Price Decisions in a Two-Server Queue Considering Customer Retrial Behavior: Profit-Driven Versus Social-Driven

This study investigates price decisions in a queue with two servers, where customers exhibit retrial behavior. There is no waiting space. Arrival customers have the option to either join the system or balk; when the two servers are occupied, those who decide to enter become repeat customers. Two scenarios where the waiting lines in orbit are unobservable and observable are considered. We analyze customers’ behavior and derive their Nash equilibrium strategies under both cases. Additionally, we examine optimal pricing decisions aimed at maximizing profit and social welfare, respectively. Moreover, we demonstrate that these objectives often lead to divergent outcomes. Compared to a single-server queue, the reduction in customers’ sojourn time is more obvious when the waiting line is unobservable. Under certain conditions—such as a large potential market size, high customer impatience, or a low retrial rate—increasing the number of service personnel can enhance both profit and social welfare. Notably, a profit-maximizing manager is more incentivized to increase servers than the social planner. These findings provide valuable insights for balancing operational efficiency, profitability, and customer satisfaction in queue management systems.