suppose that for some other MAC policy ? (·) the value of the expectation (23) is equal to that obtained for ? S) is the expression under the expectation in (23) as a function of the MAC policy. Then we have, order to prove the uniqueness ,
THE ALOHA SYSTEM, Proceedings of the November 17-19, 1970, fall joint computer conference on, AFIPS '70 (Fall), 1970. ,
DOI : 10.1145/1478462.1478502
-2 of Foundations and Trends in Networking, Stochastic Geometry and Wireless Networks, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00357952
Stochastic Geometry and Wireless Networks Volume I: Theory, volume 3 issue 3-4 of Foundations and Trends in Networking, 2009. ,
An Aloha protocol for multihop mobile wireless networks, IEEE Transactions on Information Theory, vol.52, issue.2, pp.421-436, 2006. ,
DOI : 10.1109/TIT.2005.862098
Stochastic analysis of spatial and opportunistic aloha, IEEE Journal on Selected Areas in Communications, vol.27, issue.7, pp.1105-1119, 2009. ,
DOI : 10.1109/JSAC.2009.090908
URL : https://hal.archives-ouvertes.fr/inria-00360800
Adaptive spatial Aloha, fairness and stochastic geometry, Proceedings of the Ninth Workshop on Spatial Stochastic Models for Wireless Networks, Spaswin 2013 ? in conjunction with WIOpt'13, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00797568
A random multiple access protocol with spatial interactions, Proceedings of IEEE WiOpt, pp.1-6, 2007. ,
Throughput region of randomaccess networks of general topology, IEEE Transactions on Information Theory, vol.58, issue.5, p.2012 ,
Stochastic approximation methods for decentralized control of multiaccess communications, IEEE Transactions on Information Theory, vol.31, issue.2, pp.176-184, 1985. ,
DOI : 10.1109/TIT.1985.1057025
Stochastic geometry based medium access games, 2012 Proceedings IEEE INFOCOM, 2012. ,
DOI : 10.1109/INFCOM.2012.6195554
URL : https://hal.archives-ouvertes.fr/hal-00940557
Channel-aware ALOHA with SINR capture: When is the knowledge of channel not helpful?, 2011 IEEE 22nd International Symposium on Personal, Indoor and Mobile Radio Communications, 2011. ,
DOI : 10.1109/PIMRC.2011.6140086
Fractional power control for decentralized wireless networks, IEEE Transactions on Wireless Communications, vol.7, issue.12, pp.5482-5492, 2008. ,
DOI : 10.1109/T-WC.2008.071439
Rate control for communication networks: shadow prices, proportional fairness and stability, Journal of the Operational Research Society, vol.49, issue.3, pp.237-252, 1998. ,
DOI : 10.1057/palgrave.jors.2600523
Optimal SINR-based Random Access, 2010 Proceedings IEEE INFOCOM, 2010. ,
DOI : 10.1109/INFCOM.2010.5462065
ALOHA packet system with and without slots and capture, ACM SIGCOMM Computer Communication Review, vol.5, issue.2, pp.28-42, 1975. ,
DOI : 10.1145/1024916.1024920
Distributed algorithms for max-min fair rate allocation in aloha networks, 42nd Annual Allerton Conference on Communication, Control, and Computing, 2004. ,
Random Power Control in Poisson Networks, IEEE Transactions on Communications, vol.60, issue.9, p.2012 ,
DOI : 10.1109/TCOMM.2012.071312.110730