The Evaluation of Data Fitting Approaches for Speed/Flow Density Relationships
DOI:
https://doi.org/10.17815/CD.2024.177Keywords:
Data fitting, Speed/Flow Density Relationship, Pedestrian Dynamics, Traffic DynamicsAbstract
This paper presents guidance on data-fitting approaches in the context of pedestrian and evacuation dynamics research. In particular, it examines parametric and non-parametric regression techniques for analysing speed/flow density relationships. Parametric models assume predefined functional forms, while non-parametric models provide flexibility to capture complex relationships. This paper evaluates a range of traditional statistical approaches and machine-learning techniques. It emphasises the importance of weighting unbalanced datasets to enhance model accuracy. Practical applications are illustrated using traffic and pedestrian evacuation data.
This paper is intended to stimulate discussion on best practices for developing, calibrating, and testing macroscopic and microscopic evacuation models. It does not prescribe a one-size-fits-all solution for evacuation data fitting approaches, but it provides an overview of existing methods and analyses their advantages and limitations.
References
Geroliminis, N., Sun, J.: Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transportation Research Part B: Methodological 45, 605-617 (2011). doi:10.1016/j.trb.2010.11.004
Cepolina, E.M.: Phased evacuation: An optimisation model which takes into account the capacity drop phenomenon in pedestrian flows. Fire Safety Journal 44, 532-544 (2009). doi:10.1016/j.firesaf.2008.11.002
Lighthill, M.J., Whitham, G.B.: On kinematic waves II. a theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 229, 317-345 (1955). doi:10.1098/rspa.1955.0089
Richards, P.I.: Shock waves on the highway. Operations Research 4, 42-51 (1956). doi:10.1287/opre.4.1.42
Predtechenskii, V.M., Milinskiĭ, A.I.: Planning for foot traffic flow in buildings. The National Bureau of Standards, U.S. Dept. of Commerce, and the National Science Foundation, Washington, DC (1978)
Gwynne, S.M.V., Rosenbaum, E.R.: Employing the hydraulic model in assessing emergency movement. In: SFPE Handbook of Fire Protection Engineering, pp. 2115-2151. Springer New York (2016). doi:10.1007/978-1-4939-2565-0textunderscore59
Najmanová, H., Ronchi, E.: Data for: Experimental data about the evacuation of preschool children from nursery schools, Part II: Movement characteristics and behaviour (2023). doi:10.5281/ZENODO.7377045
Rohaert, A., Kuligowski, E.D., Ardinge, A., Wahlqvist, J., Gwynne, S.M., Kimball, A., Noureddine Bénichou, Ronchi, E.: Dataset of traffic dynamics during the 2019 Kincade Wildfire Evacuation (2022). doi:10.5281/ZENODO.7410114
Rohaert, A., Araghi, N.J., Kuligowski, E.D., Ronchi, E.: Dataset of traffic dynamics during the 2020 Glass Wildfire Evacuation (2023). doi:10.5281/ZENODO.7483487
Rohaert, A.: Data fitting script for speed/flow density relationships (2024). doi:10.5281/zenodo.10990917
Greenshields, B., Bibbins, J., Channing, W., Miller, H.: A study of traffic capacity. Highway Research Board proceedings (1935)
Older, S.J.: Movement of pedestrians on footways in shopping streets. Traffic Engineering & Control 10, 160 (1968)
Fruin, J.J.: Designing for pedestrians a level of service concept. Polytechnic University (1970)
Daganzo, C.F.: The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B: Methodological 28, 269-287 (1994). doi:10.1016/0191-2615(94)90002-7
Newell, G.F.: Nonlinear Effects in the Dynamics of Car Following. Operations Research 9(2), 209-229 (1961). doi:10.1287/opre.9.2.209
Franklin, R.: The structure of a traffic shock wave. Civil Engineering Pulb. Wks. Rev 56, 1186-1188 (1961)
Del Castillo, J.M., Benítez, F.G.: On the functional form of the speed-density relationship - Part I: General theory. Transportation Research Part B: Methodological 29, 373-389 (1995). doi:10.1016/0191-2615(95)00008-2
Weidmann, U.: Transporttechnik der Fussgänger: Transporttechnische Eigenschaften des Fussgängerverkehrs. Tech. rep., ETH Zurich (1993). doi:10.3929/ETHZ-B-000242008
Qu, X., Wang, S., Zhang, J.: On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models. Transportation Research Part B: Methodological 73, 91-102 (2015). doi:10.1016/j.trb.2015.01.001
Underwood, R.T.: Speed, volume and density relationships. Quality and Theory of Traffic Flow. A Symposium, Yale University Bureau of Highway Traffic pp. 141-188 (1961). Publisher: Bureau of Highway Traffic, Yale University
Rohaert, A., Janfeshanaraghi, N., Kuligowski, E., Ronchi, E.: The analysis of traffic data of wildfire evacuation: the case study of the 2020 Glass Fire. Fire Safety Journal 141 (2023). doi:10.1016/j.firesaf.2023.103909
Rohaert, A., Kuligowski, E.D., Ardinge, A., Wahlqvist, J., Gwynne, S.M., Kimball, A., Bénichou, N., Ronchi, E.: Traffic dynamics during the 2019 Kincade wildfire evacuation. Transportation Research Part D: Transport and Environment 116 (2023). doi:10.1016/j.trd.2023.103610
Najmanová, H., Ronchi, E.: Experimental data about the evacuation of preschool children from nursery schools, Part II: Movement characteristics and behaviour. Fire Safety Journal 139 (2023). doi:10.1016/j.firesaf.2023.103797
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research 12, 2825-2830 (2011)
Hoerl, A.E., Kennard, R.W.: Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics 12, 55-67 (1970). doi:10.1080/00401706.1970.10488634
Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20, 273-297 (1995). doi:10.1007/BF00994018
Muller, P., Parmigiani, G.: Optimal Design via Curve Fitting of Monte Carlo Experiments. Journal of the American Statistical Association 90, 1322-1322 (1995). doi:10.2307/2291522
Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press (2005). doi:10.7551/mitpress/3206.001.0001
Parzen, E.: Nonparametric Statistical Data Modeling. Journal of the American Statistical Association 74, 105-121 (1979). doi:10.1080/01621459.1979.10481621
Bode, N.W., Ronchi, E.: Statistical Model Fitting and Model Selection in Pedestrian Dynamics Research. Collective Dynamics 4 (2019). doi:10.17815/CD.2019.20
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York, NY (2013)
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Arthur Rohaert, Jonathan Wahlqvist, Hana Najmanová, Nikolai Bode, Enrico Ronchi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors contributing to Collective Dynamics agree to publish their articles under the Creative Commons Attribution 4.0 license.
This license allows:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material
for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Authors retain copyright of their work. They are permitted and encouraged to post items submitted to Collective Dynamics on personal or institutional websites and repositories, prior to and after publication (while providing the bibliographic details of that publication).
