  We calculate the distribution of the distance headways (i.e., the
instantaneous gap between successive vehicles) as well as the distribution of
instantaneous distance between successive jams in the Nagel-Schreckenberg (NS)
model of vehicular traffic. When the maximum allowed speed, $V_{max}$, of the
vehicles is larger than unity, over an intermediate range of densities of
vehicles, our Monte Carlo (MC) data for the distance headway distribution
exhibit two peaks, which indicate the coexistence of "free-flowing" traffic and
traffic jams. Our analytical arguments clearly rule out the possibility of
occurrence of more than one peak in the distribution of distance headways in
the NS model when $V_{max} = 1$ as well as in the asymmetric simple exclusion
process. Modifying and extending an earlier analytical approach for the NS
model with $V_{max} = 1$, and introducing a novel transfer matrix technique, we
also calculate the exact analytical expression for the distribution of distance
between the jams in this model; the corresponding distributions for $V_{max} >
1$ have been computed numerically through MC simulation.
