Multilane bidirectional traffic in a strongly coupled exclusion model with constraint resources.

Abstract

Motivated by complex bidirectional transport processes that occur in various biological and physical systems, we examine a one-dimensional closed system comprising two parallel lanes under limited resources. One lane is characterized by driven diffusive transport, while the other supports solely unidirectional motion in the opposite direction, mutually coupled through strong coupling. The total number of particles in the system, quantified by the filling factor, regulates the inflow of particles onto the lanes. The stationary properties of the system are analyzed through both simple and vertical cluster mean-field approaches, complemented by boundary layer analysis to elucidate its detailed behavior. Our theoretical results demonstrate that, for any set of parameters, one of the lanes invariably resides in a phase of zero net particle flux, manifesting either in a completely empty or fully jammed state. Two distinct types of phase transitions are identified and characterized: bulk transitions and surface transitions. Notably, phases emerge that exhibit boundary layers in their density profiles near both boundaries. A distinctive feature of the interplay between lane coupling and bidirectional transport is the appearance of kink and dip in the boundary layers, which is scrutinized by using the residence time method and fixed point analysis. Furthermore, we investigate the dynamics of phases involving shock and its sensitivity to system parameters. All theoretical outcomes are corroborated through stochastic simulations based on the Gillespie algorithm and numerical technique.