  We numerically study the large deviation function of the total current, which
is the sum of local currents over all bonds, for the symmetric and asymmetric
simple exclusion processes with open boundary conditions. We estimate the
generating function by calculating the largest eigenvalue of the modified
transition matrix and by population Monte Carlo simulation. As a result, we
find a number of interesting behaviors not observed in the exactly solvable
cases studied previously as follows. The even and odd parts of the generating
function show different system-size dependences. Different definitions of the
current lead to the same generating function in small systems. The use of the
total current is important in the Monte Carlo estimation. Moreover, a cusp
appears in the large deviation function for the asymmetric simple exclusion
process. We also discuss the convergence property of the population Monte Carlo
simulation and find that in a certain parameter region, the convergence is very
slow and the gap between the largest and second largest eigenvalues of the
modified transition matrix rapidly tends to vanish with the system size.
