MODELING TRANSPORTATION NETWORKS VIA PRINCIPLES OF OPTIMALITY

This chapter presents different models and a brief review of the literature about the applicability of notions of optimality in the modeling of the large-scale properties of transportation networks. The models discussed are to a large extent only idealizations of real transportation networks and focus on their general, large-scale properties. However, an attempt is be made to underline what specific characteristics of real transportation networks have inspired our modeling effort.

[1]  Richie Khandelwal,et al.  PATTERNS IN NATURE , 2005 .

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

[3]  Alessandro Vespignani,et al.  The effects of spatial constraints on the evolution of weighted complex networks , 2005, physics/0504029.

[4]  Michael T. Gastner,et al.  Price of anarchy in transportation networks: efficiency and optimality control. , 2007, Physical review letters.

[5]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[6]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[7]  J R Banavar,et al.  Topology of the fittest transportation network. , 2000, Physical review letters.

[8]  P. Prusinkiewicz,et al.  Modeling and visualization of leaf venation patterns , 2005, ACM Trans. Graph..

[9]  R. Ferrer i Cancho,et al.  Scale-free networks from optimal design , 2002, cond-mat/0204344.

[10]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

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

[13]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Johannes Berg,et al.  Correlated random networks. , 2002, Physical review letters.

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

[16]  Alexandre Arenas,et al.  Optimal network topologies for local search with congestion , 2002, Physical review letters.

[17]  Alessandro Flammini,et al.  Universality Classes of Optimal Channel Networks , 1996, Science.

[18]  Anna Nagurney,et al.  On a Paradox of Traffic Planning , 2005, Transp. Sci..

[19]  N Mathias,et al.  Small worlds: how and why. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[21]  B. Palsson,et al.  Genome-scale models of microbial cells: evaluating the consequences of constraints , 2004, Nature Reviews Microbiology.

[22]  Hans Jürgen Prömel,et al.  The Steiner Tree Problem , 2002 .

[23]  Andrea Rinaldo,et al.  Network structures from selection principles. , 2004, Physical review letters.