A Note on Boundary Conditions for the LWR Model

Marušić, Sanja

doi:10.7307/ptt.v21i6.253

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…According to Marušić [42], this boundary condition can be used only if the measured density is smaller than the density ρ c , at which the flow is maximal. Higher densities on the upstream boundary, which is located on the open highway section prior to the bottleneck, can occur for two reasons; the traffic flow can already be congested prior to the bottleneck in no relation to the bottleneck, or the backward moving shockwave because of the stationary bottleneck has reached the upstream boundary.…”

Section: Research Objectivesmentioning

confidence: 99%

Numerical optimal control method for shockwaves reduction at stationary bottlenecks

Strnad

Fijavž

Žura

2016

J of Advced Transportation

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The paper introduces an optimal control method for traffic management with variable speed limits. It consists of traffic flow dynamics prediction with a non-linearized Lighthill-Whitham-Richards macroscopic traffic flow model, introduction of a cost functional, which enables stable shockwaves optimization, and numerical implementation of the optimization process with differential evolution. The method overcomes the discretization issues and provides speed limits that are in general not limited to small number of successive discrete points, i.e. variable message signs locations, nor in rounded speed limits. Performance of the method is demonstrated on a case study, which shows promising reduction of the backward moving shockwave that occurs because of a stationary bottleneck. On differential evolution algorithmsTo handle such an expanded optimal control problem a computationally effective method for numerical optimization process is required. We employ differential evolution (DE) approach introduced by Storn and Price [30,31]. DE is an evolutionary algorithm technique that is best suited for numerical optimization problems and has been found useful in many real-world optimization problems in engineering (e.g.[32] and [33]).There are three control parameters in DE, namely the mutation factor or scale factor, F ∈ [0, 2], the crossover probability, CR ∈ [0, 1], and the population size, NP ≥ 4. The selection of these parameters 842 I. STRNAD ET AL.

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Section: Research Objectivesmentioning

confidence: 99%

Numerical optimal control method for shockwaves reduction at stationary bottlenecks

Strnad

Fijavž

Žura

2016

J of Advced Transportation

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“…The visible model simulates traffic flow as a stream of fluid, with the establishment of a flow function and density at every position along a network of roads. In such a model, traffic flow behavior is considered on a global (average) level [3]. At the same time, a microscopic model analyzes the motion of each vehicle.…”

Section: Introductionmentioning

confidence: 99%

“…The Second is the product of density, and speed represents flux. And the underlying presumption is that speed and density has a unique relationship [3,4]. The PDE form of LWR is used to simulate how queues and shockwaves spread.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Local Fractional LWR Model of Vehicular Traffic Flow and Its Solution

Goswami

Pokhriyal

2023

Preprint

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In this study, a generalized nonlinear local fractional Lighthill-Whitham-Richards (LFLWR) model has been developed. The local fractional variational iteration method (LFVIM) solves and analyzes the proposed model. Numerous works have been described in past to address linear LWR and linear LFLWR models. This research highlighted on generalized nonlinear LFLWR model and LFVIM is employed to derive non-differentiable solutions of the suggested model. The existence and uniqueness of the resolution of LFLWR model have also been established. Furthermore, several exemplary instances are discussed to demonstrate the success of implementing LFVIM to the proposed model. The numerical simulations for each of the cases have also been shown. Additionally, the obtained solutions of the suggested model have been compared with the solutions of the classical LWR model with non-differentiable conditions in few examples. The study demonstrates that the employed iterative scheme is quite efficient and can be utilized for obtaining the non-differentiable solution to proposed generalized nonlinear LFLWR model of traffic flow.

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“…The visible model simulates traffic flow as a fluid stream, establishing a flow function and density at every position along a network of roads. In such a model, traffic flow behavior is considered on a global (average) level [3]. At the same time, a microscopic model analyzes the motion of each vehicle.…”

Section: Introductionmentioning

confidence: 99%

“…The second is the product of density, and speed represents flux. And the underlying presumption is that speed and density has a unique relationship [3, 4]. The PDE form of LWR is used to simulate how queues and shockwaves spread.…”

Section: Introductionmentioning

confidence: 99%

A generalized local fractional LWR model of vehicular traffic flow and its solution

Pokhriyal

Goswami

2023

Math Methods in App Sciences

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In this study, a generalized nonlinear local fractional Lighthill‐Whitham‐Richards (LFLWR) model has been developed. The local fractional variational iteration method (LFVIM) solves and analyzes the proposed model. Numerous works have been described in the past to address linear LWR and linear LFLWR models. This research highlighted on generalized nonlinear LFLWR model, and LFVIM is employed to derive non‐differentiable solutions of the suggested model. The existence and uniqueness of the solution of LFLWR model have also been established. Furthermore, several exemplary instances are discussed to demonstrate the success of implementing LFVIM to the proposed model. The numerical simulations for each of the cases have also been shown. Additionally, the obtained solutions of the suggested model have been compared with the solutions of the classical LWR model with non‐differentiable conditions in few examples. The study demonstrates that the employed iterative scheme is quite efficient and can be utilized to obtain the non‐differentiable solution to the proposed generalized nonlinear LFLWR traffic flow model.

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A Note on Boundary Conditions for the LWR Model

Abstract: ABSTRACT

Cited by 3 publications

References 12 publications

Numerical optimal control method for shockwaves reduction at stationary bottlenecks

Numerical optimal control method for shockwaves reduction at stationary bottlenecks

A Generalized Local Fractional LWR Model of Vehicular Traffic Flow and Its Solution

A generalized local fractional LWR model of vehicular traffic flow and its solution

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