<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner–inner, inner–outer and outer–outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form, where the states are vehicle densities on a particular lane and the dynamics are described by a nonlinear state constrained positive system. This model can be used directly for simulation and analysis and as a starting point for investigating various control strategies. The stability of the traffic over the network can be analyzed by constructing a linear Lyapunov function and the associated theory. The model points out that in intersection control one must take the traffic density values of both the input and the output sections into account. Generally, the control of any domain has to take the density of input and output sections into consideration.</p></abstract>

The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner–inner, inner–outer and outer–outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form, where the states are vehicle densities on a particular lane and the dynamics are described by a nonlinear state constrained positive system. This model can be used directly for simulation and analysis and as a starting point for investigating various control strategies. The stability of the traffic over the network can be analyzed by constructing a linear Lyapunov function and the associated theory. The model points out that in intersection control one must take the traffic density values of both the input and the output sections into account. Generally, the control of any domain has to take the density of input and output sections into consideration.

Modeling nonlinear road traffic networks for junction control

Department of Control and Transport Automation Budapest University of Technology and Economics (BME), Műegyetem rkp. 3, H-1111, Budapest, Hungary

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Modeling nonlinear road traffic networks for junction control"}

The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used....

Modeling nonlinear road traffic networks for junction control

Published Online: Sep 28, 2012

Page range: 723 - 732

DOI: https://doi.org/10.2478/v10006-012-0054-1

Keywords
mathematical modeling and control, traffic networks, nonlinear positive system, linear Lyapunov function

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Modeling nonlinear road traffic networks for junction control

Published Online: Sep 28, 2012

Page range: 723 - 732

DOI: https://doi.org/10.2478/v10006-012-0054-1

Keywordsmathematical modeling and control, traffic networks, nonlinear positive system, linear Lyapunov function

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
mathematical modeling and control, traffic networks, nonlinear positive system, linear Lyapunov function