Many-neighbour interaction and non-locality in traffic models

Wilson, Roger; Berg, Peter; Hooper, SM; Lunt, G

doi:10.1140/epjb/e2004-00205-y

Cited by 66 publications

(47 citation statements)

References 30 publications

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“…In multi-look-ahead models (Herman et al 1959;Wilson et al 2004) drivers respond to the motion of more than one vehicle ahead. Consequently, when monitoring M vehicles in front, the quantities…”

Section: (B) Car-following Modelsmentioning

confidence: 99%

Traffic jams: dynamics and control

Orosz

Wilson

Stépàn

2010

Phil. Trans. R. Soc. A.

352

215

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This introductory paper reviews the current state-of-the-art scientific methods used for modelling, analysing and controlling the dynamics of vehicular traffic. Possible mechanisms underlying traffic jam formation and propagation are presented from a dynamical viewpoint. Stable and unstable motions are described that may give the skeleton of traffic dynamics, and the effects of driver behaviour are emphasized in determining the emergent state in a vehicular system. At appropriate points, references are provided to the papers published in the corresponding Theme Issue.Keywords: vehicular traffic; congestion; stop-and-go waves; Hopf bifurcation; driver reaction time; unstable waves I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, 'How many arbitrary parameters did you use for your calculations?' I thought for a moment about our cut-off procedures and said, 'Four'. He said, 'I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk '. (Dyson 2004, p. 297) Background and challengesThe introduction of the assembly line in the automotive industry about a century ago allowed the mass production of automobiles, which, in turn, revolutionized land transportation. At the same time, a problem was also generated that has not yet been resolved: traffic congestion. Since then, researchers from many different disciplines (mathematics, physics and engineering) have targeted this problem, *Author for correspondence (gabor@engineering.ucsb.edu).One contribution of 10 to a Theme Issue 'Traffic jams: dynamics and control'.This journal is © 2010 The Royal Society 4455 on May 10, 2018 http://rsta.royalsocietypublishing.org/ Downloaded from 4456 G. Orosz et al. often using sophisticated mathematical tools brought from their own area of expertise. Also, analogies between traffic flow and other flows (fluid flow, gas flow and granular flow) were established. Although such analogies may help scientists to gain understanding of vehicular systems, it is becoming more and more obvious that traffic flows like no other flow in the Newtonian universe.To date, a vast number of different models have been constructed, but still no first principles have been established to guide the modelling procedure (if such principles exist at all). In many cases, authors claimed that the developed model described traffic better than models prior to that point, and such claims were often justified by fitting the models to empirical data. The quote at the beginning of this paper tries to illustrate, without questioning the importance of any specific model, that the above approach may easily lead to research capturing, but also missing, some essential characteristics. We believe that another way to conduct research in traffic can be by studying general classes of models and classifying their qualitative dynamical features (including 'hidden' unstable motions) when varying model parameters. To...

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Section: (B) Car-following Modelsmentioning

confidence: 99%

Traffic jams: dynamics and control

Orosz

Wilson

Stépàn

2010

Phil. Trans. R. Soc. A.

352

215

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“…Nagatani [16] and Ge et al [17] extended the difference equation model [18] by taking into account the next-nearest-neighbour interaction and an arbitrary number of vehicles ahead, respectively. The OV model was generalized and extended to include multiple look-ahead (many-neighbour interaction) by Wilson et al [19]. The results presented by the authors confirm the necessity of multiple look-ahead considerations.…”

mentioning

confidence: 88%

“…The results presented by the authors confirm the necessity of multiple look-ahead considerations. Chen et al [20] incorporated the drivers' reaction delay into the multianticipative model [19]. They found that the multi-anticipative consideration could partially compensate the unfavourable effect induced by driver reaction delays.…”

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confidence: 99%

A new multi-anticipative car-following model with consideration of the desired following distance

et al. 2016

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Noname manuscript No. (will be inserted by the editor)A new multi-anticipative car-following model with consideration of the desired following distanceReceived: date / Accepted: date Abstract We propose in this paper an extension of the multi-anticipative optimal velocity car-following model to consider explicitly the desired following distance. The model on the following vehicle's acceleration is formulated as a linear function of the optimal velocity and the desired distance, with reactiontime delay in elements. The linear stability condition of the model is derived. The results demonstrate that the stability of traffic flow is improved by introducing the desired following distance, increasing the time gap in the desired following distance or decreasing the reaction-time delay. The simulation results show that by taking into account the desired following distance as well as the optimal velocity, the multi-anticipative model allows longer reaction-time delay in achieving stable traffic flows.

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“…via car-following models), but very limited has been done to develop the macroscopic (or continuum) model for such intelligent traffic systems. To the best of our knowledge, only a few continuum (macroscopic) models have been developed to consider either multiple forward looking strategy (Wilson et al 2004;Ngoduy and Wilson 2014) or both single forward looking and backward looking driving strategy (Zheng, Jin, and Huang 2015). It is worth noticing that while the multi anticipative model of Ngoduy and Wilson (2014) is nonlocal (i.e.…”

Section: Introductionmentioning

confidence: 99%

Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy

Ngoduy

Jia

2016

Transportmetrica B: Transport Dynamics

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Recent development of information and communication technologies (ICT) has enabled vehicles to timely communicate with others through wireless technologies, which will form future (intelligent) traffic systems (ITS) consisting of so-called connected vehicles. Cooperative driving with the connected vehicles is regarded as a promising driving pattern to significantly improve transportation efficiency and traffic safety. Such cooperative driving has motivated many studies to model the dynamics of traffic flow under multi anticipative driving strategy (i.e. drivers react to many leading vehicles) or bidirectional strategy (i.e. drivers react to both (single) leading and following vehicles). In the vast literature of traffic flow theory, there are continuum models considering multiple forward anticipative strategy, where the driver reacts to many leaders. To the best of our knowledge, few study effort has been undertaken to include bidirectional driving strategy, where the driver reacts to both direct leader and direct follower, in the continuum traffic flow models. Moreover, the current bidirectional continuum traffic flow model still suffers some drawbacks: considers the behaviour of only a single leading vehicle in the forward looking strategy and neglects the impact of the forward space headway (e.g. the distance between two consecutive vehicles) sensitivity parameter on the (linear) stability of the model. This paper aims to derive a continuum traffic model considering both multiple forward and backward driving strategy. It is shown that the derived model is a generalized version of a current continuum model for ITS and can improve important properties of such bidirectional (continuum) model.

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Many-neighbour interaction and non-locality in traffic models

Cited by 66 publications

References 30 publications

Traffic jams: dynamics and control

Traffic jams: dynamics and control

A new multi-anticipative car-following model with consideration of the desired following distance

Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy

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