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A Payne-Whitham model of urban traffic networks in the presence of traffic lights and its application to traffic optimisation (2401.04436v2)

Published 9 Jan 2024 in math.AP, cs.NA, math.DS, math.NA, and physics.soc-ph

Abstract: Urban road transport is a major civilisational and economic challenge, affecting the quality of life and economic activity. Addressing these challenges requires a multidisciplinary approach and sustainable urban planning strategies to mitigate the negative effects of traffic in cities. In this paper, we introduce an extension of one of the most popular macroscopic traffic simulation models, the Payne-Whitham model. We investigate how this model, originally designed to model highway traffic on straight road segments, can be adapted to more realistic conditions with arbitrary road network graphs and multiple intersections with traffic signals. Furthermore, we showcase the practical application of this extension in experiments aimed at optimising traffic signal settings. For computational reasons, these experiments involve the adoption of surrogate models for approximating our extended Payne-Whitham model, and subsequently, we utilise the Differential Evolution optimization algorithm, resulting in the identification of traffic signal settings that enhance the average speed of cars and decrease the total length of queues, thereby facilitating smoother traffic flow.

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References (33)
  1. Carlo Caligaris, Simona Sacone and Silvia Siri “On the Payne-Whitham Differential Model Stability Constraints in One-Class and Two-Class Cases” In Applied Mathematical Sciences 4, 2010, pp. 3795–3821
  2. “Support vector regression machines” In Advances in neural information processing systems 9, 1996
  3. Samah El-Tantawy, Baher Abdulhai and Hesham Abdelgawad “Multiagent Reinforcement Learning for Integrated Network of Adaptive Traffic Signal Controllers (MARLIN-ATSC): Methodology and Large-Scale Application on Downtown Toronto” In IEEE Conference on Intelligent Transportation Systems 14.3, 2013, pp. 1140–1150 IEEE DOI: 10.1109/TITS.2013.2255286
  4. Alexander Forrester, Andras Sobester and Andy Keane “Engineering design via surrogate modelling: a practical guide” John Wiley & Sons, 2008
  5. P. G. Gipps “A behavioural car-following model for computer simulation” In Transportation Research Part B: Methodological 15 Elsevier, 1981, pp. 105–111
  6. Ian Goodfellow, Yoshua Bengio and Aaron Courville “Deep learning” MIT press, 2016
  7. P. Gora “A genetic algorithm approach to optimization of vehicular traffic in cities by means of configuring traffic lights” In Emergent Intelligent Technologies in the Industry, 2011, pp. 1–10
  8. “Solving Traffic Signal Setting Problem Using Machine Learning” In 2019 6th International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), 2019, pp. 1–10 IEEE DOI: 10.1109/MTITS.2019.8883380
  9. Pawel Gora “Traffic Simulation Framework - a Cellular Automaton based tool for simulating and investigating real city traffic” In Recent Advances in Intelligent Information Systems, 2009, pp. 641–653 Springer
  10. Paweł Gora “A genetic algorithm approach to optimization of vehicular traffic in cities by means of configuring traffic lights” In Emergent Intelligent Technologies in the Industry, 2011, pp. 1–10
  11. “State-of-the-art of vehicular traffic flow modelling” In Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 215, 2001, pp. 283–303 DOI: 10.1177/095965180121500402
  12. “Traffic signal optimization on a square lattice with quantum annealing” In Scientific Reports 11.1 Nature Publishing Group, 2021, pp. 1–12 DOI: 10.1038/s41598-021-82740-0
  13. “Traffic flow modeling of large-scale motorway networks using the macroscopic modeling tool METANET” In IEEE Transactions on Intelligent Transportation Systems 3.4, 2002, pp. 282–292 DOI: 10.1109/TITS.2002.806804
  14. D. Kraft “A Software Package for Sequential Quadratic Programming”, Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln: Forschungsbericht Wiss. Berichtswesen d. DFVLR, 1988 URL: https://books.google.at/books?id=4rKaGwAACAAJ
  15. M. J. Lighthill and G. B. Whitham “On kinematic waves II: a theory of traffic flow on long, crowded roads” In Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 229.1178 The Royal Society, 1955, pp. 317–345
  16. Michael G McNally “The Four-Step Model” In Handbook of Transport Modelling 1 Emerald Group Publishing Limited, 2007, pp. 35–53 DOI: 10.1108/9780857245670-003
  17. Michiel Manuel Minderhoud “Supported Driving: Impacts on Motorway Traffic Flow” Delft University Press, 1999
  18. “A cellular automaton model for freeway traffic” In Journal de Physique I 2.12 IOP Publishing, 1992, pp. 2221–2229
  19. John A Nelder and Roger Mead “A simplex method for function minimization” In The computer journal 7.4 The British Computer Society, 1965, pp. 308–313
  20. “Optimal traffic signal settings—II. A refinement of Webster’s method” In Transportation Research 7.3 Elsevier, 1973, pp. 269–292 DOI: 10.1016/0041-1647(73)90018-X
  21. OpenStreetMap contributors “Downloading data - OpenStreetMap Wiki” Accessed: 2023-12-19, https://wiki.openstreetmap.org/wiki/Downloading_data
  22. H.J. Payne “Models of freeway traffic and control” In Mathematical Models of Public Systems, Simulation Council Proceedings, 1971, pp. 51 –61
  23. Michael JD Powell “An efficient method for finding the minimum of a function of several variables without calculating derivatives” In The computer journal 7.2 Oxford University Press, 1964, pp. 155–162
  24. Ilya Prigogine “A Boltzmann-like Approach to the Statistical Theory of Traffic Flow” In Theory of Traffic Flow Amsterdam: Elsevier, 1961
  25. “Kinetic Theory of Vehicular Traffic” American Elsevier, 1971
  26. “Graph-based Sparse Neural Networks for Traffic Signal Optimization” In Proceedings of the 29th International Workshop on Concurrency, Specification and Programming, 2021, pp. 145–155
  27. “Graph-Based Sparse Neural Networks for Traffic Signal Optimization” In Concurrency, Specification and Programming. Studies in Computational Intelligence 1091 Springer, 2023 DOI: 10.1007/978-3-031-26651-5˙9
  28. John C. Strikwerda “Finite Difference Schemes and Partial Differential Equations, Second Edition” Society for IndustrialApplied Mathematics, 2004 DOI: 10.1137/1.9780898717938
  29. Bart Van Arem and Jeroen H Hogema “The Microscopic Simulation Model MIXIC 1.2”, 1995
  30. “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python” In Nature Methods 17, 2020, pp. 261–272 DOI: 10.1038/s41592-019-0686-2
  31. “CoLight: Learning Network-level Cooperation for Traffic Signal Control” In Proceedings of the 28th ACM International Conference on Information and Knowledge Management, 2019, pp. 1913–1922 ACM DOI: 10.1145/3357384.3357902
  32. G. B. Whitham “Linear and nonlinear waves” Reprint of the 1974 original, A Wiley-Interscience Publication, Pure and Applied Mathematics (New York) John Wiley & Sons, Inc., New York, 1999, pp. xviii+636
  33. Rainer Wiedemann “Simulation des Strassenverkehrsflusses” Institut für Verkehrswesen der Universität Karlsruhe, 1974

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