?. Draw-arrival_time and . Exp, 7: if at least one user is present then 8: Update users sinrs 9: Compute users' data_rates with scheduling 10: departure_times = file_sizes

E. Altman, K. Avrachenkov, and U. Ayesta, A survey on discriminatory processor sharing, Queueing Systems, vol.35, issue.6, pp.53-63, 2006.
DOI : 10.1007/978-1-4615-0359-0

E. Altman, K. Avrachenkov, and A. Garnaev, Generalized alpha-fair resource allocation in wireless networks, Proc. of IEEE CDC, pp.2414-2419, 2008.

A. Bedekar and R. Agrawal, Optimal muting and load balancing for eICIC, Proc. of WiOpt, pp.280-287, 2013.

Y. Bejerano and S. Han, Cell Breathing Techniques for Load Balancing in Wireless LANs, IEEE Transactions on Mobile Computing, vol.8, issue.6, pp.735-749, 2009.
DOI : 10.1109/TMC.2009.50

Y. Bejerano, S. Han, and L. E. Li, Fairness and load balancing in wireless LANs using association control, Proc. of ACM MobiCom, pp.315-329, 2004.

T. Bonald and M. Feuillet, Performances des réseaux et des systèmes informatiques, ser. Collection Télécom, 2011.

T. Bonald and A. Proutière, Wireless downlink data channels, Proceedings of the 9th annual international conference on Mobile computing and networking , MobiCom '03, 2003.
DOI : 10.1145/938985.939020
URL : https://hal.archives-ouvertes.fr/hal-01244817

T. Bonald and L. Massoulié, Impact of fairness on Internet performance, ACM SIGMETRICS Performance Evaluation Review, vol.29, issue.1, pp.82-91, 2001.
DOI : 10.1145/384268.378438
URL : https://hal.archives-ouvertes.fr/hal-01272522

T. Bonald, L. Massoulié, A. Proutiére, and J. T. Virtamo, A queueing analysis of max-min fairness, proportional fairness and balanced fairness, Queueing Systems, vol.48, issue.7, pp.65-84, 2006.
DOI : 10.1007/s11134-006-7587-7
URL : https://hal.archives-ouvertes.fr/hal-01244245

V. S. Borkar, Stochastic approximation, Resonance, vol.8, issue.s.471012, 2008.
DOI : 10.1002/0471722138

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

S. Boyd, L. Xiao, and A. Mutapcic, Subgradient methods, " lecture notes of EE392o, 2003.

H. Braham, S. B. Jemaa, B. Sayrac, G. Fort, and E. Moulines, Coverage mapping using spatial interpolation with field measurements, 2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), pp.1743-1747, 2014.
DOI : 10.1109/PIMRC.2014.7136450

O. Brickley, S. Rea, and D. Pesch, Load balancing for qos enhancement in ieee802. 11e wlans using cell breathing techniques, Proc. of IFIP MWCN, 2005.

V. Cardellini, M. Colajanni, and S. Y. Philip, Dynamic load balancing on Web-server systems, IEEE Internet Computing, vol.3, issue.3, pp.28-39, 1999.
DOI : 10.1109/4236.769420
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.1895

C. Chicone, Ordinary differential equations with applications, 2006.

R. Combes, Z. Altman, and E. Altman, Self-organization in wireless networks: A flow-level perspective, 2012 Proceedings IEEE INFOCOM, 2012.
DOI : 10.1109/INFCOM.2012.6195735
URL : https://hal.archives-ouvertes.fr/hal-01299912

G. Cybenko, Dynamic load balancing for distributed memory multiprocessors, Journal of Parallel and Distributed Computing, vol.7, issue.2, pp.279-301, 1989.
DOI : 10.1016/0743-7315(89)90021-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.2377

]. S. Deb, P. Monogioudis, J. Miernik, and J. P. Seymour, Algorithms for Enhanced Inter-Cell Interference Coordination (eICIC) in LTE HetNets, IEEE/ACM Transactions on Networking, vol.22, issue.1, 2013.
DOI : 10.1109/TNET.2013.2246820
URL : http://arxiv.org/abs/1302.3784

