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Macroscopic urban dynamics: Analytical and numerical comparisons of existing models

Mariotte, Guilhem ; Leclercq, Ludovic ; Laval, Jorge A.

Transportation research. Part B: methodological, 2017-07, Vol.101, p.245-267 [Periódico revisado por pares]

Oxford: Elsevier Ltd

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  • Título:
    Macroscopic urban dynamics: Analytical and numerical comparisons of existing models
  • Autor: Mariotte, Guilhem ; Leclercq, Ludovic ; Laval, Jorge A.
  • Assuntos: Accumulation ; Analytical resolution ; Computer Science ; Computer simulation ; Driving ability ; Dynamic tests ; Engineering Sciences ; Environment and Society ; Environmental Sciences ; Heterogeneity ; Inflow ; Macroscopic modeling ; Mathematical models ; Modeling and Simulation ; Other ; Outflow ; Piecewise linear functions ; Propagation ; Reservoirs ; Single-reservoir ; Taylor series ; Traffic congestion ; Traffic control ; Traffic flow ; Trip length ; Viscosity
  • É parte de: Transportation research. Part B: methodological, 2017-07, Vol.101, p.245-267
  • Descrição: •Comparing different formulations of MFD models in accumulation and travel-time.•Identifying the validity domain for demand fluctuations in the accumulation-based MFD model.•Investigating accurate solution methods for MFD models based on linear approximations.•Proposing an efficient event-based numerical scheme for the trip-based MFD model. Large-scale network modeling using the Macroscopic Fundamental Diagram (MFD) is widely based on the single-reservoir model, where the variation of the accumulation of circulating vehicles in the reservoir equals inflow minus outflow. However, inconsistent lags for information propagation between boundaries may be observed with this single accumulation-based model. For example, outflow is reacting too fast when inflow varies rapidly, whereas this information should be carried by vehicles that are never driving faster than the free-flow speed. To overcome this limitation, a trip-based model has been recently proposed, but whose solution cannot be obtained analytically. In this paper we compare both models under piecewise linear MFD and a piecewise constant demand. These assumptions allow to establish the exact solution of the accumulation-based model, and continuous approximations of the trip-based model at any order using Taylor series. Moreover, a flexible event-based simulation framework is implemented to solve the latter model, making it a promising tool to account for heterogeneity in distance traveled. Thanks to these resolution schemes we are able to measure the inaccuracy of the accumulation-based approach when the demand varies rapidly, and propose a validity domain for this model. Other applications with different trip lengths and supply limitations are also discussed.
  • Editor: Oxford: Elsevier Ltd
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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