Hamiltonian p-cycles for fiber-level protection in semi-homogeneous homogeneous and optical networks

Recently there has been interest in DWDM-based optical networks that are assumed to employ exactly two working fibers uniformly on every span (or "link"). At the fiber level such networks are referred to as homogeneous networks. An interesting and highly efficient strategy for protection of such networks is to use a single dark-fiber p-cycle formed on a Hamiltonian cycle (if it exists). We show that in a homogeneous Hamiltonian network, a Hamiltonian p-cycle is the most efficient overall solution, although interestingly it does not always correspond to the individually most efficient p-cycle that can be formed. We also consider p-cycle planning in non-Hamiltonian but homogeneous networks and introduce the concept of a semi-homogenous network, specifically linked to the p-cycle concept. The proposed semi-homogeneous class of network actually realizes the theoretical lower bound on span-restorable networks in terms of network redundancy. Such networks also provide a strategy to accommodate certain patterns of capacity growth beyond a homogenous network without any increase in protection capacity. The work also demonstrates and explains why a single Hamiltonian p-cycle is not as efficient as a specifically optimized set of individual p-cycles in a "capacitated" (non-homogeneous) network where the working capacity on each span varies in a general way. These discussions provide new options for DWDM network architecture and also clarify some possible confusions about the applicability of Hamiltonian p-cycles and generalized sets of p-cycles.