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Heterogeneity of delay information and revenue-cost structure in a multi-server queue with threshold policy: Customer behaviors and optimization

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  • Sun, Wei
  • Zhang, Zhiyuan
  • Xie, Xumeng
  • Li, Shiyong

Abstract

This paper studies customers' equilibrium joining behavior in a multi-server queue with threshold policy, and then puts forward effective schemes to control customers' behaviors and to optimize social welfare. The stream of customers consists of two parts: customers in class 1 and customers in class 2, and they wait for service in order until the system is empty. Then the servers take a vacation and they would be reactivated as soon as the queue length reaches a threshold N. The two types of customers are heterogeneous in service revenue and delay sensitivity, i.e., they have different revenue-cost structures. Besides, customers in class 1 can access to the delay information on servers' status and queue length as they arrive, but customers in class 2 can not. Distinguishing the two scenarios of whether there is a joining threshold for customers in class 1 in vacation state, we get the two types of customers' equilibrium joint joining strategies, respectively, and observe the interaction between the behaviors of the two types of customers. Moreover, we also get their socially optimal joint joining strategy for comparisons and for making control measures, and discuss the influence of the fraction of customers in class 1 on social welfare and system throughput. We find that in any scenario, the equilibrium social welfare is always unimodal with respect to the fraction of customers in class 1, which indicates that the higher fraction of customers in class 1 is not necessarily beneficial. However, on the premise of effectively controlling customer behavior, this high fraction is still necessary to optimize social welfare and increase system throughput, although the optimal social welfare is also unimodal.

Suggested Citation

  • Sun, Wei & Zhang, Zhiyuan & Xie, Xumeng & Li, Shiyong, 2024. "Heterogeneity of delay information and revenue-cost structure in a multi-server queue with threshold policy: Customer behaviors and optimization," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    • Handle: RePEc:eee:apmaco:v:465:y:2024:i:c:s0096300323005829
    DOI: 10.1016/j.amc.2023.128413
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    References listed on IDEAS

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    1. Philipp Afèche & Opher Baron & Joseph Milner & Ricky Roet-Green, 2019. "Pricing and Prioritizing Time-Sensitive Customers with Heterogeneous Demand Rates," Operations Research, INFORMS, vol. 67(4), pages 1184-1208, July.
    2. Refael Hassin & Ricky Roet-Green, 2017. "The Impact of Inspection Cost on Equilibrium, Revenue, and Social Welfare in a Single-Server Queue," Operations Research, INFORMS, vol. 65(3), pages 804-820, June.
    3. Ming Hu & Yang Li & Jianfu Wang, 2018. "Efficient Ignorance: Information Heterogeneity in a Queue," Management Science, INFORMS, vol. 64(6), pages 2650-2671, June.
    4. Moshe Haviv & Eyal Winter, 2020. "An optimal mechanism charging for priority in a queue," Papers 2002.06533, arXiv.org.
    5. Hassin, Refael & Nowik, Irit & Shaki, Yair Y., 2018. "On the price of anarchy in a single-server queue with heterogeneous service valuations induced by travel costs," European Journal of Operational Research, Elsevier, vol. 265(2), pages 580-588.
    6. 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.
    7. Bodas, Tejas & Manjunath, D., 2019. "Revenue maximization in service systems with heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 278(2), pages 686-698.
    8. Zhongbin Wang & Jinting Wang, 2019. "Information heterogeneity in a retrial queue: throughput and social welfare maximization," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 131-172, June.
    9. Chai, Xudong & Jiang, Tao & Chang, Baoxian & Liu, Liwei, 2021. "On a multiple priorities matching system with heterogeneous delay sensitive individuals," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    10. Qiao‐Chu He & Ying‐Ju Chen & Rhonda Righter, 2020. "Learning with Projection Effects in Service Operations Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 90-100, January.
    Full references (including those not matched with items on IDEAS)

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