Modeling

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of hybrid boundary conditions is needed for the problem to be well posed. The boundary conditions are represented by a hybrid automaton with switches between the modes determined by the direction of characteristics of the system at the boundary. The existence of the solution results from the convergence of a Godunov scheme derived in this article. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for...

Intersection delays are the major contributing factor to arterial delays. Methods to estimate intersection delay patterns by using measured travel times are studied. The delay patterns provide a way to estimate the delay for any vehicle arriving at the intersection at any time, which is useful for providing time-dependent intersection delay information to the driving public. The model requires sampled travel times between two consecutive locations on arterial streets, one upstream and the other downstream of a signalized intersection, without the need to know signal timing or traffic flow...

This brief derives a method for open-loop control of open channel flow, based on the Hayami model, a parabolic partial differential equation resulting from a simplification of the Saint-Venant equations. The open-loop control is represented as infinite series using differential flatness, for which convergence is assessed. A comparison is made with a similar problem available in the literature for thermal systems. Numerical simulations show the effectiveness of the approach by applying the open-loop controller to irrigation canals modeled by the full Saint-Venant equations.

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is...