J. Añorga, S. Arrizabalaga, B. Sedano, M. Alonso-arce, and J. Mendizabal, YouTube's DASHimplementation analysis, Proceedings of the 19th International Conference on Communications (part of CSCC'15), vol.50, p.53, 2015.

M. Alanyali and B. Hajek, Analysis of simple algorithms for dynamic load balancing, Mathematics of Operations Research, vol.22, issue.4, p.90, 1997.

L. Atzori, A. Iera, and G. Morabito, Computer Networks, vol.54, issue.15, pp.2787-2805, 2005.

, Ama] Amazon.com. Amazon Web Services, vol.2, p.3

V. I. , Arnol'd. Ordinary differential equations, p.43

M. Abramowitz and I. Stegun, Handbook of mathematical functions, Applied Mathematics Series, vol.55, p.119, 1972.

S. Asmussen, Applied Probability and Queues, Applications of Mathematics, vol.51, p.82, 2003.

M. Armbrust, I. Stoica, M. Zaharia, A. Fox, R. Griffith et al., A view of cloud computing, Communications of the ACM, vol.53, issue.4, pp.50-58, 2002.

N. G. Bean, R. J. Gibbens, and S. Zachary, Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks, Advances in Applied Probability, vol.27, issue.1, p.64, 1920.

N. G. Bean, R. J. Gibbens, and S. Zachary, Dynamic and equilibrium behavior of controlled loss networks, The Annals of Applied Probability, vol.7, issue.4, p.64, 1997.
DOI : 10.1214/aoap/1043862415
URL : https://doi.org/10.1214/aoap/1043862415

E. Brockmeyer, H. L. Halstrøm, and A. Jensen, The life and works of A. K. Erlang. Transactions of the Danish Academy of Technical Sciences (Akademiet for de Tekniske Videnskaber, Denmark), vol.10, p.13, 1948.

D. Y. Burman, J. P. Lehoczky, and Y. Lim, Insensitivity of blocking probabilities in a circuit-switching network, Journal of Applied Probability, vol.21, issue.4, pp.850-859, 1984.

F. Bonomi, R. Milito, J. Zhu, and S. Addepalli, Fog computing and its role in the Internet of Things, Proceedings of the First Edition of the MCCWorkshop on Mobile Cloud Computing, MCC '12, vol.5, p.105, 2012.

T. Bonald and J. Virtamo, A recursive formula for multirate systems with elastic traffic, IEEE Communications Letters, vol.9, issue.8, pp.753-755, 2005.
DOI : 10.1109/lcomm.2005.1496605
URL : https://hal.archives-ouvertes.fr/hal-01275699

H. Cartan, Elementary theory of one or several complex variables, p.97, 1950.

J. W. Cohen and O. J. Boxma, Boundary value problems in queueing system analysis, Mathematics Studies, p.15, 1984.

J. W. Cohen and O. J. Boxma, A survey of the evolution of queueing theory, Statistica Neerlandica, vol.39, issue.2, pp.143-158, 1985.

H. I. Christensen, A. Khan, S. Pokutta, and P. Tetali, Multidimensional bin packing and other related problems: A survey, 2016.

G. L. Choudhury, K. K. Leung, and W. Whitt, An algorithm to compute blocking probabilities in multi-rate multiclass multi-resource loss models, Advances in Applied Probability, vol.27, issue.4, pp.1104-1143, 1995.
DOI : 10.1017/s0001867800047819

R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol.4, p.115, 1990.

Z. Dziong and J. W. Roberts, Congestion probabilities in a circuit-switched integrated services network, Performance Evaluation, vol.7, issue.4, pp.267-284, 1987.
DOI : 10.1016/0166-5316(87)90013-7

D. P. Doane and L. E. Seward, Measuring skewness: A forgotten statistic, Journal of Statistics Education, vol.19, issue.2, p.50, 2011.
DOI : 10.1080/10691898.2011.11889611
URL : https://doi.org/10.1080/10691898.2011.11889611

E. El-hady, J. Brzd¸ekbrzd¸ek, and H. Nassar, On the structure and solutions of functional equations arising from queueing models, Aequationes mathematicae, vol.91, issue.3, pp.445-477, 2015.

A. K. Erlang, The theory of probabilities and telephone conversations (sandsynlighedsregning og telefonsamtaler), Nyt Tidsskrift for Matematik, vol.20, issue.10, pp.33-39, 1909.

A. K. Erlang, Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. The Post Office Electrical Engineers, Journal, vol.10, issue.10, pp.189-197, 1917.

