Toward Using the Network as a Switch: On the Use of TDM in Linear Optical Networks

A common problem in optical networking is that the large quantity of raw bandwidth available in such networks is often difficult to access. We show that time-division multiplexing (TDM) can be used to operate bus and ring architectures in a manner akin to a switch. Doing so substantially reduces the amount of hardware [particularly, add–drop multiplexers (ADMs)] needed to utilize fully the available bandwidth in a range of optical networks. We show that a significant fraction (and in some cases all) of the bandwidth available to the system can be utilized even if each node in the system has only a single ADM. Our approach is probabilistic in nature, using generalizations of the Birkhoff-von Neumann statistical multiplexing approaches that have been successful in switching theory. Our techniques rely on decompositions of fractional matchings (for architectures without erasures) and fractional interval graph colorings (for architectures with erasures) into integral matchings and colorings.