The Power of Static Pricing for Reusable Resources

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. This system is equivalent to the classical Erlang loss model. The objective is to maximize the steady-state revenue rate. Although an optimal policy is fully 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 90.2% 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 policy grows exponentially large in the number of classes while the static policy requires only one price per class.