  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.
