Exclusion process with scaled resources: Delocalized shocks and interplay of reservoirs

Abstract

In this paper we study a conserved system comprised of two directed lanes having identical dynamics and two reservoirs with scaled resources that are strategically connected to the boundaries of the lanes, forming a ringlike structure. The steady-state properties of the system have been analyzed in the framework of mean-field theory. Our findings display a rich behavior, emphasizing the nontrivial effects of incorporating two reservoirs. As a consequence, two distinct phases that admit delocalized shocks emerge and occupy a significant region in the phase diagram. Moreover in one of theses phases, each lane admits a delocalized shock whose movements are perfectly synchronized. In another phase, the single shock in the system may traverse both lanes or remain restricted to a single lane, depending upon the size of the system. All the findings are validated by Monte Carlo simulations.