Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far have been based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach, which facilitates a simple simulation of congestion spreading in cities. First, we show that a quantization of the macroscopic turning flows into units of single vehicles is necessary to obtain realistic fluctuations in the traffic variables, and how this can be implemented in a fluid-dynamic model. Then, we propose a new method to simulate destination flows without the requirement of individual route assignments. Combining both methods allows us to study a variety of different simulation scenarios. These reveal fundamental relationships between the average flow, the average density and the variability of the vehicle densities. Considering the inhomogeneity of traffic as an independent variable can eliminate the scattering of congested flow measurements. The variability also turns out to be a key variable of urban traffic performance. Our results can be explained through the number of full links of the road network, and approximated by a simple analytical formula.

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Yildirimoglu M, Ramezani M and Geroliminis N (2015) Equilibrium analysis and route guidance in large-scale networks with MFD dynamics, Transportation Research Part C: Emerging Technologies, 10.1016/j.trc.2015.05.009, 59, (404-420), Online publication date: 1-Oct-2015.

Anbaroğlu B, Cheng T and Heydecker B (2015) Non-recurrent traffic congestion detection on heterogeneous urban road networks, Transportmetrica A: Transport Science, 10.1080/23249935.2015.1087229, 11:9, (754-771), Online publication date: 21-Oct-2015.

Ortigosa J, Menendez M and Gayah V (2019) Analysis of Network Exit Functions for Various Urban Grid Network Configurations, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2491-02, 2491:1, (12-21), Online publication date: 1-Jan-2015.

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Tsubota T, Bhaskar A, Nantes A, Chung E and Gayah V (2019) Comparative Analysis of Traffic State Estimation, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2491-05, 2491:1, (43-52), Online publication date: 1-Jan-2015.

Knoop V, van Lint H and Hoogendoorn S (2015) Traffic dynamics: Its impact on the Macroscopic Fundamental Diagram, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2015.06.016, 438, (236-250), Online publication date: 1-Nov-2015.

Zhang Z, Parr S, Jiang H and Wolshon B (2015) Optimization model for regional evacuation transportation system using macroscopic productivity function, Transportation Research Part B: Methodological, 10.1016/j.trb.2015.07.012, 81, (616-630), Online publication date: 1-Nov-2015.

Yildirimoglu M, Ramezani M and Geroliminis N (2015) Equilibrium Analysis and Route Guidance in Large-scale Networks with MFD Dynamics, Transportation Research Procedia, 10.1016/j.trpro.2015.07.011, 9, (185-204), .

Hajiahmadi M, Haddad J, De Schutter B and Geroliminis N Optimal Hybrid Perimeter and Switching Plans Control for Urban Traffic Networks, IEEE Transactions on Control Systems Technology, 10.1109/TCST.2014.2330997, 23:2, (464-478)

Yan F, Tian F and Shi Z (2015) Iterative Learning Control Approach for Signaling Split in Urban Traffic Networks with Macroscopic Fundamental Diagrams, Mathematical Problems in Engineering, 10.1155/2015/975328, 2015, (1-12), .

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Ortigosa J, Zheng N, Menendez M and Geroliminis N (2015) Analysis of the 3D-vMFDs of the Urban Networks of Zurich and San Francisco 2015 IEEE 18th International Conference on Intelligent Transportation Systems - (ITSC 2015), 10.1109/ITSC.2015.27, 978-1-4673-6596-3, (113-118)

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Keyvan-Ekbatani M, Yildirimoglu M, Geroliminis N and Papageorgiou M Multiple Concentric Gating Traffic Control in Large-Scale Urban Networks, IEEE Transactions on Intelligent Transportation Systems, 10.1109/TITS.2015.2399303, 16:4, (2141-2154)

Geroliminis N, Zheng N and Ampountolas K (2014) A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks, Transportation Research Part C: Emerging Technologies, 10.1016/j.trc.2014.03.004, 42, (168-181), Online publication date: 1-May-2014.

