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Dynamic Scheduling of a Multiclass Queue: Discount Optimality

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  • J. Michael Harrison

    (Stanford University, Stanford, California)

Abstract

We consider a single-server queuing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and we assume a linear cost structure. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (nonpreemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy that is optimal, and a simple algorithm for its computation is presented.

Suggested Citation

  • J. Michael Harrison, 1975. "Dynamic Scheduling of a Multiclass Queue: Discount Optimality," Operations Research, INFORMS, vol. 23(2), pages 270-282, April.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:2:p:270-282
    DOI: 10.1287/opre.23.2.270
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    Cited by:

    1. Huiyin Ouyang & Nilay Taník Argon & Serhan Ziya, 2022. "Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs," Management Science, INFORMS, vol. 68(2), pages 1233-1255, February.
    2. Shen, Zuo-Jun Max & Xie, Jingui & Zheng, Zhichao & Zhou, Han, 2023. "Dynamic scheduling with uncertain job types," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1047-1060.
    3. Zhankun Sun & Nilay Tanık Argon & Serhan Ziya, 2022. "When to Triage in Service Systems with Hidden Customer Class Identities?," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 172-193, January.
    4. José Niño-Mora, 2000. "Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs," Economics Working Papers 514, 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. Haijian Si & Stylianos Kavadias & Christoph Loch, 2022. "Managing innovation portfolios: From project selection to portfolio design," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4572-4588, December.
    7. David B. Brown & Martin B. Haugh, 2017. "Information Relaxation Bounds for Infinite Horizon Markov Decision Processes," Operations Research, INFORMS, vol. 65(5), pages 1355-1379, October.
    8. Zhankun Sun & Nilay Tan?k Argon & Serhan Ziya, 2018. "Patient Triage and Prioritization Under Austere Conditions," Management Science, INFORMS, vol. 64(10), pages 4471-4489, October.
    9. Hyun-Soo Ahn & Mark E. Lewis, 2013. "Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive," Operations Research, INFORMS, vol. 61(2), pages 344-358, April.
    10. Samarghandi, Hamed, 2017. "Studying the impact of merged and divided storage policies on the profitability of a remanufacturing system with deteriorating revenues," International Journal of Production Economics, Elsevier, vol. 193(C), pages 160-171.
    11. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    12. Kyle Y. Lin & Moshe Kress & Roberto Szechtman, 2009. "Scheduling policies for an antiterrorist surveillance system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 113-126, March.

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