A novel probabilistic extension of network calculus for workload loss examinations

In this paper we define a calculus for communication networks which is suitable for workload loss estimation based on the original definition of stationary loss ratio. Our novel calculus is a probabilistic extension of the deterministic network calculus, and takes an envelope approach to describe arrivals and services for the quantification of resource requirements in the network. We introduce the effective w-arrival curve and the effective w-service curve for describing the inputs and the service and we show that the per-node results can be extended to a network of nodes with the definition of the effective network w-service curve. The derivation of effective w-arrival curves and effective w-service curves for typical arrivals processes and schedulers is also an important contribution of this paper