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When Is a Bottleneck a Bottleneck?

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Traffic and Granular Flow '15

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Abstract

Bottlenecks, i.e. local reductions of capacity, are one of the most relevant scenarios of traffic systems. The asymmetric simple exclusion process (ASEP) with a defect is a minimal model for such a bottleneck scenario. One crucial question is “What is the critical strength of the defect that is required to create global effects, i.e. traffic jams localised at the defect position”. Intuitively, one would expect that already an arbitrarily small bottleneck strength leads to global effects in the system, e.g. a reduction of the maximal current. Therefore, it came as a surprise when, based on computer simulations, it was claimed that the reaction of the system depends in non-continuous way on the defect strength and weak defects do not have a global influence on the system. Here, we reconcile intuition and simulations by showing that indeed the critical defect strength is zero. We discuss the implications for the analysis of empirical and numerical data.

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Notes

  1. 1.

    For the ASEP, due to particle-hole symmetry, \(\rho _1 = 1-\rho _2\).

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Acknowledgements

We dedicate this contribution to the memory of our friend and colleague Matthias Craesmeyer. Financial support by the DFG under grant SCHA 636/8-1 is gratefully acknowledged.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, 50937, Cologne, Germany

    Andreas Schadschneider, Johannes Schmidt & Vladislav Popkov

Authors
  1. Andreas Schadschneider
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  2. Johannes Schmidt
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  3. Vladislav Popkov
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Corresponding author

Correspondence to Andreas Schadschneider .

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Editors and Affiliations

  1. Transport & Planning, Delft University of Technology, Delft, The Netherlands

    Victor L. Knoop

  2. Transport & Planning, Delft University of Technology, Delft, The Netherlands

    Winnie Daamen

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Schadschneider, A., Schmidt, J., Popkov, V. (2016). When Is a Bottleneck a Bottleneck?. In: Knoop, V., Daamen, W. (eds) Traffic and Granular Flow '15. Springer, Cham. https://doi.org/10.1007/978-3-319-33482-0_51

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