  We show that the stationary measure for the totally asymmetric simple
exclusion process on a segment with open boundaries is given by a marginal of a
two-line measure with a simple and explicit description. We use this
representation to analyze asymptotic fluctuations of the height function near
the triple point for a larger set of parameters than was previously studied. As
a second application, we determine a single expression for the rate function in
the large deviation principle for the height function in the fan and in the
shock region. We then discuss how this expression relates to the expressions
available in the literature.
