus generalizing a well known result for M/M/1 systems. We also show that each point in the performance space may be achieved by a specific randomization of at most J + 1 absolute priority rules.

Suggested Citation

  • A. Federgruen & H. Groenevelt, 1988. "Characterization and Optimization of Achievable Performance in General Queueing Systems," Operations Research, INFORMS, vol. 36(5), pages 733-741, October.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:5:p:733-741
    DOI: 10.1287/opre.36.5.733
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    Cited by:

    1. Hellerstein, Lisa & Lidbetter, Thomas, 2023. "A game theoretic approach to a problem in polymatroid maximization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 979-988.
    2. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    3. Dimitris Bertsimas & José Niño-Mora, 2000. "Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic," Operations Research, INFORMS, vol. 48(1), pages 80-90, February.
    4. José Niño-Mora, 2000. "On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices," Economics Working Papers 456, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
    6. Santiago R. Balseiro & Ozan Candogan, 2017. "Optimal Contracts for Intermediaries in Online Advertising," Operations Research, INFORMS, vol. 65(4), pages 878-896, August.
    7. Kevin D. Glazebrook & José Niño-Mora, 2001. "Parallel Scheduling of Multiclass M/M/m Queues: Approximate and Heavy-Traffic Optimization of Achievable Performance," Operations Research, INFORMS, vol. 49(4), pages 609-623, August.
    8. Philipp Afèche, 2013. "Incentive-Compatible Revenue Management in Queueing Systems: Optimal Strategic Delay," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 423-443, July.
    9. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    10. Pavlin, J. Michael, 2017. "Dual bounds of a service level assignment problem with applications to efficient pricing," European Journal of Operational Research, Elsevier, vol. 262(1), pages 239-250.
    11. Tianhu Deng & Ying‐Ju Chen & Zuo‐Jun Max Shen, 2015. "Optimal pricing and scheduling control of product shipping," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 215-227, April.
    12. Bertsimas, Dimitris. & Niño-Mora, Jose., 1994. "Restless bandit, linear programming relaxations and a primal-dual heuristic," Working papers 3727-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case," Economics Working Papers 302, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998.
    14. Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    15. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    16. Dimitris Bertsimas & José Niño-Mora, 1994. "Restless bandits, linear programming relaxations and a primal-dual index heuristic," Economics Working Papers 301, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 1997.
    17. Dimitris Bertsimas & Velibor V. Mišić, 2016. "Decomposable Markov Decision Processes: A Fluid Optimization Approach," Operations Research, INFORMS, vol. 64(6), pages 1537-1555, December.
    18. Baris Ata & Yichuan Ding & Stefanos Zenios, 2021. "An Achievable-Region-Based Approach for Kidney Allocation Policy Design with Endogenous Patient Choice," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 36-54, 1-2.
    19. Hassin, Refael & Puerto, Justo & Fernández, Francisco R., 2009. "The use of relative priorities in optimizing the performance of a queueing system," European Journal of Operational Research, Elsevier, vol. 193(2), pages 476-483, March.
    20. Xiangqian Xu & Zhexuan Zhou & Yajie Dou & Yuejin Tan & Tianjun Liao, 2018. "Sustainable Queuing-Network Design for Airport Security Based on the Monte Carlo Method," Sustainability, MDPI, vol. 10(2), pages 1-19, January.
    21. Gad Allon & Awi Federgruen, 2009. "Competition in Service Industries with Segmented Markets," Management Science, INFORMS, vol. 55(4), pages 619-634, April.
    22. Gad Allon & Eran Hanany, 2012. "Cutting in Line: Social Norms in Queues," Management Science, INFORMS, vol. 58(3), pages 493-506, March.

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