  We introduce a theoretical framework which is suitable for the description of
all spatial and time-multiplexed periodic single-photon sources realized or
proposed thus far. Our model takes into account all possibly relevant loss
mechanisms. This statistical analysis of the known schemes shows that
multiplexing systems can be optimized in order to produce maximal single-photon
probability for various sets of loss parameters by the appropriate choice of
the number of multiplexed units of spatial multiplexers or multiplexed time
intervals and the input mean photon pair number, and reveals the physical
reasons of the existence of the optimum. We propose a novel time-multiplexed
scheme to be realized in bulk optics, which, according to the present analysis,
would have promising performance when experimentally realized. It could provide
a single-photon probability of 85\% with a choice of experimental parameters
which are feasible according to the experiments known from the literature.
