Modeling nonlinear road traffic networks for junction control

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.

An advance in infinite graph models for the analysis of transportation networks

“…Most of the problems described above can be modeled from the point of view of extremal graph theory we have considered in this paper, since d(p) and ex(n; T K p ) refer to the possibility of having a complete graph K p as a subgraph inside the network. Hence, we maintain that the search of complete graphs in networks can complement other approaches (see, e.g., Dridi and Kacem, 2004;Péter, 2012). However, we think that the greatest benefit of our generalization of the average degree comes from the fact that it is useful to model complex, increasing networks.…”

“…As graph theory is particularly related to networks (Diestel, 2000;Péter, 2012;Peng et al, 2013;Kudělka et al, 2015), we tried to solve the proposed questions with the help of graphs.…”

Mathematical Modeling of Automotive Supply Chain Networks

“…In the majority of the transportation systems the original physical meaning of the states meet this requirement (Péter, 2012).…”

Cooperative driving at isolated intersections based on the optimal minimization of the maximum exit time

“…Over the past half-century, a great deal of traffic control strategies concerning isolated intersections have emerged and have been widely used. From the earlier work of Webster (1958) to the recent works (Robertson, 1969;Allsop, 1971;1976;Sims and Dobinson 1980;Hunt, 1982;Farges et al, 1983;Gartner, 1983;Sen and Head, 1997;Lee and Hyung, 1999;Boillot et al, 2000;Mirchandani and Head 2001;Mirchandani and Lukas 2001;Péter, 2012), these systems have achieved great success in reducing the average delay of vehicles and in improving the traffic throughput, especially through the emergence of adaptive traffic control systems (Hunt, 1982;Farges et al, 1983;Sen and Head, 1997;Mirchandani and Head 2001;Mirchandani and Lukas 2001). However, the increased importance of environmental concerns and the limited economic and physical resources are among the most important reasons why these traditional traffic control systems cannot continue being the answer to the ever-increasing transportation and mobility needs of modern societies.…”