  We consider a model of priced resource sharing that combines both queueing
behavior and strategic behavior. We study a priority service model where a
single server allocates its capacity to agents in proportion to their payment
to the system, and users from different classes act to minimize the sum of
their cost for processing delay and payment. As the exact processing time of
this system is hard to compute, we introduce the notion of heavy traffic
equilibrium as an approximation of the Nash equilibrium, derived by considering
the asymptotic regime where the system load approaches capacity. We discuss
efficiency and revenue, and in particular provide a bound for the price of
anarchy of the heavy traffic equilibrium.
