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Optimal balking strategies for high-priority customers in M/G/1 queues with 2 classes of customers

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Abstract

This paper studies the optimal balking strategies of customers with a higher priority in the single-server M/G/1 queue, where there are two classes of customers who have different priorities. When a low-priority customer is being served, the high-priority customer joins in the system and will be served immediately while the low-priority customer will go back to the head of the queue of its class. Upon arrival, the high-priority customers decide for themselves whether to join or balk based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness to wait. We identify equilibrium strategies and socially optimal strategies under one information assumption. The high-priority customers make individual decisions in a unobservable queue. By deriving and solving a set of system equations, we obtain equilibrium strategies and socially optimal strategies. Finally we illustrate our results via numerical experiments.

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Acknowledgments

The authors would like to thank the support from National Natural Science Foundation of China #11201408 and Natural Science Foundation of Hebei Province, China #A2013203148.

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Authors and Affiliations

  1. College of Science, Yanshan University, Hebei, 066004, Qinhuangdao, China

    Biao Xu, Xiuli Xu & Xianying Wang

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  1. Biao Xu
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  2. Xiuli Xu
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  3. Xianying Wang
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Correspondence to Biao Xu.

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Xu, B., Xu, X. & Wang, X. Optimal balking strategies for high-priority customers in M/G/1 queues with 2 classes of customers. J. Appl. Math. Comput. 51, 623–642 (2016). https://doi.org/10.1007/s12190-015-0923-5

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  • DOI: https://doi.org/10.1007/s12190-015-0923-5

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