Abstract
This paper proposes a strategy for optimal traffic sensor placement that do not require previous traffic measurements. Our approach could be used to determine how many sensors are needed and where to place them in order to obtain an estimation of the network traffic state. We first generate a traffic-flow dataset based on the transport network and some transportation demands. Specifically, the traffic flow is obtained by calculating the Wardrop equilibrium associated with each demand. Then, a neural network autoencoder with a \(l_1\) regularization is trained with that dataset. Two initialization strategies were used and their performances were compared and validated. The final neural network weights indicates where sensors should be placed and also gives the traffic flow reconstruction from those measurements. This approach was tested on several well-known traffic networks present in the literature, including a real large-scale network, with promising results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Derived data and source codes supporting the findings of this study are available from the corresponding author Jares N. on request.
References
An S, Ma L, Wang J (2020) Optimization of traffic detector layout based on complex network theory. Sustainability 12(5):2048. https://doi.org/10.3390/su12052048
Bengio Y (2012) Practical recommendations for gradient-based training of deep architectures. In: Neural networks: tricks of the trade. Springer, pp 437–478. https://doi.org/10.1007/978-3-642-35289-8_26
Bianco L, Confessore G, Gentili M (2006) Combinatorial aspects of the sensor location problem. Ann Oper Res 144(1):201–234
Bottou L (2010) Large-scale machine learning with stochastic gradient descent. In: Proceedings of COMPSTAT’2010. Springer, pp 177–186. https://doi.org/10.1007/978-3-7908-2604-3_16
Chollet F, et al (2015) Keras. https://keras.io
Chu C, Zhmoginov A, Sandler M (2017) Cyclegan, a master of steganography. arXiv preprint arXiv:1712.02950
Codina E, Barceló J (2004) Adjustment of O–D trip matrices from observed volumes: an algorithmic approach based on conjugate directions. Eur J Oper Res 155(3):535–557
Codina E, Montero J (2006) Approximation of the steepest descent direction for the O–D matrix adjustment problem. Ann Oper Res 144:329–362
Dial RB (2006) A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration. Transp Res Part B Methodol 40(10):917–936
for Research Core Team TN (Accessed October, 29, 2021) Transportation networks for research. https://github.com/bstabler/TransportationNetworks
Lotito PA (2006) Issues in the implementation of the DSD algorithm for the traffic assignment problem. Eur J Oper Res 175(3):1577–1587. https://doi.org/10.1016/j.ejor.2005.02.029
Lotito P, Mancinelli E, Quadrat JP (2005) Traffic assignment and Gibbs–Maslov semirings. In: Idempotent mathematics and mathematical physics, contemporary mathematics. AMS, pp 209–220
Lundgren JT, Petersen A (2008) A heuristic for the bilevel origin-destination-matrix estimation problem. Transp Res B 42:339–354
Mitradjieva M, Lindberg PO (2013) The stiff is moving-conjugate direction Frank–Wolfe methods with applications to traffic assignment. Transp Sci 47(2):280–293
Ortúzar J, Willumsen L (2001) Modelling transport. Wiley, New York
Owais M (2022) Traffic sensor location problem: three decades of research. Expert Syst Appl 118134
Owais M, Moussa GS, Hussain KF (2020) Robust deep learning architecture for traffic flow estimation from a subset of link sensors. J Transp Eng Part A Systems 146(1):04019055
Patriksson M, Rockafellar RT (2003) Sensitivity analysis of aggregated variational inequality problems, with application to traffic equilibria. Transp Sci 37(1):56–68
Smith LN, Topin N (2019) Super-convergence: very fast training of neural networks using large learning rates. In: Artificial intelligence and machine learning for multi-domain operations applications. SPIE, pp 369–386. https://doi.org/10.1117/12.2520589
Spiess H (1990) A gradient approach for the OD-matrix adjustment problem. CRT Pub No 693, Centre de Recherche sur les Transports
Steenbrink PA et al (1974) Optimization of transport networks. Wiley, London
Walpen J, Mancinelli EM, Lotito PA (2015) A heuristic for the OD matrix adjustment problem in a congested transport network. Eur J Oper Res 242:807–819
Walpen J, Mancinelli EM, Lotito PA et al (2020) The demand adjustment problem via inexact restoration method. Comput Appl Math 39:204
Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civ Eng Part II 1:325–378
Acknowledgements
This work was supported by CONICET under PIP 11220150100500CO and PIP 11220200100815CO; SECyT-UNC under PID 33620180100326CB; ANPCYT under PICT 2019-2886; and UNR under Grant No. 80020190300050UR.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors report there are no competing interests to declare.
Additional information
Communicated by Hector Cancela.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Jares, N., Fernández, D., Lotito, P.A. et al. Traffic sensor location using Wardrop equilibrium. Comp. Appl. Math. 42, 290 (2023). https://doi.org/10.1007/s40314-023-02426-3
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40314-023-02426-3