  We investigate piecewise deterministic Markov processes (PDMP), where the
deterministic dynamics follows a scalar conservation law and random jumps in
the system are characterized by changes in the flux function. We show under
which assumptions we can guarantee the existence of a PDMP and conclude bounded
variation estimates for sample paths. Finally, we apply this dynamics to a
production and traffic model and use this framework to incorporate the
well-known scattering of flux functions observed in data sets.
