Dynamic routing in delay networks: ergodicity, transients and large excursions

The author interprets the design of routing protocols for networks as a feedback control problem. Protocols are decentralized controllers for nonlinear noisy systems. A general methodology is described for the design of routing protocols in a delay network. Ergodic distributions do not give information about transient behavior, in particular about transitions to locally stable equilibrium points corresponding to a band operating point result of noise. These large excursions can be analyzed via averaged dynamics and large deviations theory of Markovian models. These methods lead naturally to a decomposition of the system model into two hierarchical layers, a fast local level and a global one. The theory provides insight into the minimal global information necessary to achieve good performance in delay networks