Urban road network evolution mechanism based on the ‘direction preferred connection’ and ‘degree constraint’

The urban road network is a complex system that exhibits the properties of self-organization and emergence. Recent theoretical and empirical studies have mainly focused on the structural properties of the urban road networks. This research concentrates on some important parameters such as degree, average degree, meshedness coefficient, betweeness, etc. These parameters of the real road network exhibit specific statistical properties. Some studies show that perhaps these specific statistical properties are caused by a compromise mechanism of the formation of a minimum spanning tree and the greedy triangulation. Inspired by these results, we propose a principle to construct the network (we call it a MG network in this paper) whose structure is located between the minimum spanning tree and the greedy triangulation at first. The structural properties of the MG network are analyzed. We find the formation mechanism of the MG network cannot explain the urban road network evolution well. Then, based on the formation mechanism of the MG network, we add the ‘direction preferred connection’ and ‘degree constraint’ principles to the urban road network evolution simulation process. The result of the simulation network turns out to be a planar network that is in accordance with reality. Compared with the real road network’s structural properties, we find the simulation results are so consistent with it. It indicates the validation of the model and also demonstrates perhaps the ‘direction preferred connection’ and ‘degree constraint’ principle can explain the urban road network evolution better.

[1]  David M Levinson,et al.  The emergence of hierarchy in transportation networks , 2005 .

[2]  B. Jiang.  A topological pattern of urban street networks: Universality and peculiarity , 2007, physics/0703223.

[3]  Alessandro Flammini,et al.  Optimal traffic networks , 2006, ArXiv.

[4]  J. Hyman,et al.  Scaling laws for the movement of people between locations in a large city. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  A. P. Masucci,et al.  Random planar graphs and the London street network , 2009, 0903.5440.

[6]  V. Latora,et al.  Structural properties of planar graphs of urban street patterns. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Dirk Helbing,et al.  Scaling laws in the spatial structure of urban road networks , 2006 .

[8]  Bei-Bei Su,et al.  A game theory model of urban public traffic networks , 2007 .

[9]  J. S. Andrade,et al.  Modeling urban growth patterns with correlated percolation , 1998, cond-mat/9809431.

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[11]  Christophe Claramunt,et al.  Topological Analysis of Urban Street Networks , 2004 .

[12]  Hans J. Herrmann,et al.  Traffic gridlock on complex networks , 2012 .

[13]  Nan Li,et al.  STATISTICAL PROPERTIES OF URBAN GROUND BUS-TRANSPORT NETWORKS FROM SELF-AVOIDING RANDOM WALKS , 2007 .

[14]  Li-Jie Zhang,et al.  Network evolution by nonlinear preferential rewiring of edges , 2011 .

[15]  Hernán D. Rozenfeld,et al.  The Area and Population of Cities: New Insights from a Different Perspective on Cities , 2009, 1001.5289.

[16]  V. Palchykov,et al.  Public transport networks: empirical analysis and modeling , 2008, 0803.3514.

[17]  David Levinson,et al.  Self-Organization of Surface Transportation Networks , 2006, Transp. Sci..

[18]  Roger Guimerà,et al.  Modeling the world-wide airport network , 2004 .

[19]  Guy Theraulaz,et al.  Topological patterns in street networks of self-organized urban settlements , 2006 .

[20]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[21]  Adrian Bejan,et al.  Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point , 1998 .

[22]  V. Latora,et al.  Centrality measures in spatial networks of urban streets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Alessandro Flammini,et al.  Modeling urban street patterns. , 2007, Physical review letters.

[24]  Ziyou Gao,et al.  SIMULATION OF TRAFFIC CONGESTION WITH SIR MODEL , 2004 .