  We introduce a stochastic traffic flow model to describe random traffic
accidents on a single road. The model is a piecewise deterministic process
incorporating traffic accidents and is based on a scalar conservation law with
space-dependent flux function. Using a Lax-Friedrichs discretization, we show
that the total variation is bounded in finite time and provide a theoretical
framework to embed the stochastic process. Additionally, a solution algorithm
is introduced to also investigate the model numerically.
