Macroscopic traffic flow in multiple-loop networks

Abstract

We present a network model for traffic flow on multiple-loop lines with a single intersection. We investigate the macroscopic traffic flow and fundamental diagram in the multiple-loop network. We propose a graph representation for traffic flow on multiple-loop lines with an intersection. The dynamic equations of vehicular densities on multiple-loop networks are derived by using the graph representation. Vehicular densities approach stable equilibrium values after long times irrespective of initial densities. The equilibrium densities and currents (flows) are obtained analytically for traffic flow on double-loop lines. Also, we obtain the equilibrium densities and currents (flows) on multiple-loop networks numerically. We show how the fundamental diagram depends on the fraction of loop-changing vehicles.