C. Fricker, F. Guillemin, . Ph, G. Robert, and . Thompson, Analysis of an offloading scheme for data centers in the framework of fog computing, ACM Transactions on Modeling and Performance Evaluation of Computing Systems (ToMPECS), vol.1, issue.4, p.121, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01179206

C. Fricker, F. Guillemin, . Ph, G. Robert, and . Thompson, Analysis of downgrading for resource allocation, ACM SIGMETRICS Performance Evaluation Review, vol.44, issue.2, p.31, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01406664

C. Fricker, F. Guillemin, . Ph, G. Robert, and . Thompson, Allocation schemes of resources with downgrading, Advances in Applied Probability, vol.49, issue.2, p.82, 2017.

G. Fayolle and R. Iasnogorodski, The two coupled server: the reduction to a Riemann-Hilbert problem. Zur Wahrscheinlichkeitstheorie und verwandte Gebiete, vol.47, p.111, 1979.

G. Fayolle, R. Iasnogorodski, and V. A. Malyshev, Random Walks in the Quarter-Plane. Algebraic Methods, Boundary Value Problems and Applications, Applications of Mathematics, vol.40, p.106, 2017.
DOI : 10.1007/978-3-642-60001-2
URL : https://hal.archives-ouvertes.fr/inria-00572276

G. Fayolle, V. A. Malyshev, and M. V. Menshikov, Topics in the constructive theory of countable Markov chains, vol.15, p.109, 1995.

G. Frenkel, The grade of service in multiple-access satellite communications systems with demand assignments, IEEE Transactions on Communications, vol.22, issue.10, pp.1681-1685, 1974.

C. Fricker, . Ph, D. Robert, and . Tibi, On the fluid limits of some loss networks, vol.20, p.64, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072451

C. Fricker, . Ph, D. Robert, and . Tibi, A degenerate central limit theorem for single resource loss systems, The Annals of Applied Probability, vol.13, issue.2, pp.561-575, 1920.
URL : https://hal.archives-ouvertes.fr/inria-00072143

S. Foss and A. L. Stolyar, Large-scale join-idle-queue system with general service times, pp.2-2017
DOI : 10.1017/jpr.2017.49
URL : http://arxiv.org/pdf/1605.05968

I. Foster, Y. Zhao, I. Raicu, and S. Lu, Cloud computing and grid computing 360-degree compared, Grid Computing Environments Workshop, 2008. GCE'08, vol.1, pp.1-10, 2008.
DOI : 10.1109/gce.2008.4738445
URL : http://arxiv.org/pdf/0901.0131

F. D. Gakhov, Translated from the Russian, Reprint of the, 1966.

J. Geelan, Twenty-one experts define cloud computing

J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences, vol.42, p.21, 1983.
DOI : 10.1115/1.3167759
URL : http://appliedmechanics.asmedigitalcollection.asme.org/data/journals/jamcav/26244/947_1.pdf

F. Guillemin, T. Houdoin, and S. Moteau, Volatility of YouTubecontent in Orangenetworks and consequences, 2013 IEEEInternational Conference on Communications (ICC), p.31, 2013.

A. Goel and P. Indyk, Stochastic load balancing and related problems, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039), pp.579-586, 1999.
DOI : 10.1109/sffcs.1999.814632

F. Guillemin, B. Kauffmann, S. Moteau, and A. Simonian, Experimental analysis of caching efficiency for YouTubetraffic in an ISPnetwork, Proceedings of the 2013 25th International Teletraffic Congress (ITC), p.31, 2013.

A. Ghodsi, V. Sekar, M. Zaharia, and I. Stoica, Multi-resource fair queueing for packet processing, Proceedings of the ACM SIGCOMM 2012 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM '12, p.58, 2012.
DOI : 10.21236/ada563900
URL : http://nma.berkeley.edu/ark:/28722/bk001169310

F. Guillemin and G. Thompson, Analysis of a trunk reservation policy in the framework of fog computing, vol.58, p.64, 1928.
URL : https://hal.archives-ouvertes.fr/hal-01378533

A. Ghodsi, M. Zaharia, A. Hindman, S. Konwinski, . Shenker et al., Dominant resource fairness: Fair allocation of multiple resource types, Proceedings of the 8th USENIXConference on Networked Systems Design and Implementation, NSDI'11, p.58, 2011.

P. J. Hunt and T. G. Kurtz, Large loss networks, Stochastic Processes and their Applications, vol.53, p.109, 1994.

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, Revisiting stochastic loss networks: Structures and algorithms, ACM SIGMETRICS Performance Evaluation Review, vol.36, issue.1, pp.407-418, 2008.
DOI : 10.1287/moor.2018.0949

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, volume 288 of Grundlehren der mathematischen Wissenschaften, vol.109, 2003.

