On uniqueness and proportionality in multi-class equilibrium assignment |
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Institution: | 1. Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing, 211189, China;2. Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States;3. School of Civil and Environmental Engineering, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States |
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Abstract: | Over the past few years, much attention has been paid to computing flows for multi-class network equilibrium models that exhibit uniqueness of the class flows and proportionality (Bar-Gera et al., 2012). Several new algorithms have been developed such as bush based methods of Bar-Gera (2002), Dial (2006), and Gentile (2012) that are able to obtain very fine solutions of network equilibrium models. These solutions can be post processed (Bar-Gera, 2006) in order to ensure proportionality and class uniqueness of the flows. Recently developed, the TAPAS, algorithm (Bar Gera, 2010) is able to produce solutions that have proportionality embedded, without requiring post processing. It was generally accepted that these methods for solving UE traffic assignment are the only way to obtain unique path and class link flows. The purpose of this paper is to show that the linear approximation method and some of its variants satisfy these conditions as well. In addition, some analytical results regarding the relation between steps of the linear approximation algorithm and the path flows entropy are presented. |
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Keywords: | Network equilibrium Path flows entropy Uniqueness of path flows Proportionality |
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