We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has an exponential distribution. The objective is to maximize the steady-state revenue rate. This system is equivalent to the classical Erlang loss model with price-sensitive customers, which has applications in vehicle sharing, cloud computing, and spare parts management. Although an optimal pricing policy is dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.4\% of the revenue from the optimal dynamic policy. When there are multiple classes of customers that each have their own regular valuation distribution and service rate, we prove that static pricing guarantees 78.9\% of the revenue of the optimal dynamic policy. In this case, the optimal pricing policy is exponentially large in the number of classes while the static policy requires only one price per class. Moreover, we prove that the optimal static policy can be easily computed, resulting in the first polynomial time approximation algorithm for this problem.

翻译：我们考虑可重用资源服务系统的定价问题。潜在顾客根据泊松过程到达，若其估值超过当前价格则购买服务。若无可用资源，顾客立即离开且不接受服务。服务一位顾客相当于消耗一个可重用资源单位，服务时间服从指数分布。目标是最大化稳态收入率。该系统等价于具有价格敏感顾客的经典Erlang损失模型，广泛应用于车辆共享、云计算和备件管理等领域。尽管最优定价策略是动态的，我们提出两个主要结果表明：对于任意服务率、到达率和系统资源数量，简单的静态策略具有普适的近似最优性。当存在单类服从单调风险率（MHR）估值分布的顾客时，我们证明静态定价策略能保证最优动态策略收入的90.4%。当存在多类具有各自正则估值分布和服务率的顾客时，我们证明静态定价能保证最优动态策略收入的78.9%。在此情况下，最优定价策略的复杂度随顾客类别数呈指数增长，而静态策略每类仅需一个价格。此外，我们证明最优静态策略可轻松计算，从而为该问题首次提出多项式时间近似算法。