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A Model for Detecting Braess Paradox in General Transportation Networks  

Park, Koo-Hyun (홍익대학교 정보산업공학과)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.32, no.4, 2007 , pp. 19-35 More about this Journal
Abstract
This study is for detecting the Braess Paradox by stable dynamics in general transportation networks. Stable dynamics, suggested by Nesterov and de Palma[18], is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with user equilibrium model based on link latency function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on the congestion. Therefore it is expected to be an useful analysis tool for transportation planners. The phenomenon that increasing capacity of a network, for example creating new links, may decrease its performance is called Braess Paradox. It has been studied intensively under user equilibrium model with link latency function since Braess[5] demonstrated a paradoxical example. However it is an open problem to detect the Braess Paradox under stable dynamics. In this study, we suggest a method to detect the Paradox in general networks under stable dynamics. In our model, we decide whether Braess Paradox will occur in a given network. We also find Braess links or Braess crosses if a network permits the paradox. We also show an example how to apply it in a network.
Keywords
Braess Paradox; Stable Dynamics; Braess link; Braess Cross; User Equilibrium; Wardrop Principle; Selfish Routing; Transportation Networks;
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  • Reference
1 Beckmann, M., C. McGuire, and C. Winsten, Studies in Economics of Transportation, Yale University Press, New Haven, 1956
2 Burer, S. and D. Vandenbussche, 'A Finite Branch-and-Bound Algorithm for Nonconvex Quadratic Programming via Semidefinite Relaxation,' to appear in Mathematical Programming (Series A)
3 Dafermos, S. and A. Nagurney, 'On Some Traffic Equilibrium Theory Paradoxes,' Transportation Research B, Vol.18B, 1984, pp. 101-110
4 Fisk, C., 'More Paradoxes in the Equilibrium Assignment Problem,' Transportation Research B, Vol.13B, 1979, pp.305-309
5 Murchland, J.D., 'Braess's Paradox of Traffic Flow,' Transportation Research, Vol.4, 1970, pp.391-394   DOI
6 Nesterov, Y. and A. de Palma, 'Stable Dynamics in Transportation Systems,' CORE DP #00/27, University of Louvain, Belgium, 2000
7 Pas, E.I. and S.L. Principio, 'Braess' Paradox : Some New Insights,' Transportation Research B, Vol.31B, 1997, pp.265-276
8 Steiberg, R. and W. Zangwill, 'The Prevalence of Braess Paradox,' Transportation Science, Vol.17, 1983, pp.301-318   DOI   ScienceOn
9 U.S. Bureau of Public Roads, Traffic Assignment Manual, Washington, D.C., 1964
10 Nagurney, A., Network Economics : A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993
11 Friesz, T.L., 'Transportation Network Equilibrium, Design and Aggregation : Key Developments and Research Opportunities,' Transportation Research A, Vol.19A, 1985, pp.413-427
12 Bernstein, D.H. and T.E. Smith, 'Equilibria for Networks with Lower Semicontinuous Costs : With an Application to Congested Pricing,' Transportation Science, Vol.28, 1994, pp.221-235   DOI
13 Devarajan, S., 'A Note of Network Equilibrium and Noncooperative Games,' Transportation Research B, Vol.15B, 1981, pp. 421-426
14 Nesterov, Y. and A. de Palma, 'Park and Ride for the Day Period and Morning- Evening Commute,' Mathematical and Computational Models for Congestion Charging (Applied Optimization, Vol.101, Springer US), 2006, pp.143-157
15 Roughgarden, T., 'On the Severity of Braess's Paradox : Designing Networks for Selfish Users is Hard,' Journal of Computer and System Sciences, Vol.72, 2006, pp.922- 953   DOI   ScienceOn
16 Yang, H. and G.H. Bell, 'A Capacity Paradox in Network Design and How to Avoid It,' Transportation Research A, Vol.32A, 1998, pp.539-545
17 Braess, D., A. Nagurney and T. Wakolbinger, 'On a Paradox of Traffic Planning,' Transportation Science, Vol.39, 2005, pp.446-450. (Translated from the original German : Braess, D., 'Uber ein Paradoxon aus der Verkehrsplanung,' Unternehmensforschung, Vol.12, 1968, pp.258-268
18 Catoni, S. and S. Pallottino, 'Traffic Equilibrium Paradoxes,' Transportation Science, Vol.25, 1991, pp.240-244   DOI
19 Nesterov, Y. and A. de Palma, 'Stable Traffic Equilibria : Properties and Applications,' Optimization and Engineering, Vol.1, 2000, pp.29-50   DOI
20 'Updated BPR Parameters Using HCM Procedures,' cited from 'Traffic Engineering : Planning for Traffic Loads,' http://www.sierrafoot.org/local/gp/engineering.html
21 Frank, M., 'The Braess Paradox,' Mathematical Programming, Vol.20, 1981, pp.283- 302   DOI
22 Akamatsu, T. and B. Heydecker, 'Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks,' Transportation Science, Vol.37, 2003, pp.123-138   DOI   ScienceOn
23 Akamatsu, T., 'A Dynamic Traffic Assignment Paradox,' Transportation Research B, Vol.34B, 2000, pp.515-531
24 Harker, P.T., 'Multiple Equilibrium Behaviors on Networks,' Transportation Science, Vol.22, 1988, pp.39-46   DOI   ScienceOn
25 Wardrop, J.G., 'Some Theoretical Aspects of Road Traffic Research,' in Proceedings of the Institute of Civil Engineering, Part II, 1952, pp.325-378
26 Clarke, F.H., Optimization and Nonsmooth Analysis, J. Wiley and Sons, 1983