Traffic flow dynamics and oscillation control in conserved fractal networks

Abstract

Traffic control serves as an indispensable component in optimizing the traffic flow, especially on networks. To analyze the varied complexity of traffic dynamics, the percolation backbone fractal network is characterized via cell-transmission model. Taking into account a generalized flow-density relation, dynamic model is modified to scrutinize the impact of transition rates on traffic flow in a conserved network. The macroscopic fundamental diagrams attained through numerical simulation are investigated for homogeneous as well as heterogeneous transition rates. For first-generation fractal network, unimodal or bimodal traffic currents are observed with respect to mean density. Further, for second-generation fractal network, two types of density waves are observed depending upon the number of vehicles present in system: uniform equilibrium state and oscillatory state. It is reported that the transition rates corresponding to singly connected nodes can control the traffic dynamics to ensure a uniform stationary flow, which cannot be achieved via the doubly connected and quadruple-connected nodes.