Advance reservations and information sharing in queues with strategic customers
In many branches of the economy, including transportation, lodging, and more recently cloud computing, users can reserve resources in advance. Although advance reservations are gaining popularity, little is known about the strategic behavior of customers facing the decision whether to reserve a resource in advance or not. Making an advance reservation can reduce the waiting time or the probability of not getting service, but it is usually associated with an additional cost. To evaluate this trade-off, we develop a game-theoretic framework, called advance reservation games, that helps in reasoning about the strategic behavior of customers in systems that allow advance reservations. Using this framework, we analyze several advance reservation models, in the context of slotted loss queues and waiting queues. The analysis of the economic equilibria, from the provider perspective, yields several key insights, including: (i) If customers have no a-priori information about the availability of servers, then only customers granted service should be charged a reservation fee; (ii) Informing customers about the exact number of available servers is less profitable than only informing them that servers are available; (iii) In many cases, the reservation fee that leads to the equilibrium with maximum possible profit leads to other equilibria, including one resulting with no profit; (iv) If the game repeats many times and customers update their strategy after observing actions of other customers at previous stage, then the system converges to an equilibrium where no one makes an advance reservation, if such an equilibrium exists. Else, the system cycles and yields positive profit to the provider Finally, we study the impact of information sharing in M/M/1 queues with strategic customers. We analyze the intuitive policy of sharing the queue length with customers when it is small and hiding it when it is large. We prove that, from the provider perspective, such a policy is never optimal. That is, either always sharing the queue length or always hiding it maximizes the average number of customers joining the queue.