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Inria / Raweb 2003
Team: Rap

# Team : rap

## Section: New Results

### Processor-Sharing disciplines with heavy tailed services

Participants : Fabrice Guillemin, Philippe Robert, Bert Zwart.

The processor-sharing paradigm has emerged as a powerful concept for modeling the flow-level performance of bandwidth-sharing protocols in communication networks. In this context, the driving random variables (especially service times) of PS models are often assumed to be heavy-tailed, reflecting the extreme variability of file transfers and session lengths. In view of this, several studies have focused on the difficult problem of analyzing the tail of the sojourn time distribution for the $M/G/1$ PS queue under heavy-tailed assumptions.

The framework considered here is a bottleneck link processing TCP connections as a processor-sharing queue with a possibly varying capacity, impatient flows and maximum number of connection at a given time. Our analysis consists in showing a general sufficient condition for RSR (Reduced Service Rate) approximation for these kind of queues. It is proved that, in this setting, a ``big flow'' receives a constant fraction of the total capacity of the link capacity. These results apply to class of state- dependent PS queues, PS queues with finite buffers and/or impatience. Based on these results, an admission control policy have designed in an earlier work with jacqueline Boyer.