M. E. Fisher and A. T. Fuller, On the stabilization of matrices and the convergence of linear iterative processes, Mathematical Proceedings of the Cambridge Philosophical Society, vol.53, issue.04, pp.417-425, 1958.
DOI : 10.1090/S0002-9904-1953-09718-X

A. Galani, K. Tsagkaris, P. Demestichas, G. Nguengang, I. Benyahia et al., Core functional and network empower mechanisms of an operator-driven, framework for unifying autonomic network and service management, 2012 IEEE 17th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), pp.191-195, 2012.
DOI : 10.1109/CAMAD.2012.6335330

J. Ghimire and C. Rosenberg, Resource Allocation, Transmission Coordination and User Association in Heterogeneous Networks: A Flow-Based Unified Approach, IEEE Transactions on Wireless Communications, vol.12, issue.3, pp.1340-1351, 2013.
DOI : 10.1109/TWC.2013.013013.120940

H. Gong and J. Kim, Dynamic load balancing through association control of mobile users in wifi networks, IEEE Transactions on Consumer Electronics, vol.54, issue.2, pp.342-348, 2008.

M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.1, 2014.

T. Huckle and A. Kallischko, Frobenius norm minimization and probing for preconditioning, International Journal of Computer Mathematics, vol.22, issue.8, pp.1225-1248, 2007.
DOI : 10.1007/BF01932955

S. Hur, T. Kim, D. Love, J. Krogmeier, T. Thomas et al., Multilevel millimeter wave beamforming for wireless backhaul, 2011 IEEE GLOBECOM Workshops (GC Wkshps), pp.253-257, 2011.
DOI : 10.1109/GLOCOMW.2011.6162448

O. C. Iacoboaiea, B. Sayrac, S. B. Jemaa, and P. Bianchi, SON conflict resolution using reinforcement learning with state aggregation, Proceedings of the 4th workshop on All things cellular: operations, applications, & challenges, AllThingsCellular '14, pp.15-20, 2014.
DOI : 10.1145/2627585.2627591
URL : https://hal.archives-ouvertes.fr/hal-01179555

M. Imran, E. Katranaras, G. Auer, O. Blume, V. Giannini et al., Energy efficiency analysis of the reference systems, areas of improvements and target breakdown, 2011.

T. Jansen, M. Amirijoo, U. Turke, L. Jorguseski, K. Zetterberg et al., Embedding Multiple Self-Organisation Functionalities in Future Radio Access Networks, VTC Spring 2009, IEEE 69th Vehicular Technology Conference, pp.1-5, 2009.
DOI : 10.1109/VETECS.2009.5073530

J. L. Jensen, Sur les fonctions convexes et les in??galit??s entre les valeurs moyennes, Acta Mathematica, vol.30, issue.0, pp.175-193, 1906.
DOI : 10.1007/BF02418571

Y. Khan, B. Sayrac, and E. Moulines, Centralized self-optimization of pilot powers for load balancing in LTE, 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), pp.3039-3043, 2013.
DOI : 10.1109/PIMRC.2013.6666668
URL : https://hal.archives-ouvertes.fr/hal-00978890

J. Kiefer and J. Wolfowitz, Stochastic Estimation of the Maximum of a Regression Function, The Annals of Mathematical Statistics, vol.23, issue.3, pp.462-466, 1952.
DOI : 10.1214/aoms/1177729392

H. Kim, G. De-veciana, X. Yang, and M. Venkatachalam, alpha-Optimal User Association and Cell Load Balancing in Wireless Networks, Proc. of IEEE INFOCOM, pp.1-5, 2010.

L. Kleinrock, Queuing systems, 1975.

H. Klessig, A. Fehske, G. Fettweis, and J. Voigt, Improving coverage and load conditions through joint adaptation of antenna tilts and cell selection rules in mobile networks, 2012 International Symposium on Wireless Communication Systems (ISWCS), pp.21-25, 2012.
DOI : 10.1109/ISWCS.2012.6328322

Z. Kostic, K. K. Leung, and H. Yin, WLAN having load balancing based on access point loading, 0901.

H. J. Kushner and P. A. Whiting, Convergence of Proportional-Fair Sharing Algorithms Under General Conditions, IEEE Transactions on Wireless Communications, vol.3, issue.4, pp.1250-1259, 2004.
DOI : 10.1109/TWC.2004.830826

H. J. Kushner and G. G. Yin, Stochastic Approximation and Recursive Algorithms and Applications 2nd edition, 2003.

K. Linehan and R. Chandrasekaran, Active antennas: The next step in radio and antenna evolution, Commonscope White Paper, vol.10, 2011.

