  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.
