Nonlocal traffic flow models have been introduced to macroscopically model the effect of downstream information on driver behavior, allowing them to anticipate traffic conditions ahead. Here, the term "nonlocal" refers to the dependence of the flux function on a convolution between a kernel function and the conserved quantity. In real-world applications, we must additionally account for stochastic influences, which can arise from measurement errors in autonomous vehicles or uncertainty in human driver behavior.

In this talk, we consider nonlocal traffic flow models with random velocity functions. The randomness is introduced via a space-dependent multiplicative noise defined by a random field. For such stochastic nonlocal conservation laws, the existence, uniqueness, and stability of solutions must be reassessed in the presence of random, space-dependent fluxes. Furthermore, new challenges arise when characterizing stochastic moments, such as the expected density. To establish the pathwise well-posedness of weak solutions under space-dependent stochasticity, assumptions regarding the regularity of the random field are crucial. This talk focuses on the specific conditions under which the well-posedness of numerical solutions can be established.

Finally, we present numerical simulations using a Hilliges–Weidlich-type scheme. Suitable realizations of the random field are generated using a Karhunen–Loève expansion with a Matérn covariance kernel, and approximations of the expected density are investigated.