  The totally asymmetric simple exclusion process (TASEP) is a well studied
example of far-from-equilibrium dynamics. Here, we consider a TASEP with open
boundaries but impose a global constraint on the total number of particles. In
other words, the boundary reservoirs and the system must share a finite supply
of particles. Using simulations and analytic arguments, we obtain the average
particle density and current of the system, as a function of the boundary rates
and the total number of particles. Our findings are relevant to biological
transport problems if the availability of molecular motors becomes a
rate-limiting factor.
