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Whittle's index policy for a multi-class queueing system with convex holding costs

Author

Listed:
  • P. S. Ansell
  • K. D. Glazebrook
  • J. Niño-Mora
  • M. O'Keeffe

Abstract

Multi-class service systems are of increasing importance in the practical modelling world but present a significant challenge for analysis. Most results to date concerning the optimal dynamic control of such systems have assumed holding cost rates to be linear in the number of customers present. In response to arguments that such an assumption is often inappropriate, we develop an index heuristic for a multi-class M/M/1 system with increasing convex holding cost rates. We use a prescription of Whittle to develop the required indices. A numerical study elucidates very strong performance of the index policy. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • P. S. Ansell & K. D. Glazebrook & J. Niño-Mora & M. O'Keeffe, 2003. "Whittle's index policy for a multi-class queueing system with convex holding costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 21-39, April.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:1:p:21-39
    DOI: 10.1007/s001860200257
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. T. W. Archibald & D. P. Black & K. D. Glazebrook, 2009. "Indexability and Index Heuristics for a Simple Class of Inventory Routing Problems," Operations Research, INFORMS, vol. 57(2), pages 314-326, April.
    4. K.D. Glazebrook & C. Kirkbride, 2004. "Index policies for the routing of background jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 856-872, September.
    5. Urtzi Ayesta & Manu K. Gupta & Ina Maria Verloop, 2021. "On the computation of Whittle’s index for Markovian restless bandits," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 179-208, February.
    6. Samuli Aalto & Ziv Scully, 2023. "Minimizing the mean slowdown in the M/G/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 187-210, August.
    7. S. Duran & U. Ayesta & I. M. Verloop, 2022. "On the Whittle index of Markov modulated restless bandits," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 373-430, December.
    8. L Ding & K D Glazebrook, 2005. "A static allocation model for the outsourcing of warranty repairs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 825-835, July.
    9. Nicolas Gast & Bruno Gaujal & Chen Yan, 2023. "Exponential asymptotic optimality of Whittle index policy," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 107-150, June.
    10. Sarang Deo & Seyed Iravani & Tingting Jiang & Karen Smilowitz & Stephen Samuelson, 2013. "Improving Health Outcomes Through Better Capacity Allocation in a Community-Based Chronic Care Model," Operations Research, INFORMS, vol. 61(6), pages 1277-1294, December.
    11. K. D. Glazebrook & R. Minty, 2009. "A Generalized Gittins Index for a Class of Multiarmed Bandits with General Resource Requirements," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 26-44, February.
    12. Ece Zeliha Demirci & Joachim Arts & Geert-Jan Van Houtum, 2022. "A restless bandit approach for capacitated condition based maintenance scheduling," DEM Discussion Paper Series 22-01, Department of Economics at the University of Luxembourg.
    13. Michelle Opp & Kevin Glazebrook & Vidyadhar G. Kulkarni, 2005. "Outsourcing warranty repairs: Dynamic allocation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 381-398, August.
    14. Nicolas Gast & Bruno Gaujal & Kimang Khun, 2023. "Testing indexability and computing Whittle and Gittins index in subcubic time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 391-436, June.
    15. José Niño-Mora, 2023. "Markovian Restless Bandits and Index Policies: A Review," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    16. 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.
    17. José Niño-Mora, 2020. "A Verification Theorem for Threshold-Indexability of Real-State Discounted Restless Bandits," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 465-496, May.

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