Allocation Schemes of Ressources with Downgrading

TL;DR

This paper analyzes resource allocation policies with downgrading in a saturated video server, deriving asymptotic performance measures using stochastic process limits and Wiener-Hopf techniques.

Contribution

It introduces a novel analysis of downgrading policies in saturated systems, providing asymptotic expressions for key performance metrics.

Findings

The occupancy process converges to a limiting process under rescaling.

The invariant distribution of the limiting process is explicitly computed.

Asymptotic probability of non-downgraded transmission is derived.

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.