Time-resolved numerical analysis of a nonlinear Sagnac interferometer switch (NSIS) reveals that combined effects of group velocity dispersion (GVD), self phase modulation, cross phase modulation, and pump-probe walk-off, seriously degrade switching performance when the soliton number N of the pump pulse is under 5. This means the peak power of short pump pulses can not, even with a long fiber loop NSIS, be reduced to less than the critical value at N>5 to prevent the effect of GVD. This restriction becomes more severe for pump pulses in the anomalous dispersion region than for those in the normal dispersion region because of higher order soliton compression. System designs are discussed for time-division demultiplexers that use NSIS's and picosecond pump pulses generated by a laser-diode coupled to erbium-doped fiber amplifiers. It is found that 1:32 demultiplexing from 160 to 5 Gb/s and 1:8 demultiplexing from 80 to 10 Gb/s with a switching contrast of more than 60 are possible using diode-laser pumped 1- and 2-ps pump pulses, respectively, assuming +20 dBm satulation output power of an optical amplifier.