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Almost optimal policies for stochastic systemswhich almost satisfy conservation laws

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  • K.D. Glazebrook
  • R. Garbe

Abstract

When controlled stochastic systems have performances which satisfy generalisedconservation laws (GCL), an objective which is linear in the performance is optimised by aGittins index policy. We develop measures of the extent to which a system fails to satisfyGCL and derive suboptimality bounds for suitable index policies in terms of such measures.These bounds are used, inter alia, to explore the robustness in performance of cm‐typerules for a multiclass G/G/1 queueing system to departures from an assumption of exponentialservice times. We also study Gittins index policies for parallel processor versions of theclassical undiscounted and discounted multi‐armed bandit problems. In the undiscountedcase, the cost of an index policy comes within a constant of the optimal cost ‐ thisconstant being independent of the number of projects submitted for scheduling. In thediscounted case, under fairly mild conditions, Gittins index policies come within an O(1) quantity ofoptimality and are hence average reward optimal when the discount rate is small enough. Copyright Kluwer Academic Publishers 1999

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  • K.D. Glazebrook & R. Garbe, 1999. "Almost optimal policies for stochastic systemswhich almost satisfy conservation laws," Annals of Operations Research, Springer, vol. 92(0), pages 19-43, January.
    • Handle: RePEc:spr:annopr:v:92:y:1999:i:0:p:19-43:10.1023/a:1018934714800
    DOI: 10.1023/A:1018934714800
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    Cited by:

    1. 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.
    2. 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.
    3. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    4. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.

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