Abstract
The objective of this paper is to analyze the inclusion of one or more random parameters into the deterministic Lighthill-Whitham-Richards traffic flow model and use a semi-intrusive approach to quantify uncertainty propagation. To verify the validity of the method, we test it against real data coming from vehicle embedded GPS systems, provided by Autoroutes Trafic.
Highlights
Macroscopic traffic flow models consisting in partial differential equations are used to simulate traffic flows on road networks since decades [25]
We focus on the basic Lightwill-Whitham-Richards (LWR) first order model [17, 22], augmented with random variables in the velocity function and the initial condition to account for real data uncertainty
We show some results concerning the stochastic conservation law (4.1) with random flux function (4.4) without capacity drop and piece-wise constant initial datum ρ0(x) = ρL = 10 for x < x0 and ρ0(x) = ρR = 80 for x > x0, x0 = 0.5
Summary
Macroscopic traffic flow models consisting in (systems of) partial differential equations are used to simulate traffic flows on road networks since decades [25]. We focus on the basic Lightwill-Whitham-Richards (LWR) first order model [17, 22], augmented with random variables in the velocity function and the initial condition to account for real data uncertainty. This model is designed to cope with the traffic data set we were provided, which consists of floating car data coming from embedded GPS devices. Well-posedness results for problem (4.1) in the case F ∈ W 1,∞(R; R) can be found in [19, Theorem 3.3] and [18, Theorem 3.11]
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