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M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance Under Nonpreemptive Priority Rules

Author

Listed:
  • A. Federgruen

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • H. Groenevelt

    (Simon School of Business Administration, University of Rochester, Rochester, New York 14627)

Abstract

This paper considers an M/G/c queueing system serving a finite number (J) of distinct customer classes. Performance of the system, as measured by the vector of steady-state expected waiting times of the customer classes (the performance vector), may be controlled by adopting an appropriate priority discipline. We show that the performance space, the set of performance vectors which are achievable under some nonpreemptive work conserving priority rule, is a polyhedron described by 2 J - 1 inequalities. The special (polymatroidal) structure of this polyhedron, nevertheless, allows for efficient (O(J 2 log J)) procedures to minimize any convex (separable) function of the performance vector. Linear objectives are shown to be minimized by absolute priority rules, thus generalizing a well-known result for M/G/1 systems. We also show that each point in the performance space may be achieved by a unique, generalized dynamic priority rule, specified by J - 1 parameters, which may be determined by the recursive solution of J - 1 single variable quadratic equations. This class of rules contains the absolute priority rules and the (pure) dynamic rules as special cases. Our results are accurate up to one, extremely accurate, approximation and completely exact for M/G/1 and M/M/c systems as well as in heavy traffic.

Suggested Citation

  • A. Federgruen & H. Groenevelt, 1988. "M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance Under Nonpreemptive Priority Rules," Management Science, INFORMS, vol. 34(9), pages 1121-1138, September.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:9:p:1121-1138
    DOI: 10.1287/mnsc.34.9.1121
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    Cited by:

    1. Wenjun Ni & Jia Shu & Miao Song & Dachuan Xu & Kaike Zhang, 2021. "A Branch-and-Price Algorithm for Facility Location with General Facility Cost Functions," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 86-104, January.
    2. Lee, Heeseok, 1995. "Assignment of a job load in a distributed system: A multicriteria design method," European Journal of Operational Research, Elsevier, vol. 87(2), pages 274-283, December.
    3. Vanlerberghe, Jasper & Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2018. "Calculation of the performance region of an easy-to-optimize alternative for Generalized Processor Sharing," European Journal of Operational Research, Elsevier, vol. 270(2), pages 625-635.
    4. Veeraruna Kavitha & Jayakrishnan Nair & Raman Kumar Sinha, 2019. "Pseudo conservation for partially fluid, partially lossy queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 255-292, June.
    5. Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    6. Ryan Palmer & Martin Utley, 2020. "On the modelling and performance measurement of service networks with heterogeneous customers," Annals of Operations Research, Springer, vol. 293(1), pages 237-268, October.
    7. Hayriye Ayhan & Tava Lennon Olsen, 2000. "Scheduling of Multi-Class Single-Server Queues Under Nontraditional Performance Measures," Operations Research, INFORMS, vol. 48(3), pages 482-489, June.
    8. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. 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.
    10. R. Garbe & K. D. Glazebrook, 1998. "Submodular Returns and Greedy Heuristics for Queueing Scheduling Problems," Operations Research, INFORMS, vol. 46(3), pages 336-346, June.
    11. Masselink, Inge H.J. & van der Mijden, Thomas L.C. & Litvak, Nelly & Vanberkel, Peter T., 2012. "Preparation of chemotherapy drugs: Planning policy for reduced waiting times," Omega, Elsevier, vol. 40(2), pages 181-187, April.
    12. Muhammad El-Taha, 2017. "A general workload conservation law with applications to queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 361-381, April.
    13. 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.
    14. 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.
    15. Jing-Sheng Song & Yue Zhang, 2020. "Stock or Print? Impact of 3-D Printing on Spare Parts Logistics," Management Science, INFORMS, vol. 66(9), pages 3860-3878, September.
    16. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.

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