Optimization of link load balancing in multiple spanning tree routing networks

Abstract

In telecommunication networks based on the current Ethernet technology, routing of traffic demands is based on multiple spanning trees: the network operator configures different routing spanning trees and assigns each demand to be routed in one of the selected spanning trees. A major optimization issue in this solution is the combined determination of (i) a set of appropriate spanning trees, and (ii) assignment of demands to the trees, in order to achieve an optimal load balancing on the links of the network. In this paper we consider models and solving techniques for lexicographical optimization of two load balancing objective functions. The first objective is the min-max optimization of the n worst link loads (with n up to the total number of network links), and the second objective is the minimization of the average link load (when n is smaller than the total number of network links). Besides exact methods, a heuristic technique that can compute both feasible solutions and lower bounds for the addressed optimization problem is proposed. Finally, we discuss effectiveness of different solution using results of a numerical study of realistic case studies.

Link load balancing optimization of telecommunication networks: A column generation based heuristic approach

“…In order to understand the meaning of the two additional columns (LP and RMP), note first that the demand values of all traffic matrices are multiple of 10 Mbps and, since all link capacities are 10000 Mbps, the possible link load values µ {ij} are multiples of 0,1%. We have used this fact to improve the lower bounds obtained in the COLUMN GENERATION phase of Algorithm A using a lifting technique previously proposed in [6]. We substitute constraints (2) with their inequality version…”

“…and apply the following lifting technique: the optimal solution value θ * l obtained by solving model (4) (rounded up) to the lowest multiple of 0,1% higher than θ * l , and then used in constraint (6) in the subsequent iterations. The LP columns present the lower bounds obtained by CG with this lifting technique.…”

“…Finally, note that the min-max optimization of link loads has been previously addressed as a traffic engineering objective in the cases of (i) multiple spanning tree based routing networks [6], [8] and (ii) single path routing with path protection [7]. It will be interesting to investigate how the column generation based heuristic approach proposed here for the simplest case of single path routing can be generalized to these more complex traffic engineering variants and if its efficiency will be at least as good as in the present case.…”

“…This objective has been previously addressed for multiple spanning tree based routing [6], [8] and for routing with path protection [7]. Note that we have seen in [8] that the optimization of the average link load is very penalizing for the worst link load values, while the min-max optimization of link loads usually lead to very small penalties on the average link load values.…”

“…For each current solution, there is one neighbor solution for each k ∈ K which is computed by: (i) removing its bandwidth demand from its current path and (ii) computing a new minimum cost path using the same method as described in the previous greedy algorithm (lines [4][5][6][7][8][9][10][11][12][13][14].…”