We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a Godunov-type numerical scheme, we provide BV estimates and a discrete entropy inequality. Together with the L1-contractivity property, we prove existence and uniqueness of weak solutions. Numerical examples show the nonlocal impact compared to local flux functions and local sources.
Nonlocal approaches for multilane traffic models / Friedrich, Jan; Göttlich, Simone; Rossi, Elena. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 19:8(2021), pp. 2291-2317. [10.4310/CMS.2021.v19.n8.a10]
Nonlocal approaches for multilane traffic models
Rossi, Elena
2021
Abstract
We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a Godunov-type numerical scheme, we provide BV estimates and a discrete entropy inequality. Together with the L1-contractivity property, we prove existence and uniqueness of weak solutions. Numerical examples show the nonlocal impact compared to local flux functions and local sources.
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