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The paper considers the single-server Markovian queues with delayed multiple vacations. Once the system becomes empty, the server will experience a changeover time to begin the vacation. By using the matrix-geometric solution method, we obtain the stationary probability distribution and the mean queue length under almost unobservable and fully unobservable cases. Based on the system status information and a linear reward-cost structure reflecting the desire of customers for service and their unwillingness for waiting, the social welfare function is determined. We also investigate optimal pricing strategies of the server under the ex-postpayment scheme and the ex-antepayment scheme, and we get the customer’s equilibrium strategy under optimal pricing strategy. Finally, we illustrate the effect of several parameters and information levels on socially optimal strategies and optimal social benefit by numerical examples.

Social Optimization and Pricing Strategies in Unobservable Queues with Delayed Multiple Vacations