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Strategic customer behavior in an M / M /1 feedback queue
Queueing Systems ( IF 1.2 ) Pub Date : 2021-03-20 , DOI: 10.1007/s11134-021-09693-z
Mark Fackrell , Peter Taylor , Jiesen Wang

We investigate the behavior of equilibria in an M/M/1 feedback queue where price- and time-sensitive customers are homogeneous with respect to service valuation and cost per unit time of waiting. Upon arrival, customers can observe the number of customers in the system and then decide to join or to balk. Customers are served in order of arrival. After being served, each customer either successfully completes the service and departs the system with probability q, or the service fails and the customer immediately joins the end of the queue to wait to be served again until she successfully completes it. We analyze this decision problem as a noncooperative game among the customers. We show that there exists a unique symmetric Nash equilibrium threshold strategy. We then prove that the symmetric Nash equilibrium threshold strategy is evolutionarily stable. Moreover, if we relax the strategy restrictions by allowing customers to renege, in the new Nash equilibrium, customers have a greater incentive to join. However, this does not necessarily increase the equilibrium expected payoff, and for some parameter values, it decreases it.



中文翻译:

M / M / 1反馈队列中的战略客户行为

我们研究了M / M / 1反馈队列中的均衡行为,其中价格敏感和时间敏感的客户在服务评估和每单位等待时间的成本方面是同质的。到达后,客户可以观察系统中的客户数量,然后决定加入或拒绝。按到达顺序为客户提供服务。服务后,每个客户要么成功完成服务并以q的概率离开系统,或者服务失败,并且客户立即加入队列的末尾以等待再次获得服务,直到她成功完成服务为止。我们将此决策问题分析为客户之间的不合作博弈。我们表明,存在一个独特的对称纳什均衡阈值策略。然后,我们证明了对称Nash平衡阈值策略在进化上是稳定的。此外,如果我们通过允许客户放弃而放宽策略限制,那么在新的纳什均衡中,客户会有更大的加入动机。但是,这并不一定会增加均衡预期收益,并且对于某些参数值,它会减小均衡收益。

更新日期:2021-03-21
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