Multiple reentrance transitions in exclusion process with finite reservoir

The proposed study is motivated by the scenario of two-way vehicular traffic. We consider a totally asymmetric simple exclusion process in the presence of a finite reservoir along with the particle attachment, detachment, and lane-switching phenomena. The various system properties in terms of phase diagrams, density profiles, phase transitions, finite size effect, and shock position are analyzed, considering the available number of particles in the system and different values of coupling rate, by employing the generalized mean-field theory and the obtained results are detected to be a good match with the Monte Carlo simulation outcomes. It is discovered that the finite resources significantly affect the phase diagram for different coupling rate values, which leads to nonmonotonic changes in the number of phases in the phase plane for comparatively minor lane-changing rates and produces various exciting features. We calculate the critical value of the total number of particles in the system at which the multiple phases in the phase diagram appear or disappear. The competition between the limited particles, bidirectional motion, Langmuir kinetics, and particle lane-shifting behavior yields unanticipated and unique mixed phases, including the double shock phase, multiple reentrance and bulk-induced phase transitions, and phase segregation of the single shock phase.