COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS

Işık İlber Sırmatel

doi:10.18038/estubtda.1656397

EN

COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS

Abstract

Traffic modeling and control in large-scale urban road networks present significant challenges. The macroscopic fundamental diagram provides a means of formulating dynamical traffic models of such networks, thereby enabling the development of model-based design techniques for state estimation and feedback control. In this article we focus on the computational efficiency of macroscopic fundamental diagram-based nonlinear model predictive control schemes for perimeter control and route guidance actuated networks, which are macroscopic actuation methods involving traffic flow manipulation between adjacent network neighborhoods. A number of economic nonlinear model predictive control schemes, based on direct methods from the numerical optimal control literature, are implemented using a variety of nonlinear programming solvers. The computational efficiency of the schemes is evaluated via computer simulations of congestion control scenarios for macroscopic fundamental diagram-based network models with different numbers of regions using randomly generated traffic demand profiles. The results indicate that the proper pairing of direct methods and solvers yields significant improvements in computational efficiency for macroscopic fundamental diagram-based control schemes, thereby improving the real-time feasibility and, consequently, the field deployment potential of the resulting macroscopic road traffic flow control algorithms.

Keywords

Macroscopic fundamental diagram, Large-scale urban road networks, Traffic perimeter control, Route guidance, Model predictive control

Supporting Institution

Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Project Number

TÜBİTAK 2232 B - 121C076

Ethical Statement

All responsibility related to the article belongs to the author; financial support from TÜBİTAK does not mean that the article content is scientifically approved by TÜBİTAK.

Thanks

The author is supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK) through the 2232 B International Early Stage Researchers Program (project number: 121C076).

References

[1] Papageorgiou M, Diakaki C, Dinopoulou V, Kotsialos A, Wang Y. Review of road traffic control strategies. Proceedings of the IEEE, 2003; Dec; 91(12):2043-67. https://doi.org/10.1109/JPROC.2003.819610
[2] Godfrey JW. The mechanism of a road network. Traffic Engineering & Control. 1969; Nov;8(8). https://trid.trb.org/View/117139
[3] Geroliminis N, Daganzo CF. Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings. Transportation Research Part B: Methodological, 2008; Nov 1;42(9):759-70. https://doi.org/10.1016/j.trb.2008.02.002
[4] Loder A, Ambühl L, Menendez M, Axhausen KW. Understanding traffic capacity of urban networks. Scientific Reports, 2019; Nov 8;9(1):16283. https://doi.org/10.1038/s41598-019-51539-5
[5] Geroliminis N, Sun J. Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transportation Research Part B: Methodological, 2011; Mar 1;45(3):605-17. https://doi.org/10.1016/j.trb.2010.11.004
[6] Daganzo CF. Urban gridlock: Macroscopic modeling and mitigation approaches. Transportation Research Part B: Methodological, 2007; Jan 1;41(1):49-62. https://doi.org/10.1016/j.trb.2006.03.001
[7] Keyvan-Ekbatani M, Kouvelas A, Papamichail I, Papageorgiou M. Exploiting the fundamental diagram of urban networks for feedback-based gating. Transportation Research Part B: Methodological, 2012; Dec 1;46(10):1393-403. https://doi.org/10.1016/j.trb.2012.06.008
[8] Aboudolas K, Geroliminis N. Perimeter and boundary flow control in multi-reservoir heterogeneous networks. Transportation Research Part B: Methodological, 2013; Sep 1;55:265-81. https://doi.org/10.1016/j.trb.2013.07.003
[9] Haddad J, Mirkin B. Adaptive perimeter traffic control of urban road networks based on MFD model with time delays. International Journal of Robust and Nonlinear Control, 2016; Apr 1;26(6):1267-85. https://doi.org/10.1002/rnc.3502
[10] Kouvelas A, Saeedmanesh M, Geroliminis N. Enhancing model-based feedback perimeter control with data-driven online adaptive optimization. Transportation Research Part B: Methodological, 2017; Feb 1;96:26-45. https://doi.org/10.1016/j.trb.2016.10.011

