Institute of Fundamental Technological Research

In this paper, we study the problem of optimal balancing of vehicle density in freeway traffic. The optimization is performed in a distributed manner by utilizing the controllability properties of the freeway network represented by the Cell Transmission Model. By using these properties, we identify the subsystems to be controlled by local ramp meters. The optimization problem is then formulated as a noncooperative Nash game that is solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employs the communication channels matching the switching structure of system interconnectivity. By defining the internal model for the boundary flows, local optimal control problems are efficiently solved by utilizing the method of linear quadratic regulator. The developed control strategy is tested via numerical simulations in two scenarios for uniformly congested and transient traffic.

This paper presents the application of the idea of optimal balancing of traffic density distribution. The idea was previously studied in the papers [1], [2], and here it is implemented to the Grenoble South Ring in the context of the Grenoble Traffic Lab. The traffic on the ring is represented by the Cell Transmission Model that was tuned by using real data and Aimsun micro-simulator. A special attention is paid to the calibration of a flow merging model. A large-scale optimization problem is solved by using decomposition methods and it is implemented by introducing combinatorial procedures. The main difficulties in the implementation as well as the limitations of the designed software are highlighted. Finally, the results of different traffic scenarios on the Grenoble South Ring are presented.

The problem of equilibrium points for the Cell Transmission Model is studied. The structure of equilibrium sets is analyzed in terms of model parameters and boundary conditions. The goal is to determine constant input flows, so that the resultant steady state of vehicle density is uniformly distributed along a freeway. The necessary and sufficient conditions for the existence of one-to-one relation between input flow and density are derived. The equilibrium sets are described by formulas that allow to design a desired balanced density. A numerical example for the case of a two-cell system is presented.

Traffic control, Vectors, Vehicles, Equations, Boundary conditions, Steady-state

In this paper, we study the problem of optimal balancing of traffic density distributions. The optimization is carried out over the sets of equilibrium points for the Cell Transmission Traffic Model. The goal is to find the optimal balanced density distribution that maximizes the Total Travel Distance. The optimization is executed in two steps. At the first step, we consider a nonlinear problem to find a uniform density distribution that maximizes the Total Travel Distance. The second step is to solve the constrained quadratic problem to find the near balanced optimal equilibrium point. At both steps, we use decomposition methods. The quadratic optimization problem is solved by using the Dual Problem. The computational algorithms associated to such a problem are given.

Traffic control, Optimization, Vectors, Vehicles, Equations, Boundary conditions