Signalized and Unsignalized Road Traffic Intersection Models: A Comprehensive Benchmark Analysis

Ibrahima Ba; Antoine Tordeux

doi:10.17815/CD.2023.144

Authors

Ibrahima Ba School of Safety Engineering and Mechanical Engineering, University of Wuppertal, Germany
Antoine Tordeux School of Safety Engineering and Mechanical Engineering, University of Wuppertal, Germany https://orcid.org/0000-0001-5077-0327

DOI:

https://doi.org/10.17815/CD.2023.144

Keywords:

Road traffic intersection, First-order model, Regulated intersection model , Unregulated intersection model, Monte Carlo simulation

Abstract

Road traffic flow models allow the development and testing of intelligent transportation solutions. Macroscopic intersection models are especially relevant for the simulation of large traffic networks. In this article, we study four first-order signalized and unsignalized intersection models. The two unsignalized approaches are the first-in-first-out (FIFO) model (roundabout-type intersection) and an optimal non-FIFO model (highway-type intersection). The optimal control operates upstream for the first signalized intersection model. It occurs downstream for the second signalized model. All four models satisfy the expected physical constraints of vehicle conservation, traffic demand, and assignment. The models are minimal and allow a comprehensible analysis of the results. We determine mathematical relationships between the intersection models and empirically analyze the performances using Monte Carlo simulations. The numerical simulations assume random demand, supply, and assignment. Besides average performances, the approach accounts for the flow ranges of variation. A benchmark analysis compares the intersection models. We observe that the optimal signalized intersection models overcome the performances of the FIFO model in congested states. They may even reach the performances of the idealistic non-FIFO model. Further applications for the four intersection models are discussed.

References

Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Physics Reports 329(4-6), 199-329 (2000). doi:10.1016/S0370-1573(99)00117-9

van Wageningen-Kessels, F., Van Lint, H., Vuik, K., Hoogendoorn, S.: Genealogy of traffic flow models. EURO Journal on Transportation and Logistics 4(4), 445-473 (2015). doi:10.1007/s13676-014-0045-5

Flötteröd, G., Rohde, J.: Operational macroscopic modeling of complex urban road intersections. Transportation Research Part B: Methodological 45(6), 903-922 (2011). doi:10.1016/j.trb.2011.04.001

Daganzo, C.F.: The cell transmission model, part II: network traffic. Transportation Research Part B: Methodological 29(2), 79-93 (1995). doi:10.1016/0191-2615(94)00022-R

Tampère, C.M., Corthout, R., Cattrysse, D., Immers, L.H.: A generic class of first order node models for dynamic macroscopic simulation of traffic flows. Transportation Research Part B: Methodological 45(1), 289-309 (2011). doi:10.1016/j.trb.2010.06.004

Garavello, M., Han, K., Piccoli, B., et al.: Models for vehicular traffic on networks, vol. 9. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2016)

Moel, E.E., Wynn, T.M., Oo, M.Z., Htaik, N.M.: Analysis of intersection traffic light management system in Mandalay city. In: 2020 International Conference on Advanced Information Technologies (ICAIT), pp. 170-175. IEEE (2020). doi:10.1109/ICAIT51105.2020.9261783

Lebacque, J.P.: First-order macroscopic traffic flow models: Intersection modeling, network modeling. In: Transportation and Traffic Theory. Flow, Dynamics and Human Interaction. 16th International Symposium on Transportation and Traffic TheoryUniversity of Maryland, College Park, pp. 365-386 (2005)

Herty, M., Klar, A.: Modeling, simulation, and optimization of traffic flow networks. SIAM Journal on Scientific Computing 25(3), 1066-1087 (2003). doi:10.1137/S106482750241459X

Goatin, P., Göttlich, S., Kolb, O.: Speed limit and ramp meter control for traffic flow networks. Engineering Optimization 48(7), 1121-1144 (2016). doi:10.1080/0305215X.2015.1097099

Coogan, S., Arcak, M., Kurzhanskiy, A.A.: Mixed monotonicity of partial first-in-first-out traffic flow models. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 7611-7616. IEEE (2016). doi:10.1109/CDC.2016.7799445

Göttlich, S., Herty, M., Ziegler, U.: Modeling and optimizing traffic light settings in road networks. Computers & Operations Research 55, 36-51 (2015). doi:10.1016/j.cor.2014.10.001

Wang, Y., Yang, X., Liang, H., Liu, Y., et al.: A review of the self-adaptive traffic signal control system based on future traffic environment. Journal of Advanced Transportation 2018, 1096123 (2018). doi:10.1155/2018/1096123

Simoni, M.D., Claudel, C.G.: A semi-analytic approach to model signal plans in urban corridors and its application in metaheuristic optimization. Transportmetrica B: Transport Dynamics 7(1), 185-201 (2017). doi:10.1080/21680566.2017.1370397

