Worst-case Analysis of Tandem Queueing Systems Using Network Calculus

In this chapter we show how to derive performance bounds for tandem queueing systems using Network Calculus, a deterministic theory for performance analysis. We introduce the basic concepts of Network Calculus, namely arrival and service curves, and we show how to use them to compute performance bounds in an end-to-end perspective. As an application of the above theory, we evaluate tandems of network nodes with well-known service policies. We present the theory for two different settings: a simpler one, called ”per-flow scheduling”, where service policies at each node discriminate traffics coming from different flows and buffer them separately, and ”per-aggregate scheduling”, where schedulers manage a small number of traffic aggregates, and traffic of several flows may end up in the same queue. We show that, in the latter case, methodologies based on equivalent service curves cannot compute tight delay bounds and we present a different methodology that relies on input-output relationships and uses mathematical programming techniques.