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<p>In this paper, we introduce a novel state-dependent delay model that aims to more realistically describe the variable nature of human reaction time in car-following dynamics. Instead of the traditional approach of assuming a fixed reaction time, we consider that it is proportional to the distance between vehicles (headway) modelled by a state-dependent delay. We outline the framework for linearisation and present the possible methods for both linear and nonlinear analysis. Through a detailed benchmark case study, we demonstrate how the parameters and the state-depend delay influence whether traffic remains smooth or breaks down into congestion. Numerical simulations, linear stability, and bifurcation diagrams reveal that, unlike models with constant delays, the state-dependent delay model causes significant bistable regions, where smooth traffic flow and stop-and-go traffic can both occur under the same conditions, depending on perturbations (like a driver braking suddenly). This explains better the emergence of“phantom traffic jams”, where congestion might appear without any obvious reason. Consequently, we present the extended stability diagrams, incorporating the bistable region, that can aid in the design and study of real-world traffic systems.</p>

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Introducing state-dependent delay in the car-following model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月26日

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  • Kristof Martinovich,
  • Gabor Stepan,
  • Daniel Bachrathy,
  • Adam K. Kiss

摘要

In this paper, we introduce a novel state-dependent delay model that aims to more realistically describe the variable nature of human reaction time in car-following dynamics. Instead of the traditional approach of assuming a fixed reaction time, we consider that it is proportional to the distance between vehicles (headway) modelled by a state-dependent delay. We outline the framework for linearisation and present the possible methods for both linear and nonlinear analysis. Through a detailed benchmark case study, we demonstrate how the parameters and the state-depend delay influence whether traffic remains smooth or breaks down into congestion. Numerical simulations, linear stability, and bifurcation diagrams reveal that, unlike models with constant delays, the state-dependent delay model causes significant bistable regions, where smooth traffic flow and stop-and-go traffic can both occur under the same conditions, depending on perturbations (like a driver braking suddenly). This explains better the emergence of“phantom traffic jams”, where congestion might appear without any obvious reason. Consequently, we present the extended stability diagrams, incorporating the bistable region, that can aid in the design and study of real-world traffic systems.