Macroscopic Fundamental Diagrams: A cross-comparison of estimation methods

Abstract This paper aims to cross-compare existing estimation methods for the Macroscopic Fundamental Diagram. Raw data are provided by a mesoscopic simulation tool for two typical networks that mimic an urban corridor and a meshed urban center. We mainly focus on homogenous network loading in order to fairly cross-compare the different methods with the analytical reference. It appears that the only way to estimate the MFD without bias is to have the full information of vehicle trajectories over the network and to apply Edie’s definitions. Combining information from probes (mean network speed) and loop detectors (mean network flow) also provides accurate results even for low sampling rate (

[1]  Carlos F. Daganzo,et al.  Fundamentals of Transportation and Traffic Operations , 1997 .

[2]  E. C. Fieller SOME PROBLEMS IN INTERVAL ESTIMATION , 1954 .

[3]  Serge P. Hoogendoorn,et al.  Empirics of a Generalized Macroscopic Fundamental Diagram for Urban Freeways , 2013 .

[4]  Ludovic Leclercq,et al.  Meso Lighthill-Whitham and Richards Model Designed for Network Applications , 2012 .

[5]  C. Daganzo A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

[6]  P. I. Richards Shock Waves on the Highway , 1956 .

[7]  C. Daganzo,et al.  Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability , 2011 .

[8]  N. Geroliminis,et al.  Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings - eScholarship , 2007 .

[9]  N. Geroliminis,et al.  An analytical approximation for the macropscopic fundamental diagram of urban traffic , 2008 .

[10]  M. Cassidy BIVARIATE RELATIONS IN NEARLY STATIONARY HIGHWAY TRAFFIC , 1998 .

[11]  Christine Buisson,et al.  Exploring the Impact of Homogeneity of Traffic Measurements on the Existence of Macroscopic Fundamental Diagrams , 2009 .

[12]  Carlos F. Daganzo,et al.  Urban Gridlock: Macroscopic Modeling and Mitigation Approaches , 2007 .

[13]  Dirk Helbing,et al.  The spatial variability of vehicle densities as determinant of urban network capacity , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  I. Prigogine,et al.  A Two-Fluid Approach to Town Traffic , 1979, Science.

[15]  Vikash V. Gayah,et al.  Using Mobile Probe Data and the Macroscopic Fundamental Diagram to Estimate Network Densities , 2013 .

[16]  C. Daganzo A variational formulation of kinematic waves: Solution methods , 2005 .

[17]  Hani S. Mahmassani,et al.  Network capacity, traffic instability, and adaptive driving: findings from simulated urban network experiments , 2014, EURO J. Transp. Logist..

[18]  Meead Saberi,et al.  Urban Network Gridlock: Theory, Characteristics, and Dynamics , 2013 .

[19]  N. Chiabaut,et al.  Wave Velocity Estimation through Automatic Analysis of Cumulative Vehicle Count Curves , 2011 .

[20]  Nikolas Geroliminis,et al.  On the distribution of urban road space for multimodal congested networks , 2013 .

[21]  Nikolaos Geroliminis,et al.  Properties of a well-defined Macroscopic Fundamental Diagram for urban traffic , 2011 .

[22]  Hani S. Mahmassani,et al.  Empirical Characterization and Interpretation of Hysteresis and Capacity , 2013 .

[23]  Hani S. Mahmassani,et al.  INVESTIGATION OF NETWORK-LEVEL TRAFFIC FLOW RELATIONSHIPS: SOME SIMULATION RESULTS , 1984 .

[24]  Nikolaos Geroliminis,et al.  Estimating MFDs in Simple Networks with Route Choice. , 2013 .

[25]  G. F. Newell A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks , 1993 .

[26]  Meead Saberi,et al.  Connecting Networkwide Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow , 2013 .

[27]  Ludovic Leclercq,et al.  Cross-comparison of Macroscopic Fundamental Diagram Estimation Methods , 2011 .

[28]  C. Daganzo,et al.  Macroscopic Fundamental Diagrams for Freeway Networks: Theory and Observation , 2011 .

[29]  G. F. Newell A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[30]  Vikash V. Gayah,et al.  Inhomogeneous Flow Patterns in Undersaturated Road Networks , 2013 .

[31]  Wei Guan,et al.  Figure-Eight Hysteresis Pattern in Macroscopic Fundamental Diagrams for Urban Freeway Network in Beijing, China , 2013 .

[32]  Meead Saberi,et al.  Hysteresis and Capacity Drop Phenomena in Freeway Networks , 2013 .

[33]  Nikolaos Geroliminis,et al.  The effect of variability of urban systems characteristics in the network capacity , 2012 .

[34]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[35]  Serge P. Hoogendoorn,et al.  The impact of traffic dynamics on macroscopic fundamental diagram , 2013 .