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Allocation schemes of resources with downgrading

Part of:Special processesOperations research and management science

Published online by Cambridge University Press:  26 June 2017

Christine Fricker,
Fabrice Guillemin,
Philippe Robert and
Guilherme Thompson
Christine Fricker*
Affiliation:
INRIA
Fabrice Guillemin*
Affiliation:
Orange Labs
Philippe Robert*
Affiliation:
INRIA
Guilherme Thompson*
Affiliation:
INRIA
*
* Postal address: INRIA, 2 Rue Simone IFF, CS 42112, 75589 Paris Cedex 12, France.
** Postal address: CNC/NCA Orange Labs, 2 Avenue Pierre Marzin, 22300 Lannion, France.
* Postal address: INRIA, 2 Rue Simone IFF, CS 42112, 75589 Paris Cedex 12, France.
* Postal address: INRIA, 2 Rue Simone IFF, CS 42112, 75589 Paris Cedex 12, France.
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Abstract

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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 with bit rate adaptation. Under the assumptions of Poisson request arrivals and exponential service times, we show that, by rescaling the system, a process associated with the occupancy of the server converges to some limiting process whose invariant distribution is computed explicitly. This allows us to derive an asymptotic expression of the key performance measure of such a policy, namely the equilibrium probability that a request is transmitted at requested bitrate. Numerical applications of these results are presented.

Keywords

Resource allocationscaling methodloss system

MSC classification

Primary:60K25: Queueing theory60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary:90B18: Communication networks

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 2 , June 2017, pp. 629 - 651
Copyright
Copyright © Applied Probability Trust 2017 

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