Lentzakis A, Su R and Wen C (2014) Time-dependent partitioning of urban traffic network into homogeneous regions 2014 13th International Conference on Control Automation Robotics & Vision (ICARCV), 10.1109/ICARCV.2014.7064361, 978-1-4799-5199-4, (535-540)

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Saberi M, Mahmassani H, Hou T and Zockaie A (2014) Estimating Network Fundamental Diagram Using Three-Dimensional Vehicle Trajectories, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2422-02, 2422:1, (12-20), Online publication date: 1-Jan-2014.

Ao D, Jiang R, Hu M, Gao Z and Jia B (2014) Network operation reliability in a Manhattan-like urban system with adaptive traffic lights 2014 IEEE 17th International Conference on Intelligent Transportation Systems (ITSC), 10.1109/ITSC.2014.6957840, 978-1-4799-6078-1, (1135-1141)

Shraiber A and Haddad J (2014) Robust control design for a perimeter traffic flow controller at an urban region 2014 European Control Conference (ECC), 10.1109/ECC.2014.6862193, 978-3-9524269-1-3, (2563-2568)

Knoop V, de Jong D and Hoogendoom S (2014) Influence of Road Layout on Network Fundamental Diagram, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2421-03, 2421:1, (22-30), Online publication date: 1-Jan-2014.

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Ampountolas K, Zheng N and Geroliminis N (2014) Perimeter flow control of bi-modal urban road networks: A robust feedback control approach 2014 European Control Conference (ECC), 10.1109/ECC.2014.6862286, 978-3-9524269-1-3, (2569-2574)

Gayah V, Gao X and Nagle A (2014) On the impacts of locally adaptive signal control on urban network stability and the Macroscopic Fundamental Diagram, Transportation Research Part B: Methodological, 10.1016/j.trb.2014.09.010, 70, (255-268), Online publication date: 1-Dec-2014.

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Haddad J and Shraiber A (2014) Robust perimeter control design for an urban region, Transportation Research Part B: Methodological, 10.1016/j.trb.2014.06.010, 68, (315-332), Online publication date: 1-Oct-2014.

Geroliminis N (2014) Tutorial Session in: Large-scale hierarchical control for congested urban networks 2014 European Control Conference (ECC), 10.1109/ECC.2014.6862640, 978-3-9524269-1-3, (2268-2271)

Zockaie A, Mahmassani H, Saberi M and Verbas Ö (2014) Dynamics of Urban Network Traffic flow during a Large-Scale Evacuation, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2422-03, 2422:1, (21-33), Online publication date: 1-Jan-2014.

Tsubota T, Bhaskar A and Chung E (2014) Macroscopic Fundamental Diagram for Brisbane, Australia, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2421-02, 2421:1, (12-21), Online publication date: 1-Jan-2014.

Ji Y, Luo J and Geroliminis N (2014) Empirical Observations of Congestion Propagation and Dynamic Partitioning with Probe Data for Large-Scale Systems, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2422-01, 2422:1, (1-11), Online publication date: 1-Jan-2014.

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Yildirimoglu M and Geroliminis N (2014) Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams, Transportation Research Part B: Methodological, 10.1016/j.trb.2014.09.002, 70, (186-200), Online publication date: 1-Dec-2014.

Jin W, Gan Q and Gayah V (2013) A kinematic wave approach to traffic statics and dynamics in a double-ring network, Transportation Research Part B: Methodological, 10.1016/j.trb.2013.09.004, 57, (114-131), Online publication date: 1-Nov-2013.

Knoop V and Hoogendoorn S (2013) Two-Variable Macroscopic Fundamental Diagrams for Traffic Networks Traffic and Granular Flow '11, 10.1007/978-3-642-39669-4_34, (351-360), .

