  We consider the one-dimensional totally asymmetric simple exclusion model
(TASEP model) with open boundary conditions and present the analytical
computations leading to the exact formula for distance clearance distribution,
i.e. probability density for a clear distance between subsequent particles of
the model. The general relation is rapidly simplified for middle part of the
one-dimensional lattice using the large $N$ approximation. Both the analytical
formulas and their approximations are successfully compared with the numerical
representation of the TASEP model. Furthermore, we introduce the pertinent
estimation for so-called spectral rigidity of the model. The results obtained
are sequentially discussed within the scope of vehicular traffic theory.
