A Network Calculus with Effective Bandwidth

This paper establishes a link between two principal tools for the analysis of network traffic, namely, effective bandwidth and network calculus. It is shown that a general formulation of effective bandwidth can be expressed within the framework of a probabilistic version of the network calculus, where both arrivals and service are specified in terms of probabilistic bounds. By formulating well-known effective bandwidth expressions in terms of probabilistic envelope functions, the developed network calculus can be applied to a wide range of traffic types, including traffic that has self-similar characteristics. As applications, probabilistic lower bounds are presented on the service given by three different scheduling algorithms: Static Priority (SP), Earliest Deadline First (EDF), and Generalized Processor Sharing (GPS). Numerical examples show the impact of the traffic models and the scheduling algorithm on the multiplexing gain in a network