Numerical techniques for the simulation of an ODE-PDE model for supply chains are presented. First we describe a scheme, based on Upwind and explicit Euler methods, provide corrections to maintain positivity of solutions, prove convergence and provide convergence rate. The latter is achieved via comparison with Wave Front Tracking solutions and the use of generalized tangent vectors. Different choice of time and space meshes give similar results, both for CPU times and numerical errors. Fast algorithms, based on an accurate choice of time and space meshes and data structures, are then proposed, achieving high computational gains.

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The aim of this work is to present a technique for the optimisation of emergency vehicles travel times on assigned paths when critical situations, such as car accidents, occur. Using a fluid-dynamic model for the description of car density evolution, the attention is focused on a decentralised approach reducing to simple junctions with two incoming roads and two outgoing ones (junctions of 2 × 2 type). We assume the redirection of cars at junctions is possible and choose a cost functional that describes the asymptotic average velocity of emergency vehicles. Fixing an incoming road and an outgoing road for the emergency vehicle, we determine the local distribution coefficients that maximise such functional at a single junction. Then we use the local optimal coefficients at each node of the network. The overall traffic evolution is studied via simulations, both for simple junctions or cascade networks, evaluating global performances when optimal parameters on the network are used.

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Abstract. The aim of this work is to understand how urban traffic behavior, especially in cases of congestion, can be improved by an accurate choice of traffic coefficients. For this, we define three cost functionals that measure average velocity, average travelling time and total flux of cars. The global optimal control problem for a complex network is difficult to solve both from analytical and numerical points of view. Thus, we focus on a simple junction with one incoming road and two outgoing roads (junctions of 1 × 2 type), obtaining exact solutions to a simple optimization problem. Then, we use such results at each node of the network. The traffic evolution of some networks is then studied via simulations. In particular, it is shown that an appropriate choice of the traffic distributions can be useful in order to improve network conditions.