Theoretical study of network junction models for totally asymmetric exclusion processes with interacting particles

Biological transport phenomena frequently exhibit complex network behavior when several molecular fluxes converge to special junctions from which another fluxes move out in different directions. Similar behavior is also observed in vehicular transport. Stimulated by these observations, we developed a theoretical framework to investigate network junction models of totally asymmetric simple exclusion processes with interacting particles. Utilizing a two-site cluster mean field framework that takes into account some correlations in the system, stationary dynamic properties, such as phase diagrams, density profiles and correlations profiles, are explicitly evaluated. It is found that the number of stationary phases strongly depend on the number of segments that come and leave the network junction. The inter-particle interactions also have a strong effect of dynamic properties of the system. Our method can be extended to the systems with several junctions. All theoretical predictions are in good agreement with extensive Monte Carlo computer simulations.