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Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic

Author

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  • Tolga Tezcan

    (Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • J. G. Dai

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We consider a class of parallel server systems that are known as N -systems. In an N -system, there are two customer classes that are catered by servers in two pools. Servers in one of the pools are cross-trained and can serve customers from both classes, whereas all of the servers in the other pool can serve only one of the customer classes. A customer reneges from his queue if his waiting time in the queue exceeds his patience. Our objective is to minimize the total cost that includes a linear holding cost and a reneging cost. We prove that, when the service speed is pool dependent, but not class dependent, a c(mu) -type greedy policy is asymptotically optimal in many-server heavy traffic.

Suggested Citation

  • Tolga Tezcan & J. G. Dai, 2010. "Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic," Operations Research, INFORMS, vol. 58(1), pages 94-110, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:94-110
    DOI: 10.1287/opre.1080.0668
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    References listed on IDEAS

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    Cited by:

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    5. Mor Armony & Avishai Mandelbaum, 2011. "Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers," Operations Research, INFORMS, vol. 59(1), pages 50-65, February.
    6. Jim G. Dai & Pengyi Shi, 2021. "Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1838-1862, June.
    7. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    8. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    9. Siqiao Li & Ger Koole & Xiaolan Xie, 2020. "An adaptive priority policy for radiotherapy scheduling," Flexible Services and Manufacturing Journal, Springer, vol. 32(1), pages 154-180, March.
    10. Qin Zhang, 2023. "Dynamic Routing Policies for Multi-Skill Call Centers Using Deep Q Network," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    11. Dongyuan Zhan & Gideon Weiss, 2018. "Many-server scaling of the N-system under FCFS–ALIS," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 27-71, February.
    12. E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
    13. Arka Ghosh & Keguo Huang, 2017. "Asymptotically optimal control of N-systems with $$H_2^*$$ H 2 ∗ service times under many-server heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 35-60, June.
    14. 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.
    15. Alexander L. Stolyar & Tolga Tezcan, 2011. "Shadow-Routing Based Control of Flexible Multiserver Pools in Overload," Operations Research, INFORMS, vol. 59(6), pages 1427-1444, December.
    16. J. G. Dai & Pengyi Shi, 2019. "Inpatient Overflow: An Approximate Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 894-911, October.
    17. Golshid Baharian & Tolga Tezcan, 2011. "Stability analysis of parallel server systems under longest queue first," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 257-279, October.
    18. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    19. Ari Arapostathis & Guodong Pang, 2018. "Infinite-Horizon Average Optimality of the N-Network in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 838-866, August.
    20. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
    21. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    22. Dongyuan Zhan & Amy R. Ward, 2014. "Threshold Routing to Trade Off Waiting and Call Resolution in Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 220-237, May.
    23. Wyean Chan & Ger Koole & Pierre L'Ecuyer, 2014. "Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 544-560, October.
    24. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
    25. Samim Ghamami & Amy R. Ward, 2013. "Dynamic Scheduling of a Two-Server Parallel Server System with Complete Resource Pooling and Reneging in Heavy Traffic: Asymptotic Optimality of a Two-Threshold Policy," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 761-824, November.

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