A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows

We consider networks where tra c is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing di erentiated quality of service in integrated-services networks. We are interested in the workload of a particular ow i at the bottleneck node on its path. Flow i is assumed to have long-tailed tra c characteristics. We distinguish between two tra c scenarios, (i) ow i generates instantaneous tra c bursts and (ii) ow i generates tra c according to an on/o process. In addition, we consider two con gurations of feed-forward networks. First we focus on the situation where other ows join the path of ow i. Then we extend the model by adding ows which can branch o at any node, with cross tra c as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of ow i is equivalent to that in a two-node tandem network where ow i is served in isolation at constant rates. These rates only depend on the tra c characteristics of the other ows through their average rates. This means that the results do not rely on any speci c assumptions regarding the tra c processes of the other ows. In particular, ow i is not a ected by excessive activity of ows with `heavier-tailed' tra c characteristics. This con rms that GPS has the potential to protect individual ows against extreme behaviour of other ows, while obtaining substantial multiplexing gains. 2000 Mathematics Subject Classi cation: 60K25 (primary), 68M20, 90B18, 90B22 (secondary).