• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.4
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• pp.19-35
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• 2007

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.

• Journal of Korean Society of Transportation
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• v.26 no.1
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• pp.103-112
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• 2008

In the feasibility analysis, Braess' Paradox results in the negative social benefit in spite of adding transportation facilities. Consequently, it has been difficult to judge on the investment of SOC projects. This research aims to analyze the Braess' Paradox in the feasibility analysis and to seek a remedy for the Paradox. Several experiments were conducted on the simple network under the various conditions. From the experiments, following findings were validated: Braess' Paradox occurred only if travel demands met within certain intermediate range. In terms of traffic assignment method, the SO was more likely to reduce the effect of the Braess' Paradox than the UE. However, the Braess' Paradox in the benefit of operating cost saving occurred in all cases and the paradox in the total benefit continued. In order to solve the problem, new link cost function considered travel time and operating cost simultaneously were suggested. As a result, the negative benefit was significantly decreased in the UE case and total negative benefit was no longer shown in the SO case through the analysis.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.123-138
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• 2009

This study examined the first- and second-best pricing by stable dynamics in congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. The first-best pricing in user equilibrium models introduces user-equilibrium in the system-equilibrium by tolling the difference between the marginal social cost and the marginal private cost on each link. Nevertheless, the second-best pricing, which levies the toll on some, but not all, links, is relevant from the practical point of view. In comparison with the user equilibrium model, the stable dynamic model provides a solution equivalent to system-equilibrium if it is focused on link flows. Therefore the toll interval on each link, which keeps up the system-equilibrium, is more meaningful than the first-best pricing. In addition, the second-best pricing in stable dynamic models is the same as the first-best pricing since the toll interval is separately given by each link. As an effect of congestion pricing in stable dynamic models, we can remove the inefficiency of the network with inefficient Braess links by levying a toll on the Braess link. We present a numerical example applied to the network with 6 nodes and 9 links, including 2 Braess links.