A Fast Lax-Hopf Algorithm to Solve the Lighthill-Whitham-Richards Traffic Flow Model on Networks.
arXiv: Analysis of PDEs(2020)
Abstract
Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semianalytical Lax-Hopf algorithm in order to compute link inflows and outflows with the Lighthill-Whitham-Richards (LWR) model. Our proposed fast Lax-Hopf algorithm has a very low computational complexity. We demonstrate that some of the original algorithm's operations (associated with the initial conditions) can be discarded, leading to a faster computation of boundary demands/supplies in network simulation problems for general concave fundamental diagrams (FDs). Moreover, the computational cost can be further reduced for triangular FDs and specific space-time discretizations. The resulting formulation has a performance comparable to the link transmission model and because it solves the original LWR model for a wide range of FD shapes, with any initial configuration, it is suitable to solve a broad range of traffic operations problems. As part of the analysis, we compare the performance of the proposed scheme with that of other wellknown computational methods.
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Key words
LWR model,computational methods,Lax-Hopf formula,traffic simulation
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