Managing reusable resources with usage time limits

In reusable resources like vehicle sharing, city parking, and hotel services, resource units are used by consecutive customers for a stochastic usage time and are made available for future customers upon return. We model such reusable resources as Erlang loss systems, where customers who find all units occupied are blocked. Customers are rational decision-makers, and their willingness to join the system depends on factors such as price, time limits, service value, and resource availability. When each customer is charged a fixed price, we examine whether it is beneficial to install time limits, which increase availability at the expense of reduced usage time. We formulate and solve a two-dimensional revenue maximization problem to optimize both the usage price and the time limit. We differentiate between on-demand resources, which are immediately reusable upon return, and reserved resources, which can only be reused after the time limit expires. With on-demand resources, setting a time limit is proven to be detrimental, making the entry price the sole tool for maximizing revenue. This conclusion remains valid when the usage time increases with the entry price. In contrast, managing reserved resources involves an interplay between time limits and entry prices. Additionally, we show that loss systems (where customers do not wait) should be managed differently from systems where customers do wait. Specifically, in systems with waiting, we prove that only the time limit should be optimized, while the entry price should capture the full market share. We prove our results by analyzing the behavior of the equilibrium arrival rate and revenue, which necessitates establishing novel properties for the blocking probability. These properties yield new sharp bounds for the blocking probability and enable us to prove the convergence of the optimized model for on-demand resources to the QED regime as the number of resource units grows.