  The Periodic Event Scheduling Problem (PESP) is the central mathematical tool
for periodic timetable optimization in public transport. PESP can be formulated
in several ways as a mixed-integer linear program with typically general
integer variables. We investigate the split closure of these formulations and
show that split inequalities are identical with the recently introduced flip
inequalities. While split inequalities are a general mixed-integer programming
technique, flip inequalities are defined in purely combinatorial terms, namely
cycles and arc sets of the digraph underlying the PESP instance. It is known
that flip inequalities can be separated in pseudo-polynomial time. We prove
that this is best possible unless P $=$ NP, but also observe that the
complexity becomes linear-time if the cycle defining the flip inequality is
fixed. Moreover, introducing mixed-integer-compatible maps, we compare the
split closures of different formulations, and show that reformulation or
binarization by subdivision do not lead to stronger split closures. Finally, we
estimate computationally how much of the optimality gap of the instances of the
benchmark library PESPlib can be closed exclusively by split cuts, and provide
better dual bounds for five instances.
