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Determination of interaction potentials in freeway traffic from steady-state statistics

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  • Krbalek, Milan
  • Helbing, Dirk

Abstract

Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify compared to interactions in physical and chemical systems. We show that progress can be made by generalizing a method from equilibrium statistical physics we learned from random matrix theory. It allows one to determine the interaction potential via distributions of the netto distances s of vehicles. Assuming power-law interactions, we find that driver behavior can be approximated by a forwardly directed 1/s potential in congested traffic, while interactions in free traffic are characterized by an exponent of α≈4. This is relevant for traffic simulations and the assessment of telematic systems.

Suggested Citation

  • Krbalek, Milan & Helbing, Dirk, 2004. "Determination of interaction potentials in freeway traffic from steady-state statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 370-378.
    • Handle: RePEc:eee:phsmap:v:333:y:2004:i:c:p:370-378
    DOI: 10.1016/j.physa.2003.10.059
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    Citations

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    Cited by:

    1. Kosun, Caglar & Ozdemir, Serhan, 2016. "A superstatistical model of vehicular traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 466-475.
    2. Krbálek, Milan & Hrabák, Pavel & Bukáček, Marek, 2018. "Pedestrian headways — Reflection of territorial social forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 38-49.
    3. Kosun, Caglar & Ozdemir, Serhan, 2017. "Determining the complexity of multi-component conformal systems: A platoon-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 688-695.
    4. Wagner, Peter, 2012. "Analyzing fluctuations in car-following," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1384-1392.
    5. Wagner, Peter & Nippold, Ronald & Gabloner, Sebastian & Margreiter, Martin, 2016. "Analyzing human driving data an approach motivated by data science methods," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 37-45.
    6. Bari, Chintaman Santosh & Chandra, Satish & Dhamaniya, Ashish, 2022. "Service headway distribution analysis of FASTag lanes under mixed traffic conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    7. Helbing, Dirk & Treiber, Martin & Kesting, Arne, 2006. "Understanding interarrival and interdeparture time statistics from interactions in queuing systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 62-72.
    8. Schönhof, Martin & Kesting, Arne & Treiber, Martin & Helbing, Dirk, 2006. "Coupled vehicle and information flows: Message transport on a dynamic vehicle network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 73-81.

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