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Probabilistic physical characteristics of phase transitions at highway bottlenecks: Incommensurability of three-phase and two-phase traffic-flow theories

Boris S. Kerner1, Sergey L. Klenov2, and Michael Schreckenberg1

  • 1Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany
  • 2Moscow Institute of Physics and Technology, Department of Physics, 141700 Dolgoprudny, Moscow Region, Russia

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Phys. Rev. E 89, 052807 – Published 13 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.052807

Abstract

Physical features of induced phase transitions in a metastable free flow at an on-ramp bottleneck in three-phase and two-phase cellular automaton (CA) traffic-flow models have been revealed. It turns out that at given flow rates at the bottleneck, to induce a moving jam (F→J transition) in the metastable free flow through the application of a time-limited on-ramp inflow impulse, in both two-phase and three-phase CA models the same critical amplitude of the impulse is required. If a smaller impulse than this critical one is applied, neither F→J transition nor other phase transitions can occur in the two-phase CA model. We have found that in contrast with the two-phase CA model, in the three-phase CA model, if the same smaller impulse is applied, then a phase transition from free flow to synchronized flow (F→S transition) can be induced at the bottleneck. This explains why rather than the F→J transition, in the three-phase theory traffic breakdown at a highway bottleneck is governed by an F→S transition, as observed in real measured traffic data. None of two-phase traffic-flow theories incorporates an F→S transition in a metastable free flow at the bottleneck that is the main feature of the three-phase theory. On the one hand, this shows the incommensurability of three-phase and two-phase traffic-flow theories. On the other hand, this clarifies why none of the two-phase traffic-flow theories can explain the set of fundamental empirical features of traffic breakdown at highway bottlenecks.

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Phys. Rev. E 89, 052807– Published 13 May, 2014
  • Received 17 March 2014

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