Impact of detour on traffic flow in branching Koch curve network with bottleneck

Abstract

There are various routes with and without detours in city traffic network with a complex connectivity. Branching Koch curve fractal has such complex connectivity with singly, doubly, and multiply connecting links. We consider branching Koch curve as a city traffic network. We study the effect of detour routes (bypasses) on macroscopic traffic flow in branching Koch curve network with a bottleneck. The bottleneck effect depends on whether or not there are detour routes. We propose a mathematical dynamic model for the traffic flow with a bottleneck in the directed Koch curve network. The macroscopic dynamic equations of vehicular densities are derived in the Koch curve network. Vehicular densities and currents are obtained at all roads in the network by solving the density equations numerically. The fundamental diagrams (flow-density relations) are derived. The traffic currents (flows) depend highly on the position of the bottleneck due to the connectivity of the fractal network. It is shown where and how traffic congestion is induced by the bottleneck on the directed fractal network.