Schedulable regions and equilibrium cost for multipath flow control: the benefits of coordination

In this paper we consider deterministic differential equation models for the varying number of flows in a network. These arise naturally as limits of stochastic models under joint scaling of flow arrival rates and network capacities. We compare these dynamics under (i) coordinated multipath routing and (ii) parallel, uncoordinated routing. We show that for identical traffic demands, parallel uncoordinated routing can be unstable while balanced multipath routing is stable. In other words, coordination can strictly increase the schedulable region, that is the set of demand vectors for which the system is stable. We also show that, even when uncoordinated multipath routing stabilises the system, coordination can bring further benefits, as it naturally minimises network costs at equilibrium.