Z. Liu, P. Hong, K. Xue, and M. Peng, Conflict Avoidance between Mobility Robustness Optimization and Mobility Load Balancing, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010, pp.1-5, 2010.
DOI : 10.1109/GLOCOM.2010.5683861

D. Lopez-perez, I. Guvenc, G. De-la-roche, M. Kountouris, T. Quek et al., Enhanced intercell interference coordination challenges in heterogeneous networks, IEEE Wireless Communications, vol.18, issue.3, pp.22-30, 2011.
DOI : 10.1109/MWC.2011.5876497
URL : https://hal.archives-ouvertes.fr/hal-00632391

M. Mitzenmacher, The power of two choices in randomized load balancing, IEEE Transactions on Parallel and Distributed Systems, vol.12, issue.10, pp.1094-1104, 2001.
DOI : 10.1109/71.963420

R. R. Müller, M. A. Sedaghat, and G. Fischer, Load modulated massive MIMO, 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2015.
DOI : 10.1109/GlobalSIP.2014.7032192

R. Nasri and Z. Altman, Handover adaptation for dynamic load balancing in 3GPP Long Term Evolution systems, Proc. of MoMM. [55] Y. Nesterov, A. Nemirovskii, and Y. Ye, Interior-point polynomial algorithms in convex programming . SIAM, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00840737

A. Osseiran, Scenarios for 5G mobile and wireless communications: the vision of the METIS project, IEEE Communications Magazine, vol.52, issue.5, pp.26-35, 2014.
DOI : 10.1109/MCOM.2014.6815890

J. Pang, J. Wang, D. Wang, G. Shen, Q. Jiang et al., Optimized time-domain resource partitioning for enhanced inter-cell interference coordination in heterogeneous networks, 2012 IEEE Wireless Communications and Networking Conference (WCNC), pp.1613-1617, 2012.
DOI : 10.1109/WCNC.2012.6214040

K. I. Pedersen, Y. Wang, B. Soret, and F. Frederiksen, eICIC Functionality and Performance for LTE HetNet Co-Channel Deployments, 2012 IEEE Vehicular Technology Conference (VTC Fall), pp.1-5, 2012.
DOI : 10.1109/VTCFall.2012.6399106

G. Poulios, K. Tsagkaris, P. Demestichas, A. Tall, Z. Altman et al., Autonomics and SDN for self-organizing networks, 2014 11th International Symposium on Wireless Communications Systems (ISWCS), 2014.
DOI : 10.1109/ISWCS.2014.6933468
URL : https://hal.archives-ouvertes.fr/hal-01067258

A. Pyzara, B. Bylina, and J. Bylina, The influence of a matrix condition number on iterative methods' convergence, Proc. of IEEE FedCSIS, pp.459-464, 2011.

H. Robbins and S. Monro, A Stochastic Approximation Method, The Annals of Mathematical Statistics, vol.22, issue.3, pp.400-407, 1951.
DOI : 10.1214/aoms/1177729586

J. Rodriguez, I. De-la-bandera, P. Munoz, and R. Barco, Load Balancing in a Realistic Urban Scenario for LTE Networks, 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring), pp.1-5, 2011.
DOI : 10.1109/VETECS.2011.5956149

J. B. Rosen, Existence and Uniqueness of Equilibrium Points for Concave N-Person Games, Econometrica, vol.33, issue.3, pp.520-534, 1965.
DOI : 10.2307/1911749

S. Roy, J. Minteer, and A. Saberi, Some new results on stabilization by scaling, 2006 American Control Conference, 2006.
DOI : 10.1109/ACC.2006.1657528

