  We consider the problem of online allocation (matching and assortments) of
reusable resources where customers arrive sequentially in an adversarial
fashion and allocated resources are used or rented for a stochastic duration
that is drawn independently from known distributions. Focusing on the case of
large inventory, we give an algorithm that is $(1-1/e)$ competitive for general
usage distributions. At the heart of our result is the notion of a relaxed
online algorithm that is only subjected to fluid approximations of the
stochastic elements in the problem. The output of this algorithm serves as a
guide for the final algorithm. This leads to a principled approach for
seamlessly addressing stochastic elements (such as reusability, customer
choice, and combinations thereof) in online resource allocation problems, that
may be useful more broadly.
