Compact Models for Hop-Constrained Node Survivable Network Design: An Application to MPLS

Abstract

In this paper we discuss compact models for a hop-constrained node survivable network design problem. We discuss two models involving one set of variables associated to each path between each pair of demand nodes (a standard network flow model with additional cardinality constraints and a model with hop-indexed variables) and a third model involving one single set of hop-indexed variables for each demand pair. We show that the aggregated more compact hop-indexed model produces the same linear programming bound as the multi-path hop-indexed model. This work is given in the context of the following MPLS network design problem. Given the location of edge nodes, the candidate locations of core nodes and the pairs of locations that can be physically connected, the MPLS network design problem addressed in this paper is the determination of the physical network topology, i.e., the location of core nodes and the connections required between all nodes. The aim of the design task is to determine the least cost network. The physical network must support routing paths between all pairs of edge nodes fulfilling two types of path constraints. The first type is a MPLS hop constraint on the maximum number of edges traversed by each routing path, which guarantees a given packet level quality of service (QoS). The second type is the fault-tolerance constraint. An important component of providing QoS is the service reliability and a fault-tolerance scheme must be present in the network to deal efficiently with failure scenarios. We present computational results, taken from graphs with up to 50 nodes and slightly more than 400 edges.