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Equilibrium solutions in the observable M/M/1 queue with overtaking

The subject of this paper is a mechanism that allows customers to overtake others. In our system, customers observe the queue length upon arrival, and have the option of overtaking some or all of the customers already present in the queue. Overtaking is associated with a fixed price per overtaken customer. If a customer chooses to overtake some but not all of the present customers, overtaking applies to the last customers in the queue. Customers incur a fixed cost per every unit of time in the system, and their goal is to minimize their own expected total cost. We would like to characterize the symmetric equilibrium strategies of our model. However, it turns out that this mission is much harder in our system than in the other priority queueing systems analyzed in the literature. We consider several types of symmetric strategies and find out that the set of equilibrium symmetric strategies is quite reach and includes surprisingly odd strategies. In addition, we compare overtaking with ordinary (absolute) priority systems. We assume that the server can induce the customers to choose among the equilibrium strategies, the one which maximizes its profits. Under this assumption, we compare the server's profits in the two models and find, somewhat surprisingly, that the system of overtaking gives the server higher profits.