Robust network planning in nonuniform traffic scenarios

Robustness to the environmental variations is an important feature of any reliable communication network. This paper reports on a network theory approach to the design of such networks where the environmental changes are traffic fluctuations, topology modifications, and changes in the source of external traffic. Motivated by the definition of betweenness centrality in network science, we introduce the notion of traffic-aware betweenness (TAB) for data networks, where usually an explicit (or implicit) traffic matrix governs the distribution of external traffic into the network. We use the average normalized traffic-aware betweenness, which is referred to as traffic-aware network criticality (TANC), as our main metric to quantify the robustness of a network. We show that TANC is directly related to some important network performance metrics, such as average network utilization and average network cost. We prove that TANC is a linear function of end-to-end effective resistances of the graph. As a result, TANC is a convex function of link weights and can be minimized using convex optimization techniques. We use semi-definite programming method to study the properties of the optimization problem and derive useful results to be employed for robust network planning purposes.