Mixed equilibrium and social joining strategies in Markovian queues with Bernoulli-schedule-controlled vacation and vacation interruption

Abstract

This paper presents equilibrium and social customer behavior in a single-server queueing system with Bernoulli-schedule-controlled vacation and vacation interruption. An arriving customer takes the decision whether to join the system or balk according to an observation of the system length and the status of the server, which is more reasonable than the classical point of view that the decisions are induced by the servers and the customers are compelled to follow them. Four cases with respect to several levels of information and the corresponding Nash equilibria are discussed. The equilibrium strategies and stationary system behavior are studied for both observable and unobservable cases using the reward-cost structure of the system. We show the impact of the information level as well as several parameters on the equilibrium thresholds and social benefits through numerical results. The research outcomes might provide the managers with reference information on the pricing problem in the queueing system and will help the customers to take optimal threshold strategies.

Keywords:

• Equilibrium threshold
• balking
• strategic customers
• Bernoulli-scheduled-controlled vacation
• social benefit

Notes

No potential conflict of interest was reported by the authors.