Strategic behavior and social optimization in a constant retrial queue with the N-policy

We consider customers' strategic behavior and the corresponding social maximization problem in an M/M/1 constant retrial queue with the N-policy. There is no waiting space in front of the server and customers who find the server busy have to abandon the system, but they can leave their contact details to stay on a waiting list. Consequently, after a service completion, the server will seek a customer from the waiting list at a constant retrial rate on an FCFS basis. The server is switched off whenever the system becomes empty, and is resumed only when the number of waitlisted customers reaches a given threshold. We assume that the arriving customers who find the server busy or down decide whether to leave their contact details or to balk based on a linear reward-cost structure. We examine customers' strategic response to this mechanism and compare it to the social optimal behavior with delay information. It is shown that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system, and therefore, both multiple and unique equilibrium arrival rates could exist. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. The individual equilibrium strategies are compared with the social optimum and the Price of Anarchy (PoA) is studied as a measure to quantify the inefficiency of the equilibrium strategies. Finally, numerical examples are presented to illustrate the sensitivity of some key system performance measures.