  We study non-monetary mechanisms for the fair and efficient allocation of
reusable public resources, i.e., resources used for varying durations. We
consider settings where a limited resource is repeatedly shared among a set of
agents, each of whom may request to use the resource over multiple consecutive
rounds, receiving utility only if they get to use the resource for the full
duration of their request. Such settings are of particular significance in
scientific research where large-scale instruments such as electron microscopes,
particle colliders, or telescopes are shared between multiple research groups;
this model also subsumes and extends existing models of repeated non-monetary
allocation where resources are required for a single round only.
  We study a simple pseudo-market mechanism where upfront we endow each agent
with a budget of artificial credits, proportional to the fair share of the
resource we want the agent to receive. The endowments thus define for each
agent her ideal utility as that which she derives from her favorite allocation
with no competition, but subject to getting at most her fair share of the
resource across rounds. Next, on each round, and for each available resource
item, our mechanism runs a first-price auction with a selective reserve,
wherein each agent submits a desired duration and a per-round-bid, which must
be at least the reserve price if requesting for multiple rounds; the bidder
with the highest per-round-bid wins, and gets to use the item for the desired
duration. We consider this problem in a Bayesian setting and show that under a
carefully chosen reserve price, irrespective of how others bid, each agent has
a simple strategy that guarantees she receives a $1/2$ fraction of her ideal
utility in expectation. We also show this result is tight, i.e., no mechanism
can guarantee that all agents get more than half of their ideal utility.
