This article deals with the modeling of junctions in a road network from a macroscopic point of view. After reviewing the Aw & Rascle second order model, a compatible junction model is proposed. The properties of this model and particularly the stability are analyzed. It turns out that this model presents physically acceptable solutions, is able to represent the capacity drop phenomenon and can be used to simulate the traffic evolution on a network.

It is shown how an entropy-based Lyapunov function can be used for the stability analysis of equilibria in networks of scalar conservation laws. The analysis gives a sufficient stability condition which is weaker than the condition which was previously known in the literature. Various extensions and generalisations are briefly discussed. The approach is illustrated with an application to ramp-metering control of road traffic networks.

This article deals with the modelling of a road network from a macroscopic point of view. First, the existing models for a road network based on the LWR model are reviewed. Then, these models are extended to take account of the capacity drop phenomenon. The consequences of this modification are finally illustrated in a particular case. Copyright c 2005 IFAC

Abstract-This paper proposes two methods to speed up the demanding time-domain simulations of large power system models. First, the sparse linear system to solve at each Newton iteration is decomposed according to its bordered block diagonal structure, in order to solve only those parts that need to be solved, and update only sub-matrices of the Jacobian that need to be updated. This brings computational savings without degradation of accuracy. Next, the Jacobian structure is further exploited to localize the system response, i.e. involve only the components identified as active, with an acceptable and controllable decrease in accuracy. The accuracy and computational savings are assessed on a large-scale test system.

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