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Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

Author

Listed:
  • Juan Francisco Sánchez-Pérez

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Santiago Oviedo-Casado

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Gonzalo García-Ros

    (Department of Mining and Civil Engineering, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Manuel Conesa

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

  • Enrique Castro

    (Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain)

Abstract

Hydrodynamic traffic models are crucial to optimizing transportation efficiency and urban planning. They usually comprise a set of coupled partial differential equations featuring an arbitrary number of terms that aim to describe the different nuances of traffic flow. Consequently, traffic models quickly become complicated to solve and difficult to interpret. In this article, we present a general traffic model that includes a relaxation term and an inflow of vehicles term and utilize the mathematical technique of nondimensionalisation to obtain universal solutions to the model. Thus, we are able to show extreme sensitivity to initial conditions and parameter changes, a classical signature of deterministic chaos. Moreover, we obtain simple relations among the different variables governing traffic, thus managing to efficiently describe the onset of traffic jams. We validate our model by comparing different scenarios and highlighting the model’s applicability regimes in traffic equations. We show that extreme speed values, or heavy traffic inflow, lead to divergences in the model, showing its limitations but also demonstrating how the problem of traffic jams can be alleviated. Our results pave the way to simulating and predicting traffic accurately on a real-time basis.

Suggested Citation

  • Juan Francisco Sánchez-Pérez & Santiago Oviedo-Casado & Gonzalo García-Ros & Manuel Conesa & Enrique Castro, 2024. "Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:532-:d:1336104
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    References listed on IDEAS

    as
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    5. Juan Francisco Sánchez-Pérez & Gonzalo García-Ros & Manuel Conesa & Enrique Castro & Manuel Cánovas, 2023. "Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations: Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator," Mathematics, MDPI, vol. 11(10), pages 1-28, May.
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