L. Schmelz, M. Amirijoo, A. Eisenblaetter, R. Litjens, M. Neuland et al., A coordination framework for self-organisation in LTE networks, 12th IFIP/IEEE International Symposium on Integrated Network Management (IM 2011) and Workshops, pp.193-200, 2011.
DOI : 10.1109/INM.2011.5990691

M. Shirakabe, A. Morimoto, and N. Miki, Performance evaluation of inter-cell interference coordination and cell range expansion in heterogeneous networks for LTE-Advanced downlink, 2011 8th International Symposium on Wireless Communication Systems, pp.844-848, 2011.
DOI : 10.1109/ISWCS.2011.6125281

C. P. Simon and L. Blume, Mathematics for economists, 1994.

M. K. Simon and M. Alouini, Digital communication over fading channels, 2005.
DOI : 10.1002/0471715220

A. Tall, Z. Altman, and E. Altman, Self organizing strategies for enhanced ICIC (eICIC), 2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), pp.318-325, 2014.
DOI : 10.1109/WIOPT.2014.6850315
URL : https://hal.archives-ouvertes.fr/hal-01006097

A. Tall, R. Combes, Z. Altman, and E. Altman, Distributed Coordination of Self-Organizing Mechanisms in Communication Networks, IEEE Transactions on Control of Network Systems, vol.1, issue.4, pp.328-337, 2014.
DOI : 10.1109/TCNS.2014.2357511
URL : https://hal.archives-ouvertes.fr/hal-01101202

K. Trichias, R. Litjens, A. Tall, Z. Altman, and P. Ramachandra, Performance evaluation & SON aspects of vertical sectorisation in a realistic LTE network environment, 2014 11th International Symposium on Wireless Communications Systems (ISWCS), 2014.
DOI : 10.1109/ISWCS.2014.6933334

K. Tsagkaris, G. Poulios, P. Demestichas, A. Tall, and Z. Altman, An open framework for programmable, self-managed radio access networks, IEEE Communications Magazine, vol.53, issue.7, pp.154-161, 2015.
DOI : 10.1109/MCOM.2015.7158279

. Univerself, Unified Management Framework (UMF) Specifications Release 3, 2013.

S. Vasudevan, R. Pupala, and K. Sivanesan, Dynamic eICIC — A Proactive Strategy for Improving Spectral Efficiencies of Heterogeneous LTE Cellular Networks by Leveraging User Mobility and Traffic Dynamics, IEEE Transactions on Wireless Communications, vol.12, issue.10, pp.4956-4969, 2013.
DOI : 10.1109/TWC.2013.081413.121651

I. Viering, M. Dottling, and A. Lobinger, A Mathematical Perspective of Self-Optimizing Wireless Networks, 2009 IEEE International Conference on Communications, pp.1-6, 2009.
DOI : 10.1109/ICC.2009.5198628

P. Vlacheas, E. Thomatos, K. Tsagkaris, and P. Demestichas, Operator-governed SON coordination in downlink LTE networks, Proc. of FutureNetw, pp.1-9, 2012.

H. Wang, L. Ding, P. Wu, Z. Pan, N. Liu et al., Dynamic load balancing and throughput optimization in 3GPP LTE networks, Proceedings of the 6th International Wireless Communications and Mobile Computing Conference on ZZZ, IWCMC '10, pp.939-943, 2010.
DOI : 10.1145/1815396.1815611

Y. Wang and K. Pedersen, Performance Analysis of Enhanced Inter-Cell Interference Coordination in LTE-Advanced Heterogeneous Networks, 2012 IEEE 75th Vehicular Technology Conference (VTC Spring), pp.1-5, 2012.
DOI : 10.1109/VETECS.2012.6240233

M. H. Willebeek-lemair and A. P. Reeves, Strategies for dynamic load balancing on highly parallel computers, IEEE Transactions on Parallel and Distributed Systems, vol.4, issue.9, pp.979-993, 1993.
DOI : 10.1109/71.243526

J. Yun and K. G. Shin, CTRL, Proceedings of the sixteenth annual international conference on Mobile computing and networking, MobiCom '10, pp.61-72, 2010.
DOI : 10.1145/1859995.1860003