Traffic Engineering over Hop-Constrained Node Survivable Networks

Traffic engineering on a given network is the task of determining how traffic commodities must be routed in order to maintain an optimal performance. In this work, we aim to optimize routing by minimizing the number of routing hops, which has a positive impact on the delay provided by the network to traffic commodities, while ensuring some desired survivability guarantees. In [1], we have considered the network design of MPLS over WDM networks. In that work, we have considered a given undirected network G = (V,E) where V is the set of WDM nodes and E is the set of physical connections (fibers) between WDM nodes, and also a set S ⊂ V of traffic MPLS nodes (named Label Switched Routers or LSRs) that are origins/destinations of commodities each of which with demand tpq, p, q ∈ S(p < q). The design task was the determination of the number and routes of the WDM lightpaths and the location of core LSRs. Each WDM lightpath had an associated cost which was proportional to the length of its minimum length path on G. Each core LSR potential location had an associated given cost. The aim of the network design task was to minimize the total network cost, while guaranteeing the existence of D node disjoint hop-constrained paths for every commodity, accommodating a given demand matrix T = [tpq], p, q ∈ S(p < q). The hop-constrained paths account for a maximum number of hops that the design solution must guarantee. The D node disjoint paths, together with the capacity assigned to each path, account for the degree of survivability that the design solution must guarantee. There are two reasons to apply traffic engineering on pre-dimensioned networks. One is that the commodity paths given by a minimum cost network design solution might not be the optimal ones (the design model defines a maximum number of hops for each path but in the design solution these values might be improved). Second, the commodity demand values used on the design task are usually estimations that might be different from the traffic that is to be supported by the network when it is put in operation. Therefore, let a network design solution be represented by a network N = (X,U), where the node set X is the set of all LSRs (the traffic and the core LSRs) and edge set U is the set of pairs of LSRs with lightpaths connecting them (be represents the total capacity of the lightpaths on edge e ∈ U ). This solution supports all commodities of the given estimated demand matrix T for certain values of H (the maximum number of hops between any p, q ∈ S, p < q), D and β (a percentage coefficient associated with the survivability scheme that will be further explained below). Now, consider a new demand matrix R = [rpq] which is different from the estimated T . In this work, we generate each rpq value randomly with a uniform distribution between (1 − δ)tpq and (1 + δ)tpq , considering δ = 0.05, 0.1, 0.15 or 0.2 to accommodate different error degrees in the estimation of the initial traffic matrix. We consider a traffic engineering problem of routing the new demands (rpq) over the dimensioned network N = (X,U) complying with the installed bandwidth (be) on each edge of U and guaranteeing D node disjoint hop-constrained paths for every commodity. An optimal routing is the one that minimizes i) the average number of hops or ii) the largest number of hops, between all pairs of nodes p, q ∈ S(p < q).