  We present the detail of a newly developed relativistic transport model (ART
1.0) for high energy heavy-ion collisions. Using this model, we first study the
general collision dynamics between heavy ions at the AGS energies. We then show
that in central collisions there exists a large volume of sufficiently
long-lived superdense hadronic matter whose local baryon and energy densities
exceed the critical densities for the hadronic matter to quark-gluon plasma
transition. The size and lifetime of this matter are found to depend strongly
on the equation of state. We also investigate the degree and time scale of
thermalization as well as the radial flow during the expansion of the
superdense hadronic matter. The flow velocity profile and the temperature of
the hadronic matter at freeze-out are extracted. The transverse momentum and
rapidity distributions of protons, pions and kaons calculated with and without
the mean field are compared with each other and also with the preliminary data
from the E866/E802 collaboration to search for experimental observables that
are sensitive to the equation of state. It is found that these inclusive,
single particle observables depend weakly on the equation of state. The
difference between results obtained with and without the nuclear mean field is
only about 20\%. The baryon transverse collective flow in the reaction plane is
also analyzed. It is shown that both the flow parameter and the strength of the
``bounce-off'' effect are very sensitive to the equation of state. In
particular, a soft equation of state with a compressibility of 200 MeV results
in an increase of the flow parameter by a factor of 2.5 compared to the cascade
case without the mean field. This large effect makes it possible to distinguish
the predictions from different theoretical models and to detect the signatures
