Modeling heterogeneity in an open percolation backbone fractal traffic network

Urban road networks play a prominent role to facilitate the movement of vehicles. The network is connected by different roads and has a heterogeneous nature. The road networks have different capacities and different transition rates. In a real traffic scenario, the vehicular density is primarily influenced by the capacity of the road. When the capacity of the road is less, the density of vehicles decreases. Also, the transition rate (the number of vehicles entering the road) affects the traffic flow. Thus, to study the heterogeneity of roads in an open network, a percolation-backbone fractal network is considered. The fractal network is described with the help of a cell-transmission graph. The density equations were presented using the speed-matching model with the consideration of capacity and transition rate. The fundamental diagrams were obtained and it is observed how macroscopic fundamental diagram (MFD) varies with different cases of capacity and transition rate. To study traffic dynamics more realistically, an open network is considered. It is found that the traffic flow is affected significantly by the changes in the capacity and transition rate.