We study the process of diffusive conduction that we use in our optoelectronic switches to achieve rapid optical switching (on a picosecond time scale). We present the characteristic Green's function of the diffusive conduction derived for arbitrary initial conditions. We also report the series solutions of the diffusive conduction obtained for different boundary conditions (V=0 and del V=0 along the device contact lines) in different device geometries (rectangular and circular mesas). Using these analytical results, we investigate the effect of boundary conditions on the switching operation and the steady state behavior in optical links. We demonstrate the feasibility of using such diffusive conductive optoelectronic switches to establish optical links in return-to-zero and non-return-to-zero coding schemes. For multichannel optical switching, we discuss possible use of a single optoelectronic switch to accommodate multiple channels at once, with > 100 optical channels (with a 2000 mm(-2) channel density and < 10% cross-talk), predicted on a 300x300 mu m(2) mesa with a device switching bandwidth of > 50 GHz, leading to a 5 Tb/s aggregate transmission in principle. This approach of using multiple parallel channels on a single switch is completely opposite to the traditional idea of arraying many switches. This proposed scheme eliminates the need for on-chip switch integration and the need for the alignment of the optical channels to the integrated individual switches.