A General Per-Flow Service Curve for GPS

TL;DR

This paper extends the theoretical framework of GPS to more general traffic and link conditions, providing a universal service curve applicable to concave arrivals and variable-capacity links without assuming system stability.

Contribution

It generalizes the universal service curve for GPS to encompass concave arrival envelopes and time-varying links, removing the need for system stability assumptions.

Findings

Extended the universal service curve to concave arrivals

Applicable to links with time-variable capacity

Removed the assumption of system stability

Abstract

Generalized Processor Sharing (GPS), which provides the theoretical underpinnings for fair packet scheduling algorithms, has been studied extensively. However, a tight formulation of the available service of a flow only exists for traffic that is regulated by affine arrival envelopes and constant-rate links. In this paper, we show that the universal service curve by Parekh and Gallager can be extended to concave arrival envelopes and links with time-variable capacity. We also dispense with the previously existing assumption of a stable system.