Bistability and the emergence of oscillation in a multiple-loop traffic network

Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To study the distinct features and complexities of vehicular flow, a network consisting of multiple-loops with a single intersection is considered a directed weighted graph. The governing equations for individual loop densities are derived using the principle of mass conservation, considering a data-driven flow-density relationship. Firstly, we examine the stability of a double-loop network and explore the traffic behavior using the macroscopic fundamental diagram (MFD) for different sets of parameters. Utilizing popular techniques of nonlinear dynamics, the existence of bistability, bifurcations, oscillations, and switching dynamics is demonstrated in the case of the triple-loop network. Further, bistability is characterized by plotting the basin of attraction diagram for the coexisting attractors. Our study reveals that an increase in the number of loop lines enriches the dynamical properties of vehicular traffic flow. It is observed that depending upon the initial density configuration, a loop network can show various phases, namely free flow, stop-and-go traffic jams, and loop congestion. Additionally, we show the presence of period-2 orbits in the case of the quadruple-loop system.