One more weight is enough: Toward the optimal traffic engineering with OSPF

Traffic Engineering (TE) leverages information of network traffic to generate a routing scheme optimizing the traffic distribution so as to advance network performance. However, optimizing the link weights for OSPF to the offered traffic is an known NP-hard problem. In this paper, we model the optimal TE as the utility maximization of multi-commodity flows and theoretically prove that any given set of optimal routes corresponding to a particular objective function can be converted to shortest paths with respect to a set of positive link weights, which can be explicitly formulated using the optimal distribution of traffic and objective function. This can be directly configured on OSPF-based protocols. On these bases, we employ the Network Entropy Maximization (NEM) framework and develop a new OSPF-based routing protocol, SPEF, to realize a flexible way to split traffic over shortest paths in a distributed fashion. Actually, comparing to OSPF, SPEF only needs one more weight for each link and provably achieves optimal TE. Numerical experiments have been done to compare SPEF with the current version of OSPF, showing the effectiveness of SPEF in terms of link utilization and network load distribution.