Power-law Distribution in City-scale Traffic Simulation and Tree Structure in the Road Network

Abstract

Urban-scale traffic simulations using a digital map of Kobe City showed a power-law behaviors in the distribution of traffic volume relative to the number of road segments. In order to clarify the origin of this behavior, simulations were conducted using artificially generated random and Manhattan-type road networks. The behavior was observed in the former, but not in the latter. Similar results were obtained when the simulation was performed with uniform OD (Origin and Destination) distributions on the map of Kobe City. We also found similar results only with shortest path search without simuation for each uniformly randomized OD distribution. These suggest that the road network itself is causing the behavior. To understand its origin, we assumed a mathematical toy model in which a tree structure is embedded in the city of Kobe and random networks and confirmed the behavior appears on Cayley trees and a road network with bottlenecks which generated from the lattice networks based on the bond percolation theory. We also confirmed that such tree structures and bottlenecks are embedded in the simulation results above and each produces a power-law like distribution. The relationship between these facts and the origin of the power law is discussed.