  In this paper we describe a relation between a microscopic stochastic traffic
cellular automaton model (i.e., the STCA) and the macroscopic first-order
continuum model (i.e., the LWR model). The innovative aspect is that we
explicitly incorporate the STCA's stochasticity in the construction of the
fundamental diagram used by the LWR model. We apply our methodology to a small
case study, giving a comparison of both models, based on simulations,
numerical, and analytical calculations of their tempo-spatial behavior.

Statistical Mechanics