Optimal Survivable Routing with a Small Number of Hops

Abstract

Consider a given network defined by an undirected graph with a capacity value associated with each edge and a set of traffic commodities that must be routed through the network. Assume that the network contains at least D hop-constrained node disjoint routing paths between the origin and the destination nodes of each commodity. This paper addresses the minimum hop survivability routing problem, i.e., the determination of the routing paths optimizing hop related objective functions applied to the Δ minimum hop routing paths of each commodity, where 1 ≤ Δ ≤ D. We propose ILP formulations addressing two objective functions: the minimization of the average number of hops and the minimization of the maximum number of hops. In both cases, the proposed models let us address two common survivability mechanisms: the case with Δ = D corresponds to the Path Diversity mechanism and the case with Δ = D - 1 corresponds to the Path Protection mechanism. We present computational results using pre-dimensioned networks based on the NSF network for given estimated commodity demands. We study two traffic engineering issues: i) the relationship between the total commodity demand and the optimal values of the objective functions and ii) the impact of demand estimation errors on the feasibility of pre-dimensioned network design solutions. Concerning the efficiency of the proposed formulations, the results show that when Δ = D the proposed models are very efficient in all cases; the results also show that when Δ = D - 1 the proposed models are efficient when the total commodity demand is as much as 97.5% of the network capacity and become harder to solve when total demand reaches the limit of the network capacity.