How Bad is Single-Path Routing

This paper investigates the network performance loss of using only single-path routing when multiple paths are available. The performance metric is the aggregate utility achieved by the joint optimization of congestion control and routing. As computing the exact loss for a general network topology is NP-hard, we develop analytical bounds on this "cost of not splitting". Our bound is independent of the number of source-destination pairs when the latter one is larger than the number of links in a network. We also propose a vertex projection method and combine it with branch-and-bound to provide progressively tighter bounds on the performance loss. Numerical examples are used to show the effectiveness of our approximation technique.