  The relaxation dynamics of the one-dimensional totally asymmetric simple
exclusion process on a ring is considered in the case of step initial
condition. Analyzing the time evolution of the local particle densities and
currents by the Bethe ansatz method, we examine their full relaxation dynamics.
As a result, we observe peculiar behaviors, such as the emergence of a ripple
in the density profile and the existence of the excessive particle currents.
Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes
of the local densities and currents, we find the scaling exponents with respect
to the total number of sites to be -3/2 and -1 respectively.
