The universality of multidimensional switching networks

Multidimensional switching networks are networks that utilize more than one degree of freedom (e.g., space, wavelength, time, code). The main idea is to use several dimensions of practical size in hierarchical multiplexing to overcome the physical constraints present when using only one dimension of large size. We generalize the case of one-dimensional switching networks to k-dimensional switching networks. Such networks have high degree of connectivity (≫1000) and reduced complexity compared to one-dimensional networks. We introduce a technology-independent universal theory discussing two models, one of multidimensional selective switching, and the other of multidimensional broadcasting, concentrating on complexity and channel assignment. The required size of each dimension, hardware complexities, channel assignment, and corresponding routing algorithms and their time complexities are discussed. It is shown with examples bow the complexity of these networks can be reduced to a minimum by optimal allocation of the complexity in each dimension. Several realizations of three-dimensional wavelength-time-space networks using different technologies (e.g., fiber optics, acousto-optics, free-space and photonic switching) are described for both models