We study the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers choose their arrival time with the goal of minimizing their expected waiting times and are served on a first-come first-served basis. There are two types of customers that differ in their beliefs regarding the service-time distribution. The inconsistent beliefs may arise from randomness in the server state along with noisy signals that customers observe. Customers are aware of the two types of populations with differing beliefs. We characterize the Nash equilibrium dynamics for exponentially distributed service times and show how they substantially differ from the model with homogeneous customers. We further provide an explicit solution for a fluid approximation of the game. For general service-time distributions we provide an algorithm for computing the equilibrium in a discrete-time setting. We find that in equilibrium customers with different beliefs arrive during different (and often disjoint) time intervals. Numerical analysis further shows that the mean waiting time increases with the coefficient of variation of the service time. Furthermore, we present a learning agent-based model (ABM) in which customers make joining decisions based solely on their signals and past experience. We numerically compare the long-term average outcome of the ABM with that of the equilibrium and find that the arrival distributions are quite close if we assume (for the equilibrium solution) that customers are fully rational and have knowledge of the system parameters, while they may greatly differ if customers have limited information or computing abilities.

我们研究了在服务速度不确定的情况下，具有打开和关闭时间的单服务器队列到达时间的战略选择问题。泊松（Poisson）客户群选择到达时间的目的是最大程度地减少预期的等待时间，并以先到先得的方式提供服务。有两种类型的客户，他们对服务时间分配的看法不同。不一致的信念可能是由于服务器状态的随机性以及客户观察到的嘈杂信号引起的。客户了解具有不同信仰的两种人群。我们对服务时间呈指数分布的纳什均衡动力学进行了刻画，并显示了它们与同质客户模型之间的显着差异。我们进一步为游戏的流体逼近提供了一个明确的解决方案。对于一般服务时间分布，我们提供了一种用于计算离散时间设置中的平衡的算法。我们发现，在均衡状态下，具有不同信念的客户会在不同（且通常是不相交的）时间间隔内到达。数值分析进一步表明，平均等待时间随着服务时间的变化系数而增加。此外，我们提出了一种基于学习代理的模型（ABM），在该模型中，客户仅根据他们的信号和过去的经验来做出加入决策。