[11] Haddad J, Shraiber A. Robust perimeter control design for an urban region. Transportation Research Part B: Methodological, 2014 Oct 1;68:315-32. https://doi.org/10.1016/j.trb.2014.06.010
[12] Zhong RX, Chen C, Huang YP, Sumalee A, Lam WH, Xu DB. Robust perimeter control for two urban regions with macroscopic fundamental diagrams: A control-Lyapunov function approach. Transportation Research Part B: Methodological, 2018; Nov 1;117:687-707. https://doi.org/10.1016/j.trb.2017.09.008
[13] Haddad J. Optimal perimeter control synthesis for two urban regions with aggregate boundary queue dynamics. Transportation Research Part B: Methodological, 2017; Feb 1;96:1-25. https://doi.org/10.1016/j.trb.2016.10.016
[14] Aalipour A, Kebriaei H, Ramezani M. Analytical optimal solution of perimeter traffic flow control based on MFD dynamics: A Pontryagin’s maximum principle approach. IEEE Transactions on Intelligent Transportation Systems, 2018; Oct 18;20(9):3224-34. https://doi.org/10.1109/TITS.2018.2873104
[15] Geroliminis N, Haddad J, Ramezani M. Optimal perimeter control for two urban regions with macroscopic fundamental diagrams: A model predictive approach. IEEE Transactions on Intelligent Transportation Systems, 2012; Nov 15;14(1):348-59. https://doi.org/10.1109/TITS.2012.2216877
[16] Ramezani M, Haddad J, Geroliminis N. Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control. Transportation Research Part B: Methodological, 2015; Apr 1;74:1-9. https://doi.org/10.1016/j.trb.2014.12.010
[17] Ni W, Cassidy M. City-wide traffic control: Modeling impacts of cordon queues. Transportation Research Part C: Emerging Technologies, 2020; Apr 1;113:164-75. https://doi.org/10.1016/j.trc.2019.04.024
[18] Sirmatel II, Geroliminis N. Stabilization of city-scale road traffic networks via macroscopic fundamental diagram-based model predictive perimeter control. Control Engineering Practice, 2021; Apr 1;109:104750. https://doi.org/10.1016/j.conengprac.2021.104750
[19] Genser A, Kouvelas A. Dynamic optimal congestion pricing in multi-region urban networks by application of a Multi-Layer-Neural network. Transportation Research Part C: Emerging Technologies, 2022; Jan 1;134:103485. https://doi.org/10.1016/j.trc.2021.103485
[20] Yildirimoglu M, Ramezani M. Demand management with limited cooperation among travellers: A doubly dynamic approach. Transportation Research Part B: Methodological, 2020; Feb 1;132:267-84. https://doi.org/10.1016/j.trb.2019.02.012
[21] Sirmatel II, Geroliminis N. Economic model predictive control of large-scale urban road networks via perimeter control and regional route guidance. IEEE Transactions on Intelligent Transportation Systems, 2017; Jun 30;19(4):1112-21. https://doi.org/10.1109/TITS.2017.2716541
[22] Menelaou C, Timotheou S, Kolios P, Panayiotou CG. Joint route guidance and demand management for real-time control of multi-regional traffic networks. IEEE Transactions on Intelligent Transportation Systems, 2021; May 18;23(7):8302-15. https://doi.org/10.1109/TITS.2021.3077870
[23] Saeedmanesh M, Kouvelas A, Geroliminis N. An extended Kalman filter approach for real-time state estimation in multi-region MFD urban networks. Transportation Research Part C: Emerging Technologies, 2021; Nov 1;132:103384. https://doi.org/10.1016/j.trc.2021.103384
[24] Sirmatel II, Geroliminis N. Nonlinear moving horizon estimation for large-scale urban road networks. IEEE Transactions on Intelligent Transportation Systems, 2019; Oct 14;21(12):4983-94. https://doi.org/10.1109/TITS.2019.2946324
[25] Saeedmanesh M, Geroliminis N. Clustering of heterogeneous networks with directional flows based on “Snake” similarities. Transportation Research Part B: Methodological, 2016; Sep 1;91:250-69. https://doi.org/10.1016/j.trb.2016.05.008
[26] Yildirimoglu, M., Ramezani, M. and Geroliminis, N, Equilibrium analysis and route guidance in large-scale networks with MFD dynamics. Transportation Research Part C: Emerging Technologies, 2015; 59, pp.404-420. https://doi.org/10.1016/j.trc.2015.05.009
[27] Hicks GA, Ray WH. Approximation methods for optimal control synthesis. The Canadian Journal of Chemical Engineering, 1971; Aug;49(4):522-8. https://doi.org/10.1002/cjce.5450490416
[28] Bock HG, Plitt KJ. A multiple shooting algorithm for direct solution of optimal control problems. IFAC Proceedings Volumes, 1984; Jul 1;17(2):1603-8. https://doi.org/10.1016/S1474-6670(17)61205-9
[29] Tsang TH, Himmelblau DM, Edgar TF. Optimal control via collocation and non-linear programming. International Journal of Control, 1975; May 1;21(5):763-8. https://doi.org/10.1080/00207177508922030
[30] Andersson JA, Gillis J, Horn G, Rawlings JB, Diehl M. CasADi: a software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 2019; Mar 14;11:1-36. https://doi.org/10.1007/s12532-018-0139-4
[31] Ferreau HJ, Kirches C, Potschka A, Bock HG, Diehl M. qpOASES: A parametric active-set algorithm for quadratic programming. Mathematical Programming Computation, 2014; Dec;6:327-63. https://doi.org/10.1007/s12532-014-0071-1
[32] Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 2006; Mar;106:25-57. https://doi.org/10.1007/s10107-004-0559-y
[33] Nocedal J, Wright SJ. Numerical Optimization. New York, NY: Springer New York; 2006; Dec 11. https://doi.org/10.1007/978-0-387-40065-5

