Optimal Scheduling and Routing for Maximum Network Throughput

In this paper, we consider packet networks loaded by admissible traffic patterns, i.e., by traffic patterns that, if optimally routed, do not overload network resources. We prove that simple distributed dynamic routing and scheduling algorithms based upon link state information can achieve the same network throughput as optimal centralized routing and scheduling algorithms with complete traffic information. Our proofs apply the stochastic Lyapunov function methodology to a flow-level abstract model of the network, and consider elastic traffic, i.e., we assume that flows can adapt their transmission rates to network conditions, thus resembling traffic engineering and quality-of-service approaches being currently proposed for IP networks. Although the paper mainly brings a theoretical contribution, such dynamic routing and scheduling algorithms can be implemented in a distributed way. Moreover we prove that maximum throughput is achieved also in case of temporary mismatches between the actual links state and the link state information used by the routing algorithm. This is a particularly relevant aspect, since any distributed implementation of a routing algorithm requires a periodic exchange of link state information among nodes, and this implies delays, and thus time periods in which the current link costs are not known.