B. Jennings and R. Stadler, Resource management in clouds: Survey and research challenges, Journal of Network and Systems Management, vol.23, issue.3, pp.567-619, 2015.
DOI : 10.1007/s10922-014-9307-7

F. P. Kelly, Blocking probabilities in large circuit-switched networks, Advances in Applied Probability, vol.18, issue.2, p.64, 1920.
DOI : 10.2307/1427309

F. P. Kelly, Loss networks, The Annals of Applied Probability, vol.1, issue.3, p.86, 1991.

D. G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, The Annals of Mathematical Statistics, vol.24, issue.3, pp.338-354

J. F. Kingman, The ergodic behaviour of random walks, Biometrika, vol.48, issue.3/4, pp.391-396

J. F. Kingman, The first erlang century-and the next, Queueing Systems: Theory and Applications, vol.63, pp.3-12, 2009.

H. Khazaei, J. Misic, and V. B. Misic, Performance analysis of cloud computing centers using M/G/m/m+r queuing systems, IEEE Transactions on Parallel and Distributed Systems, vol.23, issue.5, pp.936-943, 2012.

G. Louth, M. Mitzenmacher, and F. P. Kelly, Computational complexity of loss networks, Theoretical Computer Science, vol.125, issue.1, pp.45-59, 1994.

Y. Lu, Q. Xie, G. Kliot, A. Geller, J. R. Larus et al., Join-Idle-Queue: A novel load balancing algorithm for dynamically scalable web services, Performance Evaluation, vol.68, issue.11, pp.1056-1071, 2011.

V. A. Malyshev, Networks and dynamical systems, Advances in Applied Probability, vol.25, issue.1, pp.140-175
URL : https://hal.archives-ouvertes.fr/inria-00075094

P. Mell and T. Grance, The NIST definition of cloud computing recommendations of the national institute of standards and technology, Nist Special Publication, vol.145, p.7, 2002.

. Microsoft and . Azure, , vol.58, p.85

M. Mitzenmacher, Load balancing and density dependent jump Markov processes, Proceedings of 37th Conference on Foundations of Computer Science, pp.213-222, 1996.

A. Mukhopadhyay, A. Karthik, R. R. Mazumdar, and F. Guillemin, Mean field and propagation of chaos in multi-class heterogeneous loss models. Performance Evaluation, vol.91, pp.117-131, 2015.

M. Masdari, S. S. Nabavi, and V. Ahmadi, An overview of virtual machine placement schemes in cloud computing, Journal of Network and Computer Applications, vol.66, issue.6, pp.106-127, 2016.

S. T. Maguluri, R. Srikant, and L. Ying, Stochastic models of load balancing and scheduling in cloud computing clusters, 2012 Proceedings IEEE INFOCOM, pp.3-2012

M. E. Newman, Networks: An Introduction, p.10, 2010.

A. Rai, R. Bhagwan, and S. Guha, Generalized resource allocation for the cloud, Proceedings of the Third ACM Symposium on Cloud Computing, SoCC '12, vol.15, p.105, 2012.

J. W. Roberts, A service system with heterogeneous user requirements-application to multi-service telecommunications systems, Performance of Data Communcation Systems and their Applications, pp.423-431, 1981.

. Ph and . Robert, Stochastic Networks and Queues, Applications of Mathematics, vol.52, p.111, 2003.

K. Roos, Farkas lemma, p.65, 2009.

K. W. Ross, Multiservice loss models for broadband telecommunication networks, vol.6, p.106, 1995.

A. N. Rybko and A. L. Stolyar, Ergodicity of stochastic processes describing the operation of open queueing networks, Problemy Peredachi Informatsii, vol.28, issue.3, p.70, 1992.

K. W. Ross and D. H. Tsang, The stochastic knapsack problem, IEEE Transactions on Communications, vol.37, issue.7, pp.740-747, 1989.

K. W. Ross and D. H. Tsang, Teletraffic engineering for product-form circuit-switched networks, Advances in Applied Probability, vol.22, issue.3, p.17, 1990.

W. Rudin, Real and complex analysis, Mathematics Series

M. Co, , p.48, 1987.

. Ph, A. Robert, and . Véber, A stochastic analysis of resource sharing with logarithmic weights, The Annals of Applied Probability, vol.25, issue.5, p.16, 2015.

