  This paper provides necessary conditions and sufficient conditions for the
(global) Input-to-State Stability property of simple uncertain
vehicular-traffic network models under the effect of a PI-regulator. Local
stability properties for vehicular-traffic networks under the effect of
PI-regulator control are studied as well: the region of attraction of a locally
exponentially stable equilibrium point is estimated by means of Lyapunov
functions. All obtained results are illustrated by means of simple examples.
