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Consider a multi-class preemptive-resume $M/D/1$ queueing system thatsupports advance reservations (AR). In this system, strategic customers mustdecide whether to reserve a server in advance (thereby gaining higher priority)or avoid AR. Reserving a server in advance bears a cost. In this paper, weconduct a game-theoretic analysis of this system, characterizing theequilibrium strategies. Specifically, we show that the game has two types ofequilibria. In one type, none of the customers makes reservation. In the othertype, only customers that realize early enough that they will need service makereservations. We show that the types and number of equilibria depend on theparameters of the queue and on the reservation cost. Specifically, we provethat the equilibrium is unique if the server utilization is below 1/2.Otherwise, there may be multiple equilibria depending on the reservation cost.Next, we assume that the reservation cost is a fee set by the provider. In thatcase, we show that the revenue maximizing fee leads to a unique equilibrium ifthe utilization is below 2/3, but multiple equilibria if the utilizationexceeds 2/3. Finally, we study a dynamic version of the game, where users learnand adapt their strategies based on observations of past actions or strategiesof other users. Depending on the type of learning (i.e., action learning vs.\strategy learning), we show that the game converges to an equilibrium in somecases, while it cycles in other cases.

Equilibrium and Learning in Queues with Advance Reservations