Three metrics for stochastic networks: Capacity, queue-size and complexity

We consider a class of constrained queuing network called switched networks, important sub-class of the stochastic processing network (cf. Harrison (2000)), in which there are constraints on which queues can be served simultaneously. Such networks have served as effective models for understanding various types of dynamic resource allocation problems arising in communication networks like the Internet, computer architecture, manufacturing, etc. In such systems, a scheduling policy is required to make resource allocation decisions in terms of which queues to serve at each time subject to constraints. The performance of the system is crucially determined by the scheduling policy. The performance of such scheduling policies, measured with respect to the following three metrics is of utmost importance: (a) capacity, (b) induced queue-sizes or latency, and (c) complexity of the implementation of the policy. Ideally, one is interested in determining the trade-offs achievable between these metrics characterized through the pareto performance boundary. In this note, we shall summarize the state-of-art along with recent progresses towards this somewhat ambitious program.