2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163983The 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.14 pages, 7 figures, uses iopart12.clo and iopart.clsStatistical Mechanicstext