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Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control

Author

Listed:
  • Lingjiao Zhang

    (Central University of Finance and Economics)

  • Jinting Wang

    (Central University of Finance and Economics)

  • Yilin Wang

    (Central University of Finance and Economics)

Abstract

This work aims to study customer strategic behavior and operational optimization of an M/M/1 queue with N-policy and dynamic service-rate control in general, and of a make-to-order production system with a strategic manufacturer as a practical example in particular. With the N-policy and hysteretic control, the service rate is dynamically adjusted according to the queue length. An empty system is required to initiate service only when the number of waiting customers reaches a given threshold N. If the queue length exceeds $$M(>N)$$ M ( > N ) , the server serves customers with a higher service rate until the number of customers is lower than another threshold m. Based on a linear reward-cost structure, arriving customers are allowed to decide whether to join the system or not. The focus is on comparing the self equilibrium performance and socially-optimal arrival under the interaction between the server’s states and customers’ joining decisions. The influence of N-policy and hysteretic control on customer’s equilibrium joining probability under unobservable scenario is analysed. The optimal value of threshold N and m are discussed by taking server’s operational cost into consideration. These findings have important managerial implications on the overall social welfare with dynamic service rate.

Suggested Citation

  • Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:4:d:10.1007_s11009-023-10054-x
    DOI: 10.1007/s11009-023-10054-x
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    References listed on IDEAS

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    1. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    2. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    3. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    4. Dimitrakopoulos, Y. & Burnetas, A.N., 2016. "Customer equilibrium and optimal strategies in an M/M/1 queue with dynamic service control," European Journal of Operational Research, Elsevier, vol. 252(2), pages 477-486.
    5. Richard F. Gebhard, 1967. "A queuing process with bilevel hysteretic service‐rate control," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(1), pages 55-67.
    6. M. Yu. Kitaev & Richard F. Serfozo, 1999. "M/M/1 Queues with Switching Costs and Hysteretic Optimal Control," Operations Research, INFORMS, vol. 47(2), pages 310-312, April.
    7. Zhe George Zhang, 2009. "Performance Analysis of a Queue with Congestion-Based Staffing Policy," Management Science, INFORMS, vol. 55(2), pages 240-251, February.
    8. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    9. Xianyue Shi & Liwei Liu, 2023. "Equilibrium Joining Strategies in the Retrial Queue with Two Classes of Customers and Delayed Vacations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    10. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    Full references (including those not matched with items on IDEAS)

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