Two effective temperatures in traffic flow models: analogies with granular flow

We present a model of traffic flow, with rules that describe the behaviour of automated vehicles in an open system. We show first of all that the fundamental diagram of this system collapses to a point, where states of free and jammed traffic can coexist in phase space. This leads us to consider separately the roles of average velocities and densities as better descriptors of the actual state of the traffic. Next, we observe that the transition between free and jammed traffic as a function of the braking parameter R is different for high and low initial densities, in the steady state; it turns out to be ‘smeared out’ for low densities, a behaviour which is already portended by the transient behaviour of the system. Our results indicate strongly that, at least for such models, two effective temperatures (one related to R, and the other to the density) are needed to describe the global behaviour of this system in statistical mechanical terms. Analogies with granular flow are discussed in this context.