Workload Loss Examinations with a Novel Probabilistic Extension of Network Calculus

The estimation of the expected traffic loss ratio (workload loss ratio, WLR) is a key issue in provisioning Quality of Service in packet based communication networks. Despite of its importance, the stationary (long run) loss ratio in queueing analysis is usually estimated through other assessable quantities, typically based on the approximates of the buffer overflow probability. 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.