A graph theoretical approach to traffic engineering and network control problem

This paper looks at the problem of traffic engineering and network control from a new perspective. A graph-theoretical metric, betweenness, in combination with a network weight matrix is used to characterize the robustness of a network. Theoretical results lead to a definition of "criticality" for nodes and links. It is shown that this quantity is a global network quantity and depends on the weight matrix of the graph. Strict convexity of network criticality is proved and an optimization problem is solved to minimize the network criticality as a function of weight matrix which in turn provides maximum robustness. Investigation of the condition of optimality suggests directions to design appropriate control laws and traffic engineering methods to robustly assign traffic flows. The choice of the path for routing the flow in these traffic engineering methods is in the direction of preserving the robustness of the network to the unforeseen changes in topology and traffic demands. The proposed method is useful in situations like MPLS and Ethernet networks where path assignment is required.