Equilibrium analysis and route guidance in large-scale networks with MFD dynamics

Yildirimoḡlu, Mehmet; Ramezani, Mohsen; Geroliminis, Nikolas

doi:10.1016/j.trc.2015.05.009

Cited by 155 publications

(73 citation statements)

References 39 publications

(16 reference statements)

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“…(supply constraint) (54) to reflect that, in congestion, the inflow cannot exceed the outflow. This is consistent with the idea that all links in the region, including those on its perimeter, have the same (congested) flow and therefore if demand exceeds it, a queue accumulates outside the region.…”

Section: Discrete-space Modelsmentioning

confidence: 99%

“…Only two papers, Tao et al [47] in continuum space and Yildirimoglu et al [54] in discrete space, has tried to establish DSO conditions, but the proposed solution methods are numerical. Since it is hard to extract insights from numerical solution methods, future research should focus on analytical Decomposes the urban network into zones, which are meshed into cells, and computes the turning proportion in each cell using logit solutions, possibly of simplified systems.…”

Section: System Optimummentioning

confidence: 99%

“…But in the case of origins and destinations distributed randomly in the region, we can postulate the conservation law with source term, i.e. ρ t + ∇ · f (ρ) = (λ − o(ρ))/L, where λ(x, y, t) is the demand flow, which may or may not be constrained by (54) as discussed earlier 1 . In the isotropic case, we have that the flux vector satisfies f = V (ρ) ρ, and since by definition (2) we have o(ρ) = V (ρ) ρ L , it follows that the corresponding conservation law becomes ρ t + ∇ · f (ρ) = λ/L − V (ρ) ρ/ .…”

Section: From Mfd To the Conservation Lawmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Aghamohammadi

Laval

2020

Transportation Research Part B: Methodological

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Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic Fundamental Diagram (MFD) on urban networks led to the formulation of discrete-space models, where the city is divided into a collection of reservoirs. Prior to 2008, a large body of DTA models based on pedestrian flow models had been formulated in continuum space as 2-dimensional conservation laws where the speed-density relationship can now be interpreted as the MFD. Perhaps surprisingly, we found that this continuum-space literature has been mostly unaware of MFD theory, and no attempts exist to verify the assumptions of MFD theory. This has the potential to create significant inconsistencies, and research is needed to analyze their extent and ways to resolve them. We also find that further research is needed to (i) incorporate departure time choice, (ii) improve existing numerical methods, possibly extending recent advances on the one-dimensional kinematic wave (LWR) model, (iii) study the properties of system optimum solutions, (iv) examine the real-time applicability of current continuum-space models compared to traditional DTA methods, and (v) formulate anisotropic models for the interaction of intersecting flows.

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Section: Discrete-space Modelsmentioning

confidence: 99%

Section: System Optimummentioning

confidence: 99%

Section: From Mfd To the Conservation Lawmentioning

confidence: 99%

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Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Aghamohammadi

Laval

2020

Transportation Research Part B: Methodological

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“…A crucial point is how to compute the speeds v k n . In the spirit of the MFD one might postulate v k n = V(ρ k a.s ), which is a common assumption in the literature (Yildirimoglu and Geroliminis, 2014, Yildirimoglu et al, 2015, but can lead to stalling (complete gridlock) on multi-reservoir configurations. To see this, notice that when a cell reaches jam density, both the speed and the outflow will be zero even when neighboring cells might be freely flowing.…”

Section: Vehicle Position Updatementioning

confidence: 99%

A Continuum Model for Cities Based on the Macroscopic Fundamental Diagram: a Semi-Lagrangian Solution Method

Aghamohammadi

Laval

2019

Transportation Research Procedia

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This paper presents a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -all based in Hughes' pedestrian model in 2002 -the proposed formulation (i) is consistent with reservoir-type models of the MFD literature, shedding some light into the connection between these two modeling approaches, (ii) can have destinations continuously distributed on the region, and (iii) can incorporate multi-commodity flows without additional numerical error. The proposed multi-reservoir numerical solution method treats the multi-commodity component of the model in Lagrangian coordinates, which is the natural representation to propagate origin-destination information (and any vehicle-specific characteristic) through the traffic stream. Fluxes between reservoir boundaries are computed in the Eulerian representation, and are used to calculate the speed of vehicles crossing the boundary. Simple examples are included that show the convergence of the model and its agreements with the available analytical solutions. We find that (i) when origins and destinations are uniformly distributed in a region, the distribution of the travel times can be approximated analytically, (ii) the magnitude of the detours from the optimal free-flow route due to congestion increase linearly with the inflow and decreases with the square of the speed, and (iii) the total delay of vehicles in the network converges to the analytical approximation when the size of reservoirs tends to zero.

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“…[2]); this topic has gained a lot of attraction in the research community lately. For a recent review on this research direction the reader is referred to [3], [4]. The original model for the dynamics of the multi-region process (plant) is highly nonlinear and the modelling tool that is utilized is the Macroscopic Fundamental Diagram (MFD) (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Linear-parameter-varying approximation of nonlinear dynamics for model predictive flow control of urban multi-region systems

Kouvelas

Saeedmanesh

Geroliminis

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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An alternative approach for real-time networkwide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The focus of the current work is to study two aspects that are not covered in the perimeter control literature, which are: (a) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (b) mathematical formulation of the original nonlinear problem in a linear-parameter-varying (LPV) form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. The developed scheme is applied to microsimulation in order to better investigate its applicability to real life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared to fixed-time control as all the performance indicators are improved significantly.

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Equilibrium analysis and route guidance in large-scale networks with MFD dynamics

Cited by 155 publications

References 39 publications

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

A Continuum Model for Cities Based on the Macroscopic Fundamental Diagram: a Semi-Lagrangian Solution Method

Linear-parameter-varying approximation of nonlinear dynamics for model predictive flow control of urban multi-region systems

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