Geroliminis N, Haddad J and Ramezani M Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach, IEEE Transactions on Intelligent Transportation Systems, 10.1109/TITS.2012.2216877, 14:1, (348-359)

Hajiahmadi M, Knoop V, De Schutter B and Hellendoorn H (2013) Optimal dynamic route guidance: A model predictive approach using the macroscopic fundamental diagram 2013 16th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2013), 10.1109/ITSC.2013.6728366, 978-1-4799-2914-6, (1022-1028)

Petri G, Expert P, Jensen H and Polak J (2013) Entangled communities and spatial synchronization lead to criticality in urban traffic, Scientific Reports, 10.1038/srep01798, 3:1, Online publication date: 1-Dec-2013.

Lu Shoufeng , Wang Jie , van Zuylen H and Liu Ximin (2013) Deriving the Macroscopic Fundamental Diagram for an urban area using counted flows and taxi GPS 2013 16th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2013), 10.1109/ITSC.2013.6728231, 978-1-4799-2914-6, (184-188)

Leclercq L and Geroliminis N (2013) Estimating MFDs in Simple Networks with Route Choice, Procedia - Social and Behavioral Sciences, 10.1016/j.sbspro.2013.05.008, 80, (99-118), Online publication date: 1-Jun-2013.

Arnott R (2013) A bathtub model of downtown traffic congestion, Journal of Urban Economics, 10.1016/j.jue.2013.01.001, 76, (110-121), Online publication date: 1-Jul-2013.

Leclercq L and Geroliminis N (2013) Corrigendum to “Estimating MFDs in Simple Networks with Route Choice”, Procedia - Social and Behavioral Sciences, 10.1016/j.sbspro.2013.08.329, 80, (960-979), Online publication date: 1-Jun-2013.

Mahmassani H, Saberi M and Zockaie A (2013) Urban network gridlock: Theory, characteristics, and dynamics, Transportation Research Part C: Emerging Technologies, 10.1016/j.trc.2013.07.002, 36, (480-497), Online publication date: 1-Nov-2013.

Haddad J, Ramezani M and Geroliminis N (2013) Cooperative traffic control of a mixed network with two urban regions and a freeway, Transportation Research Part B: Methodological, 10.1016/j.trb.2013.03.007, 54, (17-36), Online publication date: 1-Aug-2013.

Aboudolas K and Geroliminis N (2013) Perimeter and boundary flow control in multi-reservoir heterogeneous networks, Transportation Research Part B: Methodological, 10.1016/j.trb.2013.07.003, 55, (265-281), Online publication date: 1-Sep-2013.

Zheng N, Aboudolas K and Geroliminis N (2013) Investigation of a city-scale three-dimensional Macroscopic Fundamental Diagram for bi-modal urban traffic 2013 16th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2013), 10.1109/ITSC.2013.6728367, 978-1-4799-2914-6, (1029-1034)

Keyvan-Ekbatani M, Yildirimoglu M, Geroliminis N and Papageorgiou M (2013) Traffic signal perimeter control with multiple boundaries for large urban networks 2013 16th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2013), 10.1109/ITSC.2013.6728363, 978-1-4799-2914-6, (1004-1009)

Knoop V, van Lint H and Hoogendoorn S (2013) Route Advice Based on Subnetwork Properties Traffic and Granular Flow '11, 10.1007/978-3-642-39669-4_36, (379-388), .

Zheng N and Geroliminis N (2013) On the distribution of urban road space for multimodal congested networks, Transportation Research Part B: Methodological, 10.1016/j.trb.2013.06.003, 57, (326-341), Online publication date: 1-Nov-2013.

Saberi M and Mahmassani H (2013) Hysteresis and Capacity Drop Phenomena in Freeway Networks, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2391-05, 2391:1, (44-55), Online publication date: 1-Jan-2013.

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Zhang L, Garoni T and de Gier J (2013) A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems, Transportation Research Part B: Methodological, 10.1016/j.trb.2012.12.002, 49, (1-23), Online publication date: 1-Mar-2013.

