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This work studies the equilibrium behavior of customers and optimal pricing strategies of the sever in a continuous-time M/M/1 queueing system. In this work, we consider two pricing models. The first one is called the ex-ante payment scheme where the server charges a flat price for all services, and the second one is called the ex-post payment scheme where the server charges a price that is proportional to the time a customer spends in the system. In each pricing model, the departing customer receives the reward that is inversely proportional to his/her sojourn time. The server should make the optimal pricing decisions in order to maximize its expected profit per unit time in each payment scheme. This work also investigates customer’s equilibrium joining or balking behaviors under server’s optimal pricing strategies. Numerical experiments are conducted to help the server best select one between two pricing models.

An Optimal Pricing Strategy in An M/M/1 Queueing System Based on Customer's Sojourn Time-Dependent Reward Level