When a photon is detected by a Geiger-mode avalanche photo-diode (GMAPD), the detector is rendered inactive, or blocked, for a certain period of time. In this paper we derive the blocking probability for a GMAPD whose input is either an unmodulated, Bernoulli modulated or pulse-position-modulated (PPM) Poisson process. We demonstrate how the PPM and Bernoulli cases differ, illustrating that the...