  We obtain the large deviation function for entropy production of the medium
and its distribution function for two-site totally asymmetric simple exclusion
process(TASEP) and three-state unicyclic network. Since such systems are
described through microscopic irreversible transitions, we obtain
time-dependent transition rates by sampling the states of these systems at a
regular short time interval $\tau$. These transition rates are used to derive
the large deviation function for the entropy production in the nonequilibrium
steady state and its asymptotic distribution function. The shapes of the large
deviation function and the distribution function depend on the value of the
mean entropy production rate which has a non-trivial dependence on the particle
injection and withdrawal rates in case of TASEP. Further, it is argued that in
case of a TASEP, the distribution function tends to be like a Poisson
distribution for smaller values of particle injection and withdrawal rates.
