  We study the phase diagram of the continuum traffic flow model of a highway
with an on-ramp. Using an open boundary condition, traffic states and
metastabilities are investigated numerically for several representative values
of the upstream boundary flux $f_{up}$ and for the whole range of the on-ramp
flux $f_{rmp}$. An inhomogeneous but time-independent traffic state (standing
localized cluster state) is found and related to a recently measured traffic
state. Due to the density gradient near the on-ramp, a novel traffic jam can
occur even when the downstream density is below the critical density of the
usual traffic jam formation in homogeneous highways, and its structure varies
qualitatively with $f_{rmp}$. The free flow, the recurring hump (RH) state, and
the traffic jam can all coexist in a certain metastable region where the free
flow can undergo phase transitions either to the RH state or to the traffic jam
state. We also find two nontrivial analytic solutions. These solutions
correspond to the standing localized cluster state and the homogeneous
congested traffic state (one form of the novel traffic jam),which are observed
in numerical simulations.

Statistical Mechanics