  In the universality class of the one dimensional Kardar-Parisi-Zhang surface
growth, Derrida and Lebowitz conjectured the universality of not only the
scaling exponents, but of an entire scaling function. Since Derrida and
Lebowitz's original publication [PRL 80 209 (1998)] this universality has been
verified for a variety of continuous time, periodic boundary systems in the KPZ
universality class. Here, we present a numerical method for directly examining
the entire particle flux of the asymmetric exclusion process (ASEP), thus
providing an alternative to more difficult cumulant ratios studies. Using this
method, we find that the Derrida-Lebowitz scaling function (DLSF) properly
characterizes the large system size limit (N-->infty) of a single particle
discrete time system, even in the case of very small system sizes (N <= 22).
This fact allows us to not only verify that the DLSF properly characterizes
multiple particle discrete-time asymmetric exclusion processes, but also
provides a way to numerically solve for quantities of interest, such as the
particle hopping flux. This method can thus serve to further increase the ease
and accessibility of studies involving even more challenging dynamics, such as
the open boundary ASEP.
