Conservation versus balance laws in traffic flow

This note discusses the role of source terms in the modeling of vehicular traffic through conservation laws. As is well known, a source term in the equation for the vehicular density may represent entries or exits. When a second conservation laws is present, suitable source terms may describe various inhomogeneities of the road, such as ascents, descents or fog banks. In each of these cases, we provide an analytical framework. Finally, numerical experiments show specific phenomena that may not be reproduced by purely conservative models.