Martinovich, Kristóf and Stépán, Gábor and Bachrathy, Dániel and Kiss, Ádám (2025) Introducing state-dependent delay in the car-following model. NONLINEAR DYNAMICS, 113. pp. 22923-22941. ISSN 0924-090X
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Abstract
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.
| Item Type: | Article |
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| Additional Information: | First published online: 26 June 2025 Acknowledgements This paper was supported by the Doctoral Excellence Fellowship Programme (DCEP) is funded by the National Research Development and Innovation Fund of the Ministry of Culture and Innovation and the Budapest University of Technology and Economics, by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the Hungarian National Research, Development and Innovation Office (NKFI-KKP-133846 and FK-138500). This project has received funding from the HUN-REN Hungarian Research Network. Author contributions K.M. conducted the theoretical study and the calculations and wrote the first draft of the manuscript, A.K.K. supported the study and helped with the writing, A.K.K., D.B. and G.S. supervised the project, including the development of the theory, results and writing. Funding Open access funding provided by Budapest University of Technology and Economics. Data Availibility Statement No datasets were generated or analysed during the current study. |
| Uncontrolled Keywords: | State-dependent delay, Global Stability Analysis, Bistability, Traffic Dynamics, Phantom Traffic Jam |
| Subjects: | T Technology / alkalmazott, műszaki tudományok > TJ Mechanical engineering and machinery / gépészmérnöki tudományok |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 26 Sep 2025 08:20 |
| Last Modified: | 26 Sep 2025 08:20 |
| URI: | https://real.mtak.hu/id/eprint/225474 |
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