Nonlocal reaction traffic flow model with on-off ramps

1.1. Scope. Models of conservation laws with nonlocal flux are used to describe traffic flow dynamics in which drivers adapt their velocity with respect to what happens to the cars in front of them [3, 5, 10, 15, 18]. In this type of models, the flux function depends on a downstream convolution term between the density or the velocity of vehicles and a kernel function with support on the negative axis. However, the above models cannot be used to study the traffic flow on the highway with ramps since they did not include their presence. Indeed, ramps are an important element of traffic systems and develops some complex traffic phenomena, see [11, 14, 16, 19, 20, 21, 22]. In this work, we propose a new nonlocal traffic model which includes the effects of onand offramps. We start by considering a local reaction traffic model proposed in [16],

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