Exclusion process on two intersecting lanes with constrained resources: Symmetry breaking and shock dynamics

Exclusion processes on a roundabout traffic model with constrained resources

Motivated by the vehicular traffic phenomenon at roundabouts, we examine how the limited availability of resources affects the movement of two distinct types of particles on bidirectional lanes connected by two bridges, with each bridge specifically designated for the transportation of one species. To provide a theoretical ground for our findings, we employ a mean-field framework and successfully validate them through dynamic Monte Carlo simulations. Based on the theoretical analysis, we analytically derive various stationary properties, such as the particle densities, phase boundaries, and particle currents, for all the possible symmetric as well as asymmetric phases. The qualitative as well as quantitative behavior of the system is significantly affected by the constraint on the number of resources. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. Analytical arguments enable the identification of several critical values for the total number of particles, leading to a qualitative change in the phase diagrams. The interplay of the finite resources and the bidirectional transport yields unanticipated and unusual features such as back-and-forth transition, the presence of two congested phases where particle movement is halted, as well as shock phases induced by boundaries and the bulk of the system. Also, it is found that spontaneous symmetry-breaking phenomena are induced even for very few particles in the system. Moreover, we thoroughly examine the location of shocks by varying the parameters controlling the system's boundaries, providing insights into possible phase transitions.

Interplay of reservoirs in a bidirectional system

Motivated by the interplay of multiple species in several real world transport processes, we propose a bidirectional totally asymmetric simple exclusion process with two finite particle reservoirs regulating the inflow of oppositely directed particles corresponding to two different species. The system's stationary characteristics, such as densities, currents, etc., are investigated using a theoretical framework based on mean-field approximation and are supported by extensive Monte Carlo simulations. The impact of individual species populations, quantified by filling factor, has been comprehensively analyzed considering both equal and unequal conditions. For the equal case, the system exhibits the spontaneous symmetry-breaking phenomena and admits both symmetric as well as asymmetric phases. Moreover, the phase diagram exhibits a different asymmetric phase and displays a nonmonotonic variation in the number of phases with respect to the filling factor. For unequal filling factors, the phase schema can display at most five phases including a phase that shows maximal current for one of the species.