Off-line permutation embedding and scheduling in multiplexed optical networks with regular topologies

There are two basic approaches for establishing a connection in a reconfigurable switched optical network, whose links are multiplexed with virtual channels (e.g., wavelengths or time slots). One is called path multiplexing (PM), in which the same virtual channel has to be used on each link along a path, and the other is link multiplexing (LM), in which different virtual channels may be used. In this paper, we focus on the problem of off-line permutation embedding and scheduling as a part of the comparative study of the multiplexing approaches. Specifically, we determine the minimum number of virtual channels per link needed for a given network to be rearrangeably nonblocking in PM and LM, respectively. We also examine the schedule length of a permutation in PM and LM when the network is blocking as a result of having an insufficient number of virtual channels per link. We found that PM and LM are equally effective in linear arrays, and LM is slightly more effective than PM in rings, meshes (grids), tori, and hypercubes.