A Probabilistic Network Calculus for Characterizing Long-run Network Behavior

Network calculus is the result of recent developments in the area of network analysis, providing considerable insight into the behavior of (packet-based) communication networks. The classical approach uses deterministic bounds to describe systems having stochastic properties in nature, offering simple formulation to a set of¿otherwise analytically hardly tractable¿problems. Eliminating probabilistic nature, however, often leads to¿practically hardly usable¿loose bounds after quantification. In this paper, we address the problem of extending the network calculus theory to regain the advantage coming from the statistical multiplexing effect, preserving at the same time easy discussion that the original approach provides us. During the main part of the paper we introduce and discuss some important theorems about the novel effective w-arrival and w-service curves. As an example we show how to apply the results to the efficient computation of the workload loss ratio, as an important and widely used quality of service parameter while remaining in the framework and concept of the network calculus.