Leclercq L and Geroliminis N (2013) Estimating MFDs in simple networks with route choice, Transportation Research Part B: Methodological, 10.1016/j.trb.2013.05.005, 57, (468-484), Online publication date: 1-Nov-2013.

Knoop V and Hoogendoorn S (2013) Empirics of a Generalized Macroscopic Fundamental Diagram for Urban Freeways, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2391-13, 2391:1, (133-141), Online publication date: 1-Jan-2013.

Mahmassani H, Saberi M and K. A (2013) Urban Network Gridlock: Theory, Characteristics, and Dynamics, Procedia - Social and Behavioral Sciences, 10.1016/j.sbspro.2013.05.007, 80, (79-98), Online publication date: 1-Jun-2013.

Haddad J, Ramezani M and Geroliminis N (2012) Model predictive perimeter control for urban areas with macroscopic fundamental diagrams 2012 American Control Conference - ACC 2012, 10.1109/ACC.2012.6314693, 978-1-4577-1096-4, (5757-5762)

Ramezani M, Haddad J and Geroliminis N (2012) Macroscopic Traffic Control of a Mixed Urban and Freeway Network* *This research was financially supported by the Swiss National Science Foundation grant # 200021-130165., IFAC Proceedings Volumes, 10.3182/20120912-3-BG-2031.00017, 45:24, (89-94), Online publication date: 1-Sep-2012.

Zhou Z, Lin S and Xi Y (2012) A dynamic network partition method for heterogenous urban traffic networks 2012 15th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2012), 10.1109/ITSC.2012.6338712, 978-1-4673-3063-3, (820-825)

Ji Y and Geroliminis N (2012) On the spatial partitioning of urban transportation networks, Transportation Research Part B: Methodological, 10.1016/j.trb.2012.08.005, 46:10, (1639-1656), Online publication date: 1-Dec-2012.

Saberi M and Mahmassani H (2012) Exploring Properties of Networkwide Flow–Density Relations in a Freeway Network, Transportation Research Record: Journal of the Transportation Research Board, 10.3141/2315-16, 2315:1, (153-163), Online publication date: 1-Jan-2012.

Geroliminis N and Boyacı B (2012) The effect of variability of urban systems characteristics in the network capacity, Transportation Research Part B: Methodological, 10.1016/j.trb.2012.08.001, 46:10, (1607-1623), Online publication date: 1-Dec-2012.

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Haddad J and Geroliminis N (2012) On the stability of traffic perimeter control in two-region urban cities, Transportation Research Part B: Methodological, 10.1016/j.trb.2012.04.004, 46:9, (1159-1176), Online publication date: 1-Nov-2012.

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Orosz G, Wilson R and Stépán G (2010) Traffic jams: dynamics and control, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368:1928, (4455-4479), Online publication date: 13-Oct-2010.

Yu H, Kong J, Ren Y and Yin C (2020) On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length, Symmetry, 10.3390/sym12111852, 12:11, (1852)

Loder A, Bressan L, Wierbos M, Becker H, Emmonds A, Obee M, Knoop V, Menendez M and Axhausen K (2021) How Many Cars in the City Are Too Many? Towards Finding the Optimal Modal Split for a Multi-Modal Urban Road Network, Frontiers in Future Transportation, 10.3389/ffutr.2021.665006, 2

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Yu H and Hou Z (2020) Two-level hierarchical optimal control for urban traffic networks, Transportmetrica A: Transport Science, 10.1080/23249935.2020.1845851, (1-22)

This Issue

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences cover image

13 October 2010

Volume 368Issue 1928

Theme Issue 'Traffic jams: dynamics and control' compiled and edited by Gábor Orosz, R. Eddie Wilson and Gábor Stépán

Article Information

DOI:https://doi.org/10.1098/rsta.2010.0099
Published by:Royal Society
Print ISSN:1364-503X
Online ISSN:1471-2962

History:

Published online13/10/2010
Published in print13/10/2010

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