Dynamics of New Product Introduction in Closed Rental Systems

We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of reusable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are independent and identically distributed with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donsker's theorems. Analyzing the usage process, we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service. Further, we show that the firm is better off not imposing any deadlines for the return of the product.