L. C. Rogers, D. Williams, and . Diffusions, Markov processes and martingales, vol.2, p.109, 2000.

L. Sharifi, L. Cerdà-alabern, F. Freitag, and L. Veiga, Energy efficient cloud service provisioning: Keeping data center granularity in perspective, Journal of Grid Computing, vol.14, issue.2, pp.299-325, 2005.

C. Sieber, T. Hoßfeld, T. Zinner, . Ph, C. Tran-gia et al., Implementation and user-centric comparison of a novel adaptation logic for DASHwith SVC, IM'13, p.31, 2013.

H. Schwarz, D. Marpe, and T. Wiegand, Overview of the scalable video coding extension of the H.264/AVCstandard, IEEE Transactions on Circuits and Systems for Video Technology, vol.17, p.31, 2007.

A. L. Stolyar, An infinite server system with general packing constraints, Operations Research, vol.61, issue.5, p.33, 2013.

A. L. Stolyar, Pull-based load distribution in large-scale heterogeneous service systems, Queueing Systems: Theory and Applications, vol.80, p.33, 2015.

A. L. Stolyar and Y. Zhong, A large-scale service system with packing constraints: Minimizing the number of occupied servers, ACM SIGMETRICS Performance Evaluation Review, vol.41, issue.1, pp.41-52, 2013.

L. Takács, On Erlang's formula, The Annals of Mathematical Statistics, vol.40, issue.1, pp.71-78

Y. Tan, Y. Lu, and C. H. Xia, Provisioning for large scale cloud computing services, ACM SIGMETRICS Performance Evaluation Review, vol.40, issue.1, pp.407-408, 2012.

Y. Tan, Y. Lu, and C. H. Xia, Provisioning for large scale loss network systems with applications in cloud computing, ACM SIGMETRICS Performance Evaluation Review, vol.40, issue.3, pp.83-85, 2012.

F. Theberge, A. Simonian, and R. R. Mazumdar, Upper bounds for blocking probabilities in large multi-rate loss networks, Telecommunication Systems, vol.9, issue.1, pp.23-39, 1998.

S. Vadlakonda, A. Chotai, B. D. Ha, A. Asthana, and S. Shaffer, System and method for dynamically upgrading / downgrading a conference session, p.31, 2010.

N. D. Vvedenskaya, R. L. Dobrushin, and F. I. Karpelevich, Queueing system with selection of the shortest of two queues: An asymptotic approach, Problemy Peredachi Informatsii, vol.32, issue.1, pp.20-34, 1996.

V. Valancius, N. Laoutaris, L. Massoulié, C. Diot, and P. Rodriguez, Greening the internet with nano data centers, Proceedings of the 5th international conference on Emerging networking experiments and technologies, CoNEXT '09, pp.37-48, 2009.

[. Vaquero, L. Rodero-merino, J. Caceres, and M. Lindner, A break in the clouds: Towards a cloud definition, Computer Communication Review, vol.39, issue.1, pp.50-55, 2001.

J. Voas and J. Zhang, Cloud Computing: New wine or just a new bottle? IT Professional, vol.11, pp.15-17, 2002.

T. Wood, K. K. Ramakrishnan, P. Shenoy, and J. Van-der-merwe, CloudNet: Dynamic pooling of cloud resources by live wan migration of virtual machines, IEEE/ACM Transactions on Networking, vol.46, issue.7, p.105, 2005.

Q. Xie, X. Dong, Y. Lu, and R. Srikant, Power of d choices for large-scale bin packing: A loss model, ACM SIGMETRICS Performance Evaluation Review, vol.43, issue.1, pp.321-334, 2015.

Z. Xiao, W. Song, and Q. Chen, Dynamic resource allocation using virtual machines for cloud computing environment. Parallel and Distributed Systems, IEEE Transactions on, vol.24, issue.6, pp.1107-1117, 2013.

L. Youseff, M. Butrico, and D. D. Silva, Toward a unified ontology of cloud computing, Grid Computing Environments Workshop, 2008. GCE'08, pp.1-10, 2001.

B. Yang, F. Tan, Y. Dai, and S. Guo, Performance Evaluation of Cloud Service Considering Fault Recovery, pp.571-576, 2009.

Q. Zhang, L. Cheng, and R. Boutaba, Cloud computing: stateof-the-art and research challenges, Journal of Internet Services and Applications, vol.1, issue.1, pp.7-18, 2004.

S. Zachary and I. Ziedins, A refinement of the Hunt-Kurtz theory of large loss networks, with an application to virtual partitioning, The Annals of Applied Probability, vol.12, issue.1, p.34, 2002.

S. Zachary and I. Ziedins, Loss Networks, International Series in Operations Research & Management Science, vol.154, p.35, 2011.