Information heterogeneity in a retrial queue: throughput and social welfare maximization

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.