  In 1992, Bitar and Goles introduced the parallel chip-firing game on
undirected graphs. Two years later, Prisner extended the game to directed
graphs. While the properties of parallel chip-firing games on undirected graphs
have been extensively studied, their analogs for parallel chip-firing games on
directed graphs have been sporadic. In this paper, we prove the outstanding
analogs of the core results of parallel chip-firing games on undirected graphs
for those on directed graphs. We find the possible periods of a parallel
chip-firing game on a directed simple cycle and use Gauss-Jordan Elimination on
a Laplacian-like matrix to establish a lower bound on the maximum period of a
parallel chip-firing game on a directed complete graph and a directed complete
bipartite graph. Finally, we use the method of motors by Jiang, Scully, and
Zhang to show that a binary string $s$ can be the atomic firing sequence of a
vertex in a parallel chip-firing game on a strongly connected directed graph if
and only if $s$ contains 1 or $s=0$.
