  Using Monte Carlo simulations and a domain wall theory, we discuss the effect
of coupling several totally asymmetric simple exclusion processes (TASEPs) to a
finite reservoir of particles. This simple model mimics directed biological
transport processes in the presence of finite resources, such as protein
synthesis limited by a finite pool of ribosomes. If all TASEPs have equal
length, we find behavior which is analogous to a single TASEP coupled to a
finite pool. For the more generic case of chains with different lengths,
several unanticipated new regimes emerge. A generalized domain wall theory
captures our findings in good agreement with simulation results.
