Urban Transport and Traffic Systems: An Approach to the Shortest Path Problem and Network Flow Through Colored Graphs
Urban transport systems generally present complex topologies and constraints, and consequently model them and propose solutions that are not simple. Because of the importance of proposing solutions that improve urban mobility and the people’s quality of l
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Urban Transport and Traffic Systems: An Approach to the Shortest Path Problem and Network Flow Through Colored Graphs Juliana Verga Shirabayashi, Akebo Yamakami, Ricardo Coelho Silva, and Wesley Vagner Inês Shirabayashi
Abstract Urban transport systems generally present complex topologies and constraints, and consequently model them and propose solutions that are not simple. Because of the importance of proposing solutions that improve urban mobility and the people’s quality of life, in this work, we propose two algorithms applicable to transport network and traffic systems. The first algorithm approaches the shortest path problem in colored graphs. In this case, the graphs’ coloration is used in a different and innovative form: each transport mode is represented by a color (label) and various edges exist between two nodes of the graph (each edge represents a transport mode). The second algorithm, in addition to the coloration used to find the shortest path, considers the multimodal flow network problem by an incremental process. Some examples are presented and the behavior of both algorithms is shown.
J. V. Shirabayashi () Federal University of Paraná, Jandaia do Sul, PR, Brazil e-mail: [email protected] A. Yamakami Department of Systems and Energy, FEEC, University of Campinas, Campinas, SP, Brazil e-mail: [email protected] R. C. Silva Department of Statistics and Applied Mathematics, Federal University of Ceará, Fortaleza, CE, Brazil e-mail: [email protected] W. V. I. Shirabayashi Department of Mathematics, State University of Maringá, Maringá, PR, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 V. N. Coelho et al. (eds.), Smart and Digital Cities, Urban Computing, https://doi.org/10.1007/978-3-030-12255-3_3
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3.1 Introduction The fast growth of cities has brought with it the need for a better plan and to make urban mobility more efficient, that is, fully influenced by transport systems. Besides, in the last few years, the called Smart City became an object of study in the most diverse areas of knowledge, with the objective of becoming big centers, integrated, better planned, sustainable, and with a better quality of life. In this context, we study how the planning of transport networks is very important and is one of the principal problems of Smart Cities. Urban transport networks are characterized by traffic jams and their corresponding impact on individual accessibility, air pollution, and the development of economic urban activities [14]. In most cities, people’s workplaces are often far away from home, which means that they use more than one mode of transportation to move from their home to the workplace. Transport networks are considered multimodal when they have various transport modes, such as bus, subway, and train. Thus, passengers can use various transport modes in one journey and are usually not willing to change means of transportation often. In the literature, there are several works that approach multimodal network tran
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