We consider an M/M/1 queue with retrials. There are two streams of customers, one informed about the server’s state upon arrival (idle or busy) and the other not informed. Both informed and uninformed customers decide whether to join the system or not upon arrival. Upon joining, customers who are faced with a busy server will retry several times until the server is idle to acquire service. The interval of retrials is exponentially distributed. We investigate equilibrium strategies for the customers and study the impact of information heterogeneity on the system throughput and social welfare. We find that social welfare is increasing in the fraction of informed customers and the maximum social welfare is reached when all customers are informed about the state of the server. On the other hand, we find that when the workload is low (or high), the throughput-maximizing server should conceal (or disclose) the state of the server to customers. When the workload falls in an intermediate range, information heterogeneity in the population (i.e., revealing the information to a certain portion of customers) leads to more efficient outcomes. Finally, numerical analyses are presented to verify our results and illustrate the impact of the retrial behavior on the system performance.

中文翻译：

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重审队列中的信息异质性：吞吐量和社会福利最大化

我们考虑带有重试的 M/M/1 队列。有两种客户流，一种在到达时获悉服务器的状态（空闲或忙碌），另一种未获知。知情和不知情的客户在到达时决定是否加入系统。加入后，面对服务器繁忙的客户会多次重试，直到服务器空闲才能获取服务。重试间隔呈指数分布。我们调查客户的均衡策略并研究信息异质性对系统吞吐量和社会福利的影响。我们发现社会福利在知情客户的比例中增加，并且当所有客户都了解服务器的状态时达到最大的社会福利。另一方面，我们发现当工作量低（或高）时，吞吐量最大化服务器应该向客户隐藏（或公开）服务器的状态。当工作量落在中间范围内时，群体中的信息异质性（即向特定部分客户透露信息）会导致更有效的结果。最后，通过数值分析来验证我们的结果并说明重试行为对系统性能的影响。