Optimal strategies and pricing analysis in M/M/1 queues with a single working vacation and multiple vacations

This paper considers the customers’ equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with a single working vacation and multiple vacations. Arriving customers decide whether to join the system or balk based on the system states and a linear reward-cost structure, which incorporates the desire of customers for service and their dislike to wait. We consider that the system states are almost unobservable and fully unobservable, respectively. For these two cases, we first analyze the stationary behavior of the system, and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies using numerical examples. We also study the pricing problem that maximizes the server’s profit and derive the optimal pricing strategy. Finally, the social benefits of the almost and fully unobservable queues are compared by numerical examples