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Threshold control policies for heterogeneous server systems

Author

Listed:
  • Hsing Paul Luh
  • Ioannis Viniotis

Abstract

We study the problem of optimally controlling a multiserver queueing system. Customers arrive in a Poisson fashion and join a single queue, served by N servers, S 1 ,S 2 ,… , S N . The servers have different rates. The service times at each server are independent and exponentially distributed. The objective is to determine the policy which minimizes the average number of customers in the system. We show that any optimal, nonpreemptive policy is of threshold type, i.e., it assigns a customer to server S i , if this server is the fastest server available and the number of customers in the queue is m i or more. The threshold m i may depend on the condition of other (slower) servers at the decision instant. In order to establish the results, we reformulate the optimal control problem as a linear program and use a novel argument based on the structure of the constraint matrix. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Hsing Paul Luh & Ioannis Viniotis, 2002. "Threshold control policies for heterogeneous server systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 121-142, March.
    • Handle: RePEc:spr:mathme:v:55:y:2002:i:1:p:121-142
    DOI: 10.1007/s001860100168
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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. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik & Andreas Plank, 2020. "Approximations in Performance Analysis of a Controllable Queueing System with Heterogeneous Servers," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    3. Benjamin Legros, 2018. "M/G/1 queue with event-dependent arrival rates," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 269-301, August.
    4. Ger Koole, 2022. "The slow-server problem with multiple slow servers," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 469-471, April.
    5. Erhun Özkan & Jeffrey Kharoufeh, 2015. "Incompleteness of results for the slow-server problem with an unreliable fast server," Annals of Operations Research, Springer, vol. 226(1), pages 741-745, March.
    6. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner, 2024. "Queue-length-aware dispatching in large-scale heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 125-184, October.
    7. Francis de Véricourt & Yong-Pin Zhou, 2005. "Managing Response Time in a Call-Routing Problem with Service Failure," Operations Research, INFORMS, vol. 53(6), pages 968-981, December.

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