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Asymptotic Optimality of Balanced Routing

Author

Listed:
  • Hong Chen

    (Shanghai Advanced Institute of Finance, Shanghai Jiaotong University, Shanghai, China)

  • Heng-Qing Ye

    (Faculty of Business, Hong Kong Polytechnic University, Hung Hom, Hong Kong)

Abstract

Consider a system with K parallel servers, each with its own waiting room. Upon arrival, a job is routed to the queue of one of the servers. Finding a routing policy that minimizes the total workload in the system is a known difficult problem in general. Even if the optimal policy is identified, the policy would require the full queue length information at the arrival of each job; for example, the join-the-shortest-queue policy (which is known to be optimal for identical servers with exponentially distributed service times) would require comparing the queue lengths of all the servers. In this paper, we consider a balanced routing policy that examines only a subset of c servers, with 1 (le) c (le) K : specifically, upon the arrival of a job, choose a subset of c servers with a probability proportional to their service rates, and then route the job to the one with the shortest queue among the c chosen servers. Under such a balanced policy, we derive the diffusion limits of the queue length processes and the workload processes. We note that the diffusion limits are the same for these processes regardless the choice of c , as long as c (ge) 2. We further show that the proposed balanced routing policy for any fixed c (ge) 2 is asymptotically optimal in the sense that it minimizes the workload over all time in the diffusion limit. In addition, the policy helps to distribute work among all the servers evenly.

Suggested Citation

  • Hong Chen & Heng-Qing Ye, 2012. "Asymptotic Optimality of Balanced Routing," Operations Research, INFORMS, vol. 60(1), pages 163-179, February.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:1:p:163-179
    DOI: 10.1287/opre.1110.0998
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    References listed on IDEAS

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    1. 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.
    2. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    3. Ward Whitt, 1986. "Deciding Which Queue to Join: Some Counterexamples," Operations Research, INFORMS, vol. 34(1), pages 55-62, February.
    4. Bruce Hajek, 1985. "Extremal Splittings of Point Processes," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 543-556, November.
    5. 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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    Citations

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    Cited by:

    1. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner & Alexander Wickeham, 2022. "A general “power-of-d” dispatching framework for heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 431-480, December.
    2. Rami Atar & Isaac Keslassy & Gal Mendelson, 2019. "Replicate to the shortest queues," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 1-23, June.
    3. Jonatha Anselmi & Francois Dufour, 2020. "Power-of- d -Choices with Memory: Fluid Limit and Optimality," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 862-888, August.
    4. Chihoon Lee & Amy R. Ward & Heng-Qing Ye, 2021. "Stationary distribution convergence of the offered waiting processes in heavy traffic under general patience time scaling," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 283-303, December.
    5. Cao, Ping & Zhong, Zhiheng & Huang, Junfei, 2021. "Dynamic routing in a distributed parallel many-server service system: The effect of ξ-choice," European Journal of Operational Research, Elsevier, vol. 294(1), pages 219-235.
    6. Rami Atar & Isaac Keslassy & Gal Mendelson, 2019. "Subdiffusive Load Balancing in Time-Varying Queueing Systems," Operations Research, INFORMS, vol. 67(6), pages 1678-1698, November.
    7. Zhong, Zhiheng & Cao, Ping, 2023. "Balanced routing with partial information in a distributed parallel many-server queueing system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 618-633.
    8. Dinard van der Laan, 2015. "Assigning Multiple Job Types to Parallel Specialized Servers," Tinbergen Institute Discussion Papers 15-102/III, Tinbergen Institute.
    9. Chihoon Lee & Amy R. Ward & Heng-Qing Ye, 2020. "Stationary distribution convergence of the offered waiting processes for $$GI/GI/1+GI$$GI/GI/1+GI queues in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 147-173, February.

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