Optimization of Traffic on Road Networks

Abstract

This paper focuses on the optimization of traffic flow on a road network, modeled by a fluid-dynamic approach. Three cost functionals that measure average velocity, average traveling time, and total flux of cars, are considered. First, such functionals are optimized for two simple networks that consist of a single junction: one with two incoming and one outgoing roads (junctions of 2 × 1 type), and the other with one incoming and two outgoing roads (junctions of 1 × 2 type). The optimization is made with respect to right of way parameters and traffic distribution coefficients, obtaining an explicit solution. Then, through simulations, the traffic behavior for complex networks is studied. The main result is that the local optimization ensures a very good result also for the complete network. This is shown by the case study of Re di Roma Square, a big traffic circle of the urban network of Rome.

A discussion about the homogenization of moving interfaces

“…Models about the optimal control of traffic flow have attracted considerable attention recently; see, for example, the monograph [5] and to the survey papers [6,23]. In fact, several optimal control problems of the type discussed above have been looked at in the literature, some of which having for more general junction conditions; see, for instance, [5,7,8,9,10,14,15,17,18,24]. In particular, [17] derives optimality conditions assuming the smoothness of the optimal solution.…”

“…In particular, [17] derives optimality conditions assuming the smoothness of the optimal solution. In [14], the controls are assumed to be constant in time. Reference [15] discusses how to minimize the queue length, the total variation of traffic speed (see also [16]), and general functions of the density as in (1.2) for problems on the half-line.…”

Stochastic optimal control problem of constrained switching system with delay

“…Investigated stochastic delay systems are widely used in various optimization problems of nuclear fission, communication , self-oscillating, biology, technology, engineering and economy [9,13,21,23,32,45,47]. A classical approach for optimization, and particularly for control problems are to derive necessary conditions satisfied by an optimal solution.…”

“…By (9) and (11) , through the simple transformations, expression (12) can be rewritten under the following form:…”

“…The differential equations with time delay can be used in modeling of processes with a memory; that is, the behaviour of the system is dependent of the past [33,38]. Many problems in physics,engineering, biological and economical sciences are expressed in terms of optimality principles, which often provide the most compact description of the laws governing dynamics and design of a systems [9,40,47]. Optimization problems for delay control systems have attracted a lot of interest [21,23,25,27].…”