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Infinite horizon asymptotic average optimality for large-scale parallel server networks

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  • Arapostathis, Ari
  • Pang, Guodong

Abstract

We study infinite-horizon asymptotic average optimality for parallel server networks with multiple classes of jobs and multiple server pools in the Halfin–Whitt regime. Three control formulations are considered: (1) minimizing the queueing and idleness cost, (2) minimizing the queueing cost under constraints on idleness at each server pool, and (3) fairly allocating the idle servers among different server pools. For the third problem, we consider a class of bounded-queue, bounded-state (BQBS) stable networks, in which any moment of the state is bounded by that of the queue only (for both the limiting diffusion and diffusion-scaled state processes). We show that the optimal values for the diffusion-scaled state processes converge to the corresponding values of the ergodic control problems for the limiting diffusion. We present a family of state-dependent Markov balanced saturation policies (BSPs) that stabilize the controlled diffusion-scaled state processes. It is shown that under these policies, the diffusion-scaled state process is exponentially ergodic, provided that at least one class of jobs has a positive abandonment rate. We also establish useful moment bounds, and study the ergodic properties of the diffusion-scaled state processes, which play a crucial role in proving the asymptotic optimality.

Suggested Citation

  • Arapostathis, Ari & Pang, Guodong, 2019. "Infinite horizon asymptotic average optimality for large-scale parallel server networks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 283-322.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:1:p:283-322
    DOI: 10.1016/j.spa.2018.03.005
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    References listed on IDEAS

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    1. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Itay Gurvich & Ward Whitt, 2009. "Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 237-253, June.
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    Cited by:

    1. Arapostathis, Ari & Pang, Guodong & Zheng, Yi, 2020. "Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6733-6756.
    2. Ari Arapostathis & Hassan Hmedi & Guodong Pang, 2021. "On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 772-796, May.
    3. Hassan Hmedi & Ari Arapostathis & Guodong Pang, 2022. "Uniform stability of some large-scale parallel server networks," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 509-552, December.
    4. Silviya Valeva & Guodong Pang & Andrew J. Schaefer & Gilles Clermont, 2023. "Acuity-Based Allocation of ICU-Downstream Beds with Flexible Staffing," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 403-422, March.

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