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Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation

Author

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  • Heng-Qing Ye

    (Department of Logistics, Faculty of Business, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, and School of Business, National University of Singapore, Singapore)

  • 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 a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job classes in a head-of-the-line processor-sharing mechanism. The allocation of the service capacities is a real-time control mechanism: in each network state, the resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation optimizes in a “greedy” fashion with respect to each state, we establish its asymptotic optimality in terms of (a) deriving the fluid and diffusion limits of the network under this allocation scheme, and (b) identifying a cost function that is minimized in the diffusion limit, along with a characterization of the so-called fixed-point state of the network.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:2:p:453-470
    DOI: 10.1287/opre.1070.0455
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    References listed on IDEAS

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    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. Alexander L. Stolyar, 2005. "On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation," Operations Research, INFORMS, vol. 53(1), pages 12-25, February.
    4. Hong Chen & Hanqin Zhang, 2000. "Stability of Multiclass Queueing Networks Under Priority Service Disciplines," Operations Research, INFORMS, vol. 48(1), pages 26-37, February.
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    Cited by:

    1. 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.
    2. 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.
    3. Hong Chen & Heng-Qing Ye, 2012. "Asymptotic Optimality of Balanced Routing," Operations Research, INFORMS, vol. 60(1), pages 163-179, February.
    4. Wanyang Dai, 2013. "Optimal Rate Scheduling via Utility-Maximization for J -User MIMO Markov Fading Wireless Channels with Cooperation," Operations Research, INFORMS, vol. 61(6), pages 1450-1462, December.
    5. 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.
    6. 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.
    7. Heng-Qing Ye & David D. Yao, 2016. "Diffusion Limit of Fair Resource Control—Stationarity and Interchange of Limits," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1161-1207, November.

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