Strategic priority-purchasing and joining rules in a retrial queue

This paper considers a retrial queueing system with a pay-for-priority option. A queueing-game-theoretic model that captures the interaction among the customers, the service provider (SP) and the social planner is developed. We obtain the equilibrium strategy of customers for any fixed priority premium and identify the unique Pareto-dominant strategy. The optimal pricing strategies for the SP and the social planner are derived and compared extensively. Interestingly, we find that the equilibrium outcome of customers is non-monotone in the service reward and the profit of the SP is bimodal in the priority premium. We reveal the fact that the SP’s optimization makes the system more congested than what is socially desirable. Finally, numerical examples indicate that the customer welfare can be improved by providing priorities when the market size is large.