Kamalanathsharma, R.K., Rakha, H.A.: Multi-stage dynamic programming algorithm for eco-speed control at traffic signalized intersections. In: 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), pp. 2094-2099. IEEE (2013). doi:10.1109/ITSC.2013.6728538

Long, Q., Zhang, J.F., Zhou, Z.M.: Multi-objective traffic signal control model for traffic management. Transportation Letters 7(4), 196-200 (2015). doi:10.1179/1942787515Y.0000000002

Teknomo, K., Gardon, R.W.: Intersection analysis using the ideal flow model. In: 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), pp. 1-6. IEEE (2017). doi:10.1109/ITSC.2017.8317739

Gao, R., Liu, Z., Li, J., Yuan, Q.: Cooperative traffic signal control based on multi-agent reinforcement learning. In: Blockchain and Trustworthy Systems: First International Conference, BlockSys 2019, Guangzhou, China, December 7-8, 2019, Proceedings 1, pp. 787-793. Springer (2020). doi:10.1007/978-981-15-2777-7_65

Zhang, T., Jin, J., Yang, H., Guo, H., Ma, X.: Link speed prediction for signalized urban traffic network using a hybrid deep learning approach. In: 2019 IEEE Intelligent Transportation Systems Conference (ITSC), pp. 2195-2200. IEEE (2019). doi:10.1109/ITSC.2019.8917509

Li, D., Wu, J., Xu, M., Wang, Z., Hu, K.: Adaptive traffic signal control model on intersections based on deep reinforcement learning. Journal of Advanced Transportation 2020, 1-14 (2020). doi:10.1155/2020/6505893

Paul, A., Mitra, S.: Deep reinforcement learning based traffic signal optimization for multiple intersections in ITS. In: 2020 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), pp. 1-6. IEEE (2020). doi:10.1109/ANTS50601.2020.9342819

Giraka, O., Selvaraj, V.K.: Short-term prediction of intersection turning volume using seasonal ARIMA model. Transportation letters 12(7), 483-490 (2020). doi:10.1080/19427867.2019.1645476

Costeseque, G., Lebacque, J.P.: Intersection modeling using a convergent scheme based on hamilton-jacobi equation. Procedia-Social and Behavioral Sciences 54, 736-748 (2012). doi:10.1016/j.sbspro.2012.09.791

Yperman, I., Logghe, S., Immers, B.: The link transmission model: An efficient implementation of the kinematic wave theory in traffic networks. In: Proceedings of the 10th EWGT Meeting, vol. 24, pp. 122-127 (2005)

Mueller, J., Claudio, D.: Simulating unsignalized intersection right-of-way. In: Proceedings of the Winter Simulation Conference 2014, pp. 2092-2100. IEEE (2014). doi:10.1109/WSC.2014.7020054

Ge, Y.E., Zhou, X.: An alternative definition of dynamic user optimum on signalised road networks. Journal of Advanced Transportation 46(3), 236-253 (2012). doi:10.1002/atr.207

Bedini, A., Zhang, L., Garoni, T.M.: A case study of a continuous flow intersection and its impact on public transport. In: 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), pp. 959-964. IEEE (2017). doi:10.1109/ITSC.2017.8317892

Han, K., Gayah, V.V., Piccoli, B., Friesz, T.L., Yao, T.: On the continuum approximation of the on-and-off signal control on dynamic traffic networks. Transportation Research Part B: Methodological 61, 73-97 (2014). doi:10.1016/j.trb.2014.01.001

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM Journal on scientific computing 16(5), 1190-1208 (1995). doi:10.1137/0916069

Bhouri, N., Aron, M., Lebacque, J.P., Haj-Salem, H.: Effectiveness of travel time reliability indicators in the light of the assessment of dynamic managed lane strategy. Journal of Intelligent Transportation Systems 21(6), 492-506 (2017). doi:10.1080/15472450.2017.1327815

Manseur, F., Farhi, N., Van Phu, C.N., Haj-Salem, H., Lebacque, J.P.: Robust routing, its price, and the tradeoff between routing robustness and travel time reliability in road networks. European Journal of Operational Research 285(1), 159-171 (2020). doi:10.1016/j.ejor.2018.10.053

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(1178), 317-345 (1955). doi:10.1098/rspa.1955.0089

Richards, P.I.: Shock waves on the highway. Operations Research 4(1), 42-51 (1956). doi:10.1287/opre.4.1.42

Tordeux, A., Roussignol, M., Lebacque, J.P., Lassarre, S.: A stochastic jump process applied to traffic flow modelling. Transportmetrica A: Transport Science 10(4), 350-375 (2014). doi:10.1080/23249935.2013.769648