Generalized processor sharing with long-tailed traffic sources

We analyze the queueing behavior of longtailed traffic sources under the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing, have emerged as important mechanisms for accommodating heterogeneous quality-of-service requirements in integrated-services networks. Under mild stability conditions, we show that the tail behavior of the buffer content of an individual source with long-tailed traffic characteristics is equivalent to the tail behavior when that source is served in isolation at a constant rate which is equal to the link rate minus the aggregate average rate of all other sources. Thus, asymptotically, the buffer content of the source is only affected by the traffic characteristics of the other sources through their aggregate average rate. In particular, the source is essentially immune from excessive activity of sources with 'heavier'-tailed traffic characteristics. This suggests that GPS-based scheduling algorithms provide an effective mechanism for extracting high multiplexing gains, while protecting individual connections.