S. Ramanath, V. Kavitha, and M. Debbah, Satisfying demands in a multicellular network: A universal power allocation algorithm, 2011 International Symposium of Modeling and Optimization of Mobile, Ad Hoc, and Wireless Networks
DOI : 10.1109/WIOPT.2011.5930011

URL : https://hal.archives-ouvertes.fr/hal-00648524

M. Chiang, P. Hande, T. Lan, and C. W. Tan, Power Control in Wireless Cellular Networks, Foundations and Trends?? in Networking, vol.2, issue.4, 2008.
DOI : 10.1561/1300000009

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

S. Vivek and . Borkar, Stochastic approximation with two time scales, Systems & Control Letters, vol.29, pp.291-294, 1997.

L. C. Piccinini, G. Stampacchia, and G. Vidossich, Ordinary Differential Equations in Rn, 1978.
DOI : 10.1007/978-1-4612-5188-0

A. Proofs, . To, . Time, and . Algorithms, We obtain this proof via the [3, Theorem 6.1, pp 287]. The [3, Assumptions A6.0, A6.1, A6.2, A6.3 and A63.5, pp 287] hold for this example. Thus it remains to prove the [3, Assumption A6.4], in order to apply [3, Theorem 6.1, pp 287]. The ODE corresponding to the faster component (BS 1) for a given value of the other user's parameters P ?1 equals (for any k and see