Spyridoula Kanta and Antonis Economou. Equilibrium customer strategies and social-profit maximization in the single server constant retrial queue

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 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.