Inverse Shortest Path Routing Problems in the Design of IP Networks

This thesis is concerned with problems related to shortest path routing (SPR) in Internet protocol (IP) networks. In IP routing, all data traffic is routed in accordance with an SPR protocol, e.g. OSPF. That is, the routing paths are shortest paths w.r.t. some artificial metric. This implies that the majority of the Internet traffic is directed by SPR. Since the Internet is steadily growing, efficient utilization of its resources is of major importance. In the operational planning phase the objective is to utilize the available resources as efficiently as possible without changing the actual design. That is, only by re-configuration of the routing. This is referred to as traffic engineering (TE). In this thesis, TE in IP networks and related problems are approached by integer linear programming. Most TE problems are closely related to multicommodity routing problems and they are regularly solved by integer programming techniques. However, TE in IP networks has not been studied as much, and is in fact a lot harder than ordinary TE problems without IP routing since the complicating shortest path aspect has to be taken into account. In a TE problem in an IP network the routing is performed in accordance with an SPR protocol that depends on a metric, the so called set of administrative weights. The major difference between ordinary TE problems and TE in IP networks is that all routing paths must be simultaneously realizable as shortest paths w.r.t. this metric. This restriction implies that the set of feasible routing patterns is significantly reduced and that the only means available to adjust and control the routing is indirectly, via the administrative weights. A constraint generation method for solving TE problems in IP networks is outlined in this thesis. Given an "original" TE problem, the idea is to iteratively generate and augment valid inequalities that handle the SPR aspect of IP networks. These valid inequalities are derived by analyzing the inverse SPR problem. The inverse SPR problem is to decide if a set of tentative routing patterns is simultaneously realizable as shortest paths w.r.t. some metric. When this is not the case, an SPR conflict exists which must be prohibited by a valid inequality that is then augmented to the original TE problem. To derive strong valid inequalities that prohibit SPR conflicts, a thorough analysis of the inverse SPR problem is first performed. In the end, this allows us to draw conclusions for the design problem, which was the initial primary concern.