Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops

Gun, J.P.T. van der; Pel, Adam J.; Arem, Bart van

doi:10.1016/j.trb.2016.12.011

Cited by 14 publications

(3 citation statements)

References 40 publications

(65 reference statements)

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“…The main feature of this model based the simplified theory of Newell (1993a; consists in using the characteristic speeds (free-flow and congested flow) to derive the upstream and downstream boundary conditions. Recently, extensions of the original LTM formulation have been proposed to allow for larger time steps (Himpe et al, 2016) and to consider non-triangular FDs with capacity drops (Gun et al, 2017) and initial conditions (Gun, 2018). In recent years, the LTM has become very popular for the dynamic network loading (DNL) procedure within the dynamic traffic assignment (DTA), where simulations can involve thousands of links, and where the solution only needs to be computed on the link boundaries.…”

Section: Methodsmentioning

confidence: 99%

A Fast Lax–Hopf Algorithm to Solve the Lighthill–Whitham–Richards Traffic Flow Model on Networks

Simoni

Claudel

2020

Transportation Science

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Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semianalytical Lax–Hopf algorithm in order to compute link inflows and outflows with the Lighthill–Whitham–Richards (LWR) model. Our proposed fast Lax–Hopf algorithm has a very low computational complexity. We demonstrate that some of the original algorithm’s operations (associated with the initial conditions) can be discarded, leading to a faster computation of boundary demands/supplies in network simulation problems for general concave fundamental diagrams (FDs). Moreover, the computational cost can be further reduced for triangular FDs and specific space–time discretizations. The resulting formulation has a performance comparable to the link transmission model and because it solves the original LWR model for a wide range of FD shapes, with any initial configuration, it is suitable to solve a broad range of traffic operations problems. As part of the analysis, we compare the performance of the proposed scheme with that of other well-known computational methods.

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Section: Methodsmentioning

confidence: 99%

A Fast Lax–Hopf Algorithm to Solve the Lighthill–Whitham–Richards Traffic Flow Model on Networks

Simoni

Claudel

2020

Transportation Science

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“…The first approach is to explicitly incorporate capacity drop into the fundamental diagram of LWR, with two flow values around the critical density [2,5,14,[51][52][53]. Similar modifications have also been made on the cell transmission model (CTM), a popular timespace-discretized version of LWR with a triangular or trapezoidal fundamental diagram proposed by Daganzo [54].…”

Section: Capacity Drops In Macroscopic Traffic Simulations 221 First-...mentioning

confidence: 99%

Capacity Drop at Freeway Ramp Merges with Its Replication in Macroscopic and Microscopic Traffic Simulations: A Tutorial Report

Wang

et al. 2023

Sustainability

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Capacity drop (CD) at overloaded bottlenecks is a puzzling traffic flow phenomenon with some internal and complicated mechanisms at the microscopic level. Capacity drop is not only important for traffic flow theory and modelling, but also significant for traffic control. A traffic model evaluating traffic control measures needs to be able to reproduce capacity drop in order to deliver reliable evaluation results. This paper delivers a comprehensive overview on the subject from the behavioral mechanism perspective, as well as from microscopic and macroscopic simulation points of view. The paper also conducts comparable studies to replicate capacity drop at freeway ramp merges from both macroscopic and microscopic perspectives. Firstly, the subject is studied using the macroscopic traffic flow model METANET with respect to ramp merging scenarios with and without ramp metering. Secondly, one major weakness of commercial microscopic traffic simulation tools in creating capacity drop at ramp merges is identified and a forced lane changing model for ramp-merging vehicles is studied and incorporated into the commercial traffic simulation tool AIMSUN. The extended AIMSUN carefully calibrated against real data is then examined for its capability of reproducing capacity drop in a complicated traffic scenario with merging bottlenecks. The obtained results demonstrate that reproducible capacity drop can be delivered for the targeted bottlenecks using both macroscopic and microscopic simulation tools.

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“…Some researchers have proposed methods to relax this restriction. For example, the LTM was extended to handle general concave fundamental diagrams 22 , and a concave piecewise linear fundamental diagram was used to send and receive flows to represent driving behaviour and environmental conditions Table 5. Table 7.…”

Section: Evacuation Simulation Via An Ltm Considering Different Watermentioning

confidence: 99%

Modelling fundamental diagrams according to different water film depths from the perspective of the dynamic hydraulic pressure

Liu

Chiaki

Oeda

et al. 2020

Sci Rep

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In this paper, we propose enhanced fundamental diagrams based on different water film depths by considering the effects of hydroplaning using a physical method. Various factors are calculated to describe the total safe distance headway of main vehicle components. These factors include the driver reaction times, reaction distances, vehicle braking times, and vehicle braking distances corresponding to different water film depths. An excellent match is found between the computed braking distance, the braking time calculated using the proposed numerical model, and the results published in other papers. These calculations are performed to estimate the distance headway and quantitatively analyse the relationships between the speed, density, and water film depth. By using three road-specific parameters estimated by our proposed model, namely, the free-flow speed, jam density, and capacity flow, a link transmission model is developed to analyse the dynamic impact of the water film depth.Urban flooding is one of the most severe types of flooding in terms of economic damage, health impact, and loss of life. It has become a significant challenge for the development and sustainability of coastal cities. Under more frequent extreme weather conditions, floods and inundations become more severe. For example, devastating torrential rains and subsequent flooding in western Japan left over 200 people dead in 2018. Evacuation can be an efficient solution for securing human safety in major disasters. One effective method for handling the consequences of hydrological disasters is to establish a prudent and comprehensive emergency management plan. Recently, several studies 1,2 , have attempted to model potential network capacity losses to estimate evacuation times from a probabilistic perspective. The objective of these studies was to estimate reliable evacuation times under realistic transportation network conditions.Despite the fact that evacuation environments in flood conditions are typically characterised by great risk (road capacities and vehicle speeds may be reduced by water film depth), very few studies in the evacuation literature have explicitly considered this type of risk. A traffic model for representing traffic flow characteristics according to different water film depths is necessary to represent the traffic situation during emergency evacuations accurately. However, research in this field is very limited, especially regarding the evaluation of the influence of the water film depth. Therefore, it is essential to re-evaluate and enhance urban transportation planning models to capture the effects of flooding disasters related to water depth.All traffic situations in the real world can be considered combinations of homogenous states, meaning they can be described by essential traffic flow characteristics (e.g., flow Q, speed V, and density K). Fundamental diagrams capture the relationships between these characteristics and play an essential role in traffic flow theory and transportation engineering. Various models have be...

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Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops

Cited by 14 publications

References 40 publications

A Fast Lax–Hopf Algorithm to Solve the Lighthill–Whitham–Richards Traffic Flow Model on Networks

A Fast Lax–Hopf Algorithm to Solve the Lighthill–Whitham–Richards Traffic Flow Model on Networks

Capacity Drop at Freeway Ramp Merges with Its Replication in Macroscopic and Microscopic Traffic Simulations: A Tutorial Report

Modelling fundamental diagrams according to different water film depths from the perspective of the dynamic hydraulic pressure

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