Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system.

中文翻译：

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用延迟信息打破队列的对称性

向客户提供有关服务系统的队列长度信息可能会影响客户加入队列的决定。因此，排队系统的管理人员必须了解他们提供的信息将如何影响系统的性能。为此，我们构建并分析了一个包含客户选择行为的二维确定性流体模型延迟队列长度信息。现有文献中的报告总是假设所有队列都具有相同的参数，并且底层的动力系统是对称的。然而，在本文中，我们通过允许每个队列的到达率、服务率和选择模型参数不同来放松这种对称性假设。我们的方法利用多尺度和渐近分析的方法来了解如何打破对称性。我们发现不对称性会对排队系统的基本动态产生很大影响。