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Utility-Maximizing Resource Control: Diffusion Limit and Asymptotic Optimality for a Two-Bottleneck Model

Author

Listed:
  • Heng-Qing Ye

    (Department of Logistics and Maritime Studies, Hong Kong Polytechnic University, Hong Kong)

  • David D. Yao

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We study a stochastic network that consists of two servers shared by two classes of jobs. Class 1 jobs require a concurrent occupancy of both servers while class 2 jobs use only one server. The traffic intensity is such that both servers are bottlenecks, meaning the service capacity is equal to the offered workload. The real-time allocation of the service capacity among the job classes takes the form of a solution to an optimization problem that maximizes a utility function. We derive the diffusion limit of the network and establish its asymptotic optimality. In particular, we identify a cost objective associated with the utility function and show that it is minimized at the diffusion limit by the utility-maximizing allocation within a broad class of “fair” allocation schemes. The model also highlights the key issues involved in multiple bottlenecks.

Suggested Citation

  • Heng-Qing Ye & David D. Yao, 2010. "Utility-Maximizing Resource Control: Diffusion Limit and Asymptotic Optimality for a Two-Bottleneck Model," Operations Research, INFORMS, vol. 58(3), pages 613-623, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:613-623
    DOI: 10.1287/opre.1090.0758
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    References listed on IDEAS

    as
    1. Heng-Qing Ye & Jihong Ou & Xue-Ming Yuan, 2005. "Stability of Data Networks: Stationary and Bursty Models," Operations Research, INFORMS, vol. 53(1), pages 107-125, February.
    2. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    3. Heng-Qing Ye & David D. Yao, 2008. "Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation," Operations Research, INFORMS, vol. 56(2), pages 453-470, April.
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    Cited by:

    1. Josh Reed & Bert Zwart, 2014. "Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints," Operations Research, INFORMS, vol. 62(6), pages 1453-1466, December.
    2. Xiaowei Mei & Hsing Kenneth Cheng & Subhajyoti Bandyopadhyay & Liangfei Qiu & Lai Wei, 2022. "Sponsored Data: Smarter Data Pricing with Incomplete Information," Information Systems Research, INFORMS, vol. 33(1), pages 362-382, March.
    3. Heng-Qing Ye & David D. Yao, 2012. "A Stochastic Network Under Proportional Fair Resource Control---Diffusion Limit with Multiple Bottlenecks," Operations Research, INFORMS, vol. 60(3), pages 716-738, June.
    4. Maria Remerova & Josh Reed & Bert Zwart, 2014. "Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 746-774, August.

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