### James M. Greenberg, Department of Mathematical Sciences, Carnegie
Mellon University

### Congestion on Multilane Highways

On the multilane freeways one often observes distinct stable equilibrium relationships between auto velocity and density.
Prototypical situations involve two equilibria

where and are monotone decreasing
and satisfy
. The upper
curve is typically stable for densities satisfying
whereas the lower curve is stable for densities satisfying
. Our interest is in the
situation where
and
.

In this paper we present a model which incorporates both equilibrium
curves and a simple switching mechanism which allows drivers to
transition from one equilibrium curve to the other. What we observe
with this model are relaxation oscillations seen in congested traffic;
i.e. periodic waves separating fast and slow moving traffic which
propagate upstream.

Joint work with A. Klar and M. Rascle.

**Location:** PPB 300

**Time:** 1:30 P.M.