# Allocation Schemes of Ressources with Downgrading

2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We consider a server with large capacity delivering video files encoded in various resolutions. We assume that the system is under saturation in the sense that the total demand exceeds the server capacity $C$. In such a case, requests may be rejected. For the policies considered in this paper, instead of rejecting a video request, it is downgraded. When the occupancy of the server is above some value $C_0{<}C$, the server delivers the video at a minimal bit rate. The quantity $C_0$ is the bit rate adaptation threshold. For these policies, request blocking is thus replaced by bit rate adaptation. Under the assumptions of Poisson request arrivals and exponential service times, we show that, by rescaling the system, a process associated to the occupancy of the server converges to some limiting process whose invariant distribution is computed by a Wiener-Hopf technique. This allows us to derive an asymptotic expression of the key performance measure of such a policy, the equilibrium probability that a request is transmitted without downgrading. Numerical applications of these results are presented.
Document type :
Journal articles

https://hal.inria.fr/hal-01301291
Contributor : Philippe Robert Connect in order to contact the contributor
Submitted on : Tuesday, April 12, 2016 - 7:43:30 AM
Last modification on : Monday, July 25, 2022 - 3:44:28 AM

### Citation

Christine Fricker, Fabrice Guillemin, Philippe Robert, Guilherme Raposo Thompson. Allocation Schemes of Ressources with Downgrading. Advances in Applied Probability, Applied Probability Trust, 2017, 49 (2), ⟨10.1017/apr.2017.15⟩. ⟨hal-01301291⟩

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