Geodesic
Spatially decentralized protocols in random multiple access networks
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 135-152.

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We analyse a spatial ALOHA-type random multiple-access protocol in a stochastic network with local interactions. We formulate and prove a stability criterion and provide convergence rates to stationarity. Finally, we compare various ALOHA-type protocols in a symmetric network.
Keywords: ALOHA protocol, random multiple access, spatial interactions, spatially decentralized protocol, positive recurrence, (in)stability, Foster criterion. 
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M. G. Chebunin; E. I. Prokopenko; A. S. Tarasenko. Spatially decentralized protocols in random multiple access networks. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 135-152. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a34/

[1] C. Bordenave, S. Foss, V. Shneer, “A Random Multiple Access Protocol with Spatial Interactions”, Journal of Applied Probability, 46:3 (2009), 844–865 | DOI | MR

[2] A. A. Borovkov, Probability Theory, Universitext, Springer, London, 2013 | DOI | MR

[3] A. A. Borovkov, D. A. Korshunov, “Large-deviation probabilities for one-dimensional Markov chains. Part 1: Stationary distributions”, Theory of Probability and its Applications, 41:1 (1997), 1–24 | DOI | MR

[4] M. Bramson, Stability of queueing networks, Lecture Notes in Mathematics, 1950, Springer, Berlin, 2008 | MR

[5] J. L. Capetanakis, “Tree algorithms for packet broadcast channels”, IEEE Transactions on Information Theory, 25:5 (1979), 505–515 | DOI | MR

[6] M. G. Chebunin, “On ergodic algorithms in systems of multiple access with partial feedback”, Siberian Elektronic Mathematical Reports, 13 (2016), 762–781 | MR

[7] A. Ephremides, B. Hajek, “Information theory and communication networks: An unconsummated union”, IEEE Trans. Inform. Theory, 44:6 (1998), 2416–2434 | DOI | MR

[8] G. I. Falin, Random processes in structurally complex queueing systems, Dissertation d.f.-m.s., MSU, M., 1989 | MR

[9] G. Fayolle, E. Gelembe, J. Labetoulle, “Stability and optimal control of the packet switching broadcast channel”, J. of Assoc. Comput. Mach., 24 (1977), 375–386 | DOI | MR

[10] S. G. Foss, Stochastic recursive sequences and their applications in Queueing, Dissertation d.f.-m.s., IM SB RAS, Novosibirsk, 1992

[11] S. G. Foss, D. E. Denisov, “On transience conditions for Markov chains”, Sibirsk. Mat. Zh., 42:2 (2001), 425–433 | MR

[12] S. G. Foss, B. Hajek, A. M. Turlikov, “Doubly Randomised Protocols for a Random Multiple Access Channel with «Success-Nonsuccess» Feedback”, Problems of Information Transmission, 52:2 (2016), 61–71 | DOI | MR

[13] B. Hajek, T. van Loon, “Decentralized dynamic control of a multiaccess broadcast channel”, IEEE Trans. Automatic Control, 27:3 (1982), 559–569 | DOI | Zbl

[14] V. V. Kalashnikov, Mathematical methods in queuing theory, Kluwer Academic Publishers Group, Dordrecht, 1994 | MR

[15] V. V. Kalashnikov, “Estimates of convergence rates and stability for regeneration and renewal Markov processes”, Queueing theory, VNIISI, M., 1981, 7–12

[16] A. Malkov, A. Turlikov, “Random multiple access protocols for communication systems with «success-failure» feedback”, IEEE International Workshop on Information Theory (1995), 1–39

[17] N. Mehravari, T. Berger, “Poisson multiple-access contention with binary feedback”, IEEE Transactions on Information Theory, 30:5 (1984), 745–751 | DOI | MR

[18] S. Meyn, R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, 1993 | MR

[19] V. A. Mikhailov, “Geometrical Analysis of the Stability of Markov Chains in ${\mathbf R}^n_+$ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm”, Problems of Information Transmission, 24:1 (1988), 47–56 | MR

[20] B. Paris, B. Aazhang, “Near-optimum control of multiple-access collision channels”, IEEE Transactions on Wireless Communications, 40 (1992), 1298–1308 | DOI | Zbl

[21] B. S. Tsybakov, A. N. Beloyarov, “Random multiple access in a channel with a binary feedback «Success-Failure»”, Problems of Information Transmission, 26:3 (1990), 67–82 | MR

[22] B. S. Tsybakov, A. N. Beloyarov, “Random multiple access in a channel with a binary feedback”, Problems of Information Transmission, 26:4 (1990), 83–97 | MR | Zbl

[23] B. S. Tsybakov, V. A. Mikhailov, “Free synchronized access in a broadcast channel with a feedback”, Problems of Information Transmission, 14:4 (1978), 32–59 | MR

[24] A. Turlikov, S. Foss, “On ergodic algorithms in random multiple access systems with «success-failure» feedback”, Problems of Information Transmission, 46:2 (2010), 184–200 | DOI | MR