The role of occupancy on traffic flow in a multiple-loop network

A dynamic model for traffic flow is proposed to analyze the impact of occupancy in a multiple-loop network with a single intersection. The graph representation of multiple-loop lines is obtained utilizing the cell-transmission model, and consequently, the density equations are derived. The macroscopic fundamental diagrams are investigated for different cases of occupancy and the fraction of vehicles. For the double-loop lines, equilibrium densities, traffic currents, and travel time are obtained theoretically and validated via simulation. It is observed that the equilibrium densities increase linearly against the mean density for an equal fraction of vehicles while the traffic currents remain symmetric, unlike the case of an unequal fraction of vehicles. The travel time varies inversely with respect to the occupancy of the loop line. Additionally, when the fraction of vehicles and occupancy at both nodes are different, a critical value of mean density is obtained below (above), in which the travel time at one node is less (more) than the other. To analyze the traffic flow on multiple-loop lines, stability analysis is conducted using the tools from cooperative theory and repelling boundaries. As a result, the vehicular densities converge to a unique equilibrium point irrespective of the initial densities in the multiple-loop network. The theoretical results agree well with the simulation results.