EQUILIBRIUM CUSTOMER STRATEGIES AND SOCIAL-PROFIT MAXIMIZATION IN THE SINGLE SERVER CONSTANT RETRIAL QUEUE ANTONIS ECONOMOU AND SPYRIDOULA KANTA Abstract. We consider the single server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers’ behavior and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed. Keywords: queueing, constant retrials, balking, equilibrium strategies, pricing, social optimiza- tion, profit maximization, Nash equilibrium, partial information Published in 2011 in Naval Research Logistics 58, 107–122 The original publication is available with DOI: 10.1002/nav.20444 1. Introduction In most studies in queueing theory, it is usually assumed that blocked customers (those who cannot get immediately service or waiting space to stay) abandon the system for ever. However, in most applications, it is reasonable to assume that the customers retry for service after some random period of time. This is crucial for the accurate representation of a given system with a queueing model. Kosten (1973) notes that “any theoretical result that does not take into consideration this repetition effect should be considered suspect”. Retrial queues have been introduced to model exactly this repetition effect. In the majority of papers in the retrial queueing literature, each blocked customer joins the so- called retrial orbit and becomes a source of repeated requests for service at rate ν , independently of the other customers. This is the classical retrial policy in which the total retrial rate when there are j customers in the orbit is jν . In contrast to this, there are some applications in computer and communication networks, where the time between two successive repeated attempts is controlled by some automatic mechanism and consequently the total retrial rate is α, independently of the number j of customers in orbit. This constant retrial policy is also used to model systems in which the blocked customers leave their contact details when they find the server busy. Then, after a service completion, the server seeks for a customer at a constant (retrial) rate α, among those that have left their contact details. The literature on retrial queueing systems is already very extensive. For a recent account we point to the recent books of Falin and Templeton (1997) and Artalejo and Gomez-Corral (2008) that summarize the main models and methods. The constant retrial policy was introduced in Fayolle (1986). Subsequently several authors considered various complicated systems operating under this policy or its generalization, the so-called linear retrial policy (see e.g. Falin and Gomez-Corral (2000)). However, the vast majority of papers on retrial queueing systems is devoted on performance evaluation and control problems that are solved using stochastic processes and dynamic program- ming techniques. There are very few papers that study this type of systems from an economic viewpoint, that is when the customers are allowed to take their own decisions (e.g. to join or balk, 1