Abstract:
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 backand-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.
