A continuum model for cities based on the macroscopic fundamental diagram: A semi-Lagrangian solution method

Aghamohammadi, Rafegh; Laval, Jorge A.

doi:10.1016/j.trb.2019.04.011

Cited by 14 publications

(5 citation statements)

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“…4 show that I Q > 1 depending on the intensity ρ. The simulation experiments consider, separately, three trip-length distributions: exponential, uniform and the "square" distribution arising when origins and destinations are uniformly distributed on a square; see Aghamohammadi and Laval (2020). The parameters of these distributions were set such that they all have the same mean, but different coefficient of variation: the C 2 L is 1, 1/27 and 1/4 for the exponential, uniform and square distribution, respectively.…”

Section: Queueing Approximation For the Stochastic Problemmentioning

confidence: 99%

“…A single experiment consists of an initially empty system with Poisson arrivals with a constant rate λ. Each arrival has a trip length drawn from the distribution f , which can be the exponential, uniform distributions and the "square" distribution of trip length when origins and destinations are uniformly distributed on a square; see Aghamohammadi and Laval (2020) for details. Notice that all these distributions have the same mean of ℓ = 3, but different coefficient of variation: the C 2 L is 1, 1/27 and 1/4 for the exponential, uniform and square distribution, respectively.…”

Section: Appendix a Simulation Experimentsmentioning

confidence: 99%

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Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

Laval

2023

Transportation Research Part C: Emerging Technologies

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Section: Queueing Approximation For the Stochastic Problemmentioning

confidence: 99%

Section: Appendix a Simulation Experimentsmentioning

confidence: 99%

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

Laval

2023

Transportation Research Part C: Emerging Technologies

Self Cite

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“…The simulation experiments consider, separately, three trip-length distributions: exponential, uniform and the "square" distribution arising when origins and destinations are uniformly distributed on a square; see Aghamohammadi and Laval (2020). The parameters of these distributions were set such that they all have the same mean, but different coefficient of variation: the C 2 L is 1, 1/27 and 1/4 for the exponential, uniform and square distribution, respectively.…”

Section: Queueing Approximation For the Stochastic Problemmentioning

confidence: 99%

Effect of the Trip-Length Distribution on Network-Level Traffic Dynamics: Exact and Statistical Results

Laval¹

2023

Preprint

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This paper presents additional results of the generalized bathtub model for urban networks, including a simpler derivation and exact solutions for uniformly distributed trip lengths. It is shown that in steady state this trip-based model is equivalent to the more parsimonious accumulation-based model, and that the trip-length distribution has merely a transient effect on traffic dynamics, which converge to the same point in the macroscopic fundamental diagram (MFD). To understand the statistical properties of the system, a queueing approximation method is proposed to compute the network accumulation variance. It is found that (i) the accumulation variance is much larger than predicted by traditional queueing models, due to the nonlinear dynamics imposed by the MFD, (ii) the trip-length distribution has no effect on the accumulation variance, indicating that the proposed formula for the variance might be universal, (iii) the system exhibits critical behavior near the capacity state where the variance diverges to infinity. This indicates that the tools from critical phenomena and phase transitions might be useful to understand congestion in cities.

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“…In this paper, we focused directly on link-level within the region so that the dynamics of boundary nodes can be obtained from the dynamics of the links in all directions. For the network separability, Aghamohammadi and Laval (2019) [28] verify that the large-scale network or region can partition into smaller "cells" (subregions) and assume that congestion is homogeneously distributed in each cell. We adopt this point in this paper as an assumption to divide the experimental network into four regions (see in Section 3) and the region is further divided into sub-regions (see in Section 4.3).…”

Section: Introductionmentioning

confidence: 99%

Approximating Dynamic Equilibrium Analysis in Multi-Region Network Based on Macroscopic Fundamental Diagram

Liu

Cen

Song

2022

Journal of Advanced Transportation

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Modeling and control of road traffic in large-scale urban networks present considerable challenges. The traffic equilibrium phenomena, with the question of route choice behavior in case of heterogeneous urban networks, has not been thoroughly investigated in parsimonious and classical models due to the limitation, like large network size, spatiotemporal propagation of congestion, and the interaction between driver decisions, etc. In this paper, we propose a bi-level approximating dynamic equilibrium model (BLADEM) for the approximating dynamic equilibrium analysis in multi-region network based on macroscopic fundamental diagram (MFD). The proposed model combines the region-based model and the internal-region model. With the information from region MFD, the region-based model is used to implement the time-dependent regional route choice estimation. Traffic equilibrium condition (dynamic user equilibrium, DUE) is considered in an internal-region model with time-aggregated regional OD demand from the region level. Furthermore, the complexity of the proposed model is derived. Then, the comparative analysis of the algorithm complexity between the proposed model and the DUE model is given. The proposed model is evaluated based on the high-resolution vehicle trajectory data (or connected vehicles trajectory data) from the DiDi platform collected in Chengdu, China with more than 3,000,000 GPS points during a typical workday. The evaluation results show that the proposed model can obtain the approximating traffic dynamics compared with the DUE algorithm. Pleasantly, the improved calculation efficiency is between 21% and 42%. The results indicate the promising potential of using the proposed model to analyze approximating dynamic equilibrium in the multi-region heterogeneous network.

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A continuum model for cities based on the macroscopic fundamental diagram: A semi-Lagrangian solution method

Cited by 14 publications

References 32 publications

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

Effect of the Trip-Length Distribution on Network-Level Traffic Dynamics: Exact and Statistical Results

Approximating Dynamic Equilibrium Analysis in Multi-Region Network Based on Macroscopic Fundamental Diagram

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