Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T21:39:07.870Z Has data issue: false hasContentIssue false
  • English
  • Français

Allocation schemes of resources with downgrading

Part of: Special processes Operations 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.
Get access Rights & Permissions [Opens in a new window]

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 C0 < C, the server delivers the video at a minimal bit rate. The quantity C0 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 theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 90B18: Communication networks
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 2 , June 2017 , pp. 629 - 651
Copyright
Copyright © Applied Probability Trust 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Añorga, J. et al. (2015). YouTube's DASH implementation analysis. In Recent Advances in Communications (Proc. 19th Internat. Conf. on Communications; Recent Adv. Electrical Eng. Ser. 50), pp. 61–66. Google Scholar
[2] Arnol'd, V. I. (1992). Ordinary Differential Equations. Springer, Berlin. Google Scholar
[3] Asmussen, S. (2003). Applied Probability and Queues (Appl. Math. 51), 2nd edn. Springer, New York. Google Scholar
[4] Bean, N. G., Gibbens, R. J. and Zachary, S. (1995). Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks. Adv. Appl. Prob. 27, 273–292. Google Scholar
[5] Bean, N. G., Gibbens, R. J. and Zachary, S. (1997). Dynamic and equilibrium behavior of controlled loss networks. Ann. Appl. Prob. 7, 873–885. CrossRefGoogle Scholar
[6] Doane, D. P. and Seward, L. E. (2011). Measuring skewness: a forgotten statistic? J. Statist. Education 19, 1–18. CrossRefGoogle Scholar
[7] Fricker, C., Guillemin, F., Robert, P. and Thompson, G. (2016). Analysis of downgrading for resource allocation. ACM SIGMETRICS Performance Evaluation Rev. 44, 24–26. CrossRefGoogle Scholar
[8] Fricker, C., Guillemin, F., Robert, P. and Thompson, G. (2016). Analysis of an offloading scheme for data centers in the framework of Fog computing. ACM Trans. Model. Performance Evaluation Comput. Systems 1, 12pp. Google Scholar
[9] Gakhov, F. D. (1990). Boundary Value Problems. Dover, New York. Google Scholar
[10] Guillemin, F., Houdoin, T. and Moteau, S. (2013). Volatility of YouTube content in Orange networks and consequences. In Proc. IEEE Internat. Conf. on Communications, IEEE, pp. 2381–2385. Google Scholar
[11] Guillemin, F., Kauffmann, B., Moteau, S. and Simonian, A. (2013). Experimental analysis of caching efficiency for YouTube traffic in an ISP network. In Proc. 25th Internat. Teletraffic Congress, IEEE, 9pp. Google Scholar
[12] Hunt, P. J. and Kurtz, T. G. (1994). Large loss networks. Stoch. Process. Appl. 53, 363–378. CrossRefGoogle Scholar
[13] Kelly, F. P. (1986). Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505. Google Scholar
[14] Kelly, F. P. (1991). Loss networks. Ann. Appl. Prob. 1, 319–378. Google Scholar
[15] Robert, P. (2003). Stochastic Networks and Queues (Appl. Math. 52). Springer, Berlin. Google Scholar
[16] Rudin, W. (1987). Real and Complex Analysis, 3rd edn. McGraw-Hill, New York. Google Scholar
[17] Schwarz, H., Marpe, D. and Wiegand, T. (2007). Overview of the scalable video coding extension of the H.264/AVC standard. IEEE Trans. Circuits Systems Video Tech. 17, 1103–1120. Google Scholar
[18] Sieber, C. et al. (2013). Implementation and user-centric comparison of a novel adaptation logic for DASH with SVC. In 2013 IFIP/IEEE Internat. Symp. on Integrated Network Management, IEEE, pp. 1318–1323. Google Scholar
[19] Stolyar, A. L. (2013). An infinite server system with general packing constraints. Operat. Res. 61, 1200–1217. CrossRefGoogle Scholar
[20] Stolyar, A. L. (2015). Pull-based load distribution in large-scale heterogeneous service systems. Queueing Systems 80, 341–361. Google Scholar
[21] Vadlakonda, S. et al. (2010). System and method for dynamically upgrading / downgrading a conference session. Patent US7694002 B2. Google Scholar
[22] Zachary, S. and Ziedins, I. (2002). A refinement of the Hunt–Kurtz theory of large loss networks, with an application to virtual partitioning. Ann. Appl. Prob. 12, 1–22. Google Scholar
[23] Zachary, S. and Ziedins, I. (2011). Loss networks. In Queueing Networks (Internat. Ser. Operat. Res. Manag. Sci. 154), eds R. J. Boucherie and N. M. van Dijk, Springer, New York, pp. 701–728. Google Scholar