Optimal balancing of road traffic density distributions for the Cell Transmission Model

Abstract

Abstract-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.

Density/Flow reconstruction via heterogeneous sources and Optimal Sensor Placement in road networks

“…The latter are commonly considered a good representation of the state of the system, providing more information than average speed alone. In particular, they are of crucial importance for 1) forecasting travel time and traffic evolution, along with historical data; 2) informing in real-time drivers about the state of the network through navigation systems; 3) providing public authorities with statistical data to monitor the state of the network and predict dangerous scenarios; 4) computing and actuating control actions through traffic lights, ramp metering and speed limits, or, in the future, lane change and semi-autonomous routing and navigation (Papageorgiou et al, 2003(Papageorgiou et al, , 1991Pisarski and Canudas de Wit, 2012;Como et al, 2013).…”

Adaptive networked model predictive control of freeway traffic systems

“…For this reason researchers are currently investigating solutions to control traffic in such a way that the traffic state is kept far from congestion, or an optimal balancing of traffic density distributions is attained [1], so that secondary problems related to congested traffic, such as pollution and safety, are alleviated [2].…”

“…Note that the use of MPC to control freeway traffic has already been investigated in the literature (see for instance [5], [6], [10], [11]). Moreover, optimal arguments have been involved to design efficient traffic control algorithms [6], [1]. The originality of the present proposal mainly relies on the adaptive tuning of the MPC optimization horizon, which is designed so as to take into account the network non idealities.…”

Optimal traffic control in highway transportation networks using linear programming

“…A large number of estimation and control methods for PDEs rely on model reduction, that is, the conversion of the PDE into a discrete or continuous time lumped parameter system [9]. Examples of such methods include [10], [11], [12], [13], [14], [15], [16]. Some methods however do not require such an approximation, such as backstepping methods in [17] for chemical reactors and Lyapunov methods in [18] for the the stabilization of the Burgers equation.…”