Details

Primary Language

English

Subjects

Transportation and Traffic

Journal Section

Research Article

Authors

Işık İlber Sırmatel ^*
0000-0002-3679-7635
Türkiye

Publication Date

September 25, 2025

Submission Date

March 12, 2025

Acceptance Date

July 8, 2025

Published in Issue

Year 2025 Volume: 26 Number: 3

DOI

https://doi.org/10.18038/estubtda.1656397

IZ

https://izlik.org/JA26BP33JB

APA

Sırmatel, I. İ. (2025). COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 26(3), 203-216. https://doi.org/10.18038/estubtda.1656397

AMA

1.Sırmatel Iİ. COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS. Estuscience - Se. 2025;26(3):203-216. doi:10.18038/estubtda.1656397

Chicago

Sırmatel, Işık İlber. 2025. “COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26 (3): 203-16. https://doi.org/10.18038/estubtda.1656397.

EndNote

Sırmatel Iİ (September 1, 2025) COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26 3 203–216.

IEEE

[1]I. İ. Sırmatel, “COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS”, Estuscience - Se, vol. 26, no. 3, pp. 203–216, Sept. 2025, doi: 10.18038/estubtda.1656397.

ISNAD

Sırmatel, Işık İlber. “COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26/3 (September 1, 2025): 203-216. https://doi.org/10.18038/estubtda.1656397.

JAMA

1.Sırmatel Iİ. COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS. Estuscience - Se. 2025;26:203–216.

MLA

Sırmatel, Işık İlber. “COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 26, no. 3, Sept. 2025, pp. 203-16, doi:10.18038/estubtda.1656397.

Vancouver

1.Işık İlber Sırmatel. COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS. Estuscience - Se. 2025 Sep. 1;26(3):203-16. doi:10.18038/estubtda.1656397

Abstract

Project Number

COMPUTATIONAL EFFICIENCY ANALYSIS OF MACROSCOPIC FUNDAMENTAL DIAGRAM-BASED OPTIMAL ROAD TRAFFIC FLOW CONTROL METHODS

Abstract

Keywords

Supporting Institution

Project Number

Ethical Statement

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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