Strategic Joining and Pricing Policies in a Retrial Queue With Orbital Search and Its Application to Call Centers

This paper treats strategic joining and pricing policies in an M/M/1 retrial queue with orbital search which is motivated by the application in call centers, where the server will make orbital search or remain idle whenever he completes a service, the orbital search time follows exponential distribution. Given a natural reward-cost structure and imposed on an admission fee, all arriving customers decide to whether to join the orbit or balk when they find the server busy. Using queueing theory and game theory, we first analyze the Nash equilibrium mixed joining strategy for individual customer. Further we investigate the optimal joining probabilities and corresponding admission pricing problems that maximize the administrator's revenue and social profit, respectively. Finally, we present some numerical examples to demonstrate the effect of some system parameters on the sensitivity of the solutions of the individual maximization, administrator's maximization and social optimization.