  Multiple partonic interactions are widely used to simulate the hadronic final
state in high energy hadronic collisions, and successfully describe many
features of the data. It is important to make maximum use of the available
physical constraints on such models, particularly given the large extrapolation
from current high energy data to LHC energies. In eikonal models, the rate of
multiparton interactions is coupled to the energy dependence of the total cross
section. Using a Monte Carlo implementation of such a model, we study the
connection between the total cross section, the jet cross section, and the
underlying event. By imposing internal consistency on the model, we derive
constraints on its parameters at the LHC. By imposing internal consistency on
the model and comparing to current data we constrain the allowed range of its
parameters. We show that measurements of the total proton-proton cross-section
at the LHC are likely to break this internal consistency, and thus to require
an extension of the model. Likely such extensions are that hard scatters probe
a denser matter distribution inside the proton in impact parameter space than
soft scatters, a conclusion also supported by Tevatron data on double-parton
scattering, and/or that the basic parameters of the model are energy dependent.
