  We investigate the distribution of waiting times between electrons emitted
from a periodically driven single-electron turnstile. To this end, we develop a
scheme for analytic calculations of the waiting time distributions for
arbitrary periodic driving protocols. We illustrate the general framework by
considering a driven tunnel junction before moving on to the more involved
single-electron turnstile. The waiting time distributions are evaluated at low
temperatures for square-wave and harmonic driving protocols. In the adiabatic
regime, the dynamics of the turnstile is synchronized with the external drive.
As the non-adiabatic regime is approached, the waiting time distribution
becomes dominated by cycle-missing events in which the turnstile fails to emit
within one or several periods. We also discuss the influence of finite
electronic temperatures. The waiting time distributions provide a useful
characterization of the driven single-electron turnstile with complementary
information compared to what can be learned from conventional current
measurements.
