Equilibrium and optimal balking strategies of customers in Markovian queues with multiple vacations and N-policy

This paper studies the customers’ equilibrium and socially optimal balking strategies in single-server Markovian queues with multiple vacations and N-policy. That is, the server starts taking a vacation time once the system becomes empty, and reactivates in case at least N customers waiting in the queue after completing the vacation. Otherwise, he/she continues taking another vacation. We discuss the fully observable and fully unobservable queues, respectively. For each type of queues, we get both customers’ equilibrium and optimal balking strategies, and make numerical comparisons between them. We observe that the customers’ individual behavior in stable equilibrium always makes the system more congested than the socially optimal one. Moreover, we also make sensitivity analysis of customers’ equilibrium and optimal strategies and social welfare with respect to N and the vacation parameter, respectively. It shows that customers and the social planner all prefer a classical Markovian queue without vacations and N-policy. By comparing social welfare under the two information cases, we find that whether the system information should be revealed to customers depends on the potential arrivals of demand.