A quantum random number generation method based on measuring the time differences between photon detections is analyzed mathematically in terms of bit generation efficiency and bit generation rate. It was found that these two values cannot be maximized simultaneously by altering the incident photon rate of a light source with Poisson statistics, but the generation rate can be increased at the expense of efficiency. Analytical results are presented for both an idealized and a practical case. The detector’s dead time has been taken into consideration in the latter case, implying that, for certain combinations of the dead time and the measurement clock period, the generation rate becomes a two-peaked function of the incident photon rate. The theoretical results are confirmed by simulations, showing excellent agreement between the two.