提前预订系统的均衡与学习
Equilibrium and Learning in Queues with Advance Reservations
摘要：
考虑支持提前预留（AR）的多类抢占式恢复$M/D/1$排队系统。在这个系统中，战略客户必须决定是否提前预订服务器（从而获得更高的优先级）或避免AR。提前预订服务器是有成本的。在本文中，我们进行了博弈论分析，这个系统的均衡策略的特点。具体来说，我们表明，游戏有两种类型的均衡。在一种类型中，没有客户进行预订。在另一种类型中，只有足够早地意识到他们将需要服务的客户才进行预订。我们表明，平衡的类型和数量取决于参数的队列和保留成本。具体来说，我们证明了均衡是唯一的，如果服务器利用率低于1/2。否则，可能存在多个均衡，这取决于预留成本。接下来，我们假设预订成本是由提供商设置的费用。在这种情况下，我们表明，收入最大化的费用导致一个唯一的均衡，如果利用率低于2/3，但多个均衡，如果利用率超过2/3。最后，我们研究了一个动态版本的游戏，用户学习和调整他们的策略的基础上观察过去的行动或其他用户的策略。根据学习的类型（即，行动学习与策略学习），我们表明，在某些情况下，游戏收敛到一个均衡，而在其他情况下，它的周期。
英文摘要：
Consider a multi-class preemptive-resume $M/D/1$ queueing system that supports advance reservations (AR). In this system, strategic customers must decide 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, we conduct a game-theoretic analysis of this system, characterizing the equilibrium strategies. Specifically, we show that the game has two types of equilibria. In one type, none of the customers makes reservation. In the other type, only customers that realize early enough that they will need service make reservations. We show that the types and number of equilibria depend on the parameters of the queue and on the reservation cost. Specifically, we prove that 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 that case, we show that the revenue maximizing fee leads to a unique equilibrium if the utilization is below 2/3, but multiple equilibria if the utilization exceeds 2/3. Finally, we study a dynamic version of the game, where users learn and adapt their strategies based on observations of past actions or strategies of 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 some cases, while it cycles in other cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
