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Problemy Peredachi Informatsii, 1988, Volume 24, Issue 1, Pages 61–73 (Mi ppi687)  

This article is cited in 10 scientific papers (total in 10 papers)

Communication Network Theory

Geometrical Analysis of the Stability of Markov Chains in $R_+^n$ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm

V. A. Mikhailov
Abstract: The method of stochastic Lyapunov functions is applied to derive sufficient conditions of recurrence and nonrecurrence of Markov chains with values in a many-dimensional Euclidean space. In the two-dimensional case, the stability conditions are stated in terms of the limit mean drift vector function. The results are applied to evaluate the throughput of an adaptive random multiple access algorithm for packets in a broadcasting channel with feedback.
Received: 28.10.1985
Bibliographic databases:
Document Type: Article
UDC: 621.391.1:519.27
Language: Russian
Citation: V. A. Mikhailov, “Geometrical Analysis of the Stability of Markov Chains in $R_+^n$ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm”, Probl. Peredachi Inf., 24:1 (1988), 61–73; Problems Inform. Transmission, 24:1 (1988), 47–56
Citation in format AMSBIB
\Bibitem{Mik88}
\by V.~A.~Mikhailov
\paper Geometrical Analysis of the Stability of Markov Chains in~$R_+^n$ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm
\jour Probl. Peredachi Inf.
\yr 1988
\vol 24
\issue 1
\pages 61--73
\mathnet{http://mi.mathnet.ru/ppi687}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=939575}
\zmath{https://zbmath.org/?q=an:0673.60072|0652.60070}
\transl
\jour Problems Inform. Transmission
\yr 1988
\vol 24
\issue 1
\pages 47--56
Linking options:
  • https://www.mathnet.ru/eng/ppi687
  • https://www.mathnet.ru/eng/ppi/v24/i1/p61
  • This publication is cited in the following 10 articles:
    1. A. V. Daraseliya, E. S. Sopin, K. E. Samuilov, E. A. Kucheryavyi, “Minimizatsiya zaderzhki v sistemakh 5G/6G IoT s gruppovym postupleniem v voskhodyaschem i niskhodyaschem napravleniyakh”, Inform. i ee primen., 18:4 (2024), 59–67  mathnet  crossref
    2. M. G. Chebunin, S. G. Foss, “O stabilnosti sistem sluchainogo mnozhestvennogo dostupa s minimalnoi obratnoi svyazyu”, Sib. elektron. matem. izv., 16 (2019), 1805–1821  mathnet  crossref
    3. M. G. Chebunin, E. I. Prokopenko, A. S. Tarasenko, “Prostranstvenno detsentralizovannye protokoly v setyakh sluchainogo mnozhestvennogo dostupa”, Sib. elektron. matem. izv., 15 (2018), 135–152  mathnet  crossref
    4. Foss S., Turlikov A., Grankin M., “Spatial Random Multiple Access With Multiple Departure”, 2017 IEEE International Symposium on Information Theory (ISIT), IEEE International Symposium on Information Theory, IEEE, 2017, 2728–2731  isi
    5. M. G. Chebunin, “Ob ergodicheskikh algoritmakh v sistemakh sluchainogo mnozhestvennogo dostupa s chastichnoi obratnoi svyazyu”, Sib. elektron. matem. izv., 13 (2016), 762–781  mathnet  crossref
    6. S. G. Foss, B. Hajek, A. M. Turlikov, “Doubly randomized protocols for a random multiple access channel with “success–nonsuccess” feedback”, Problems Inform. Transmission, 52:2 (2016), 156–165  mathnet  crossref  mathscinet  isi  elib  elib
    7. N. D. Vvedenskaya, Yu. M. Suhov, “Multiuser Multiple-Access System: Stability and Metastability”, Problems Inform. Transmission, 43:3 (2007), 263–269  mathnet  crossref  mathscinet  zmath  isi
    8. D. Yu. Kuznetsov, A. A. Nazarov, “Analysis of a Communication Network Governed by an Adaptive Random Multiple Access Protocol under Critical Load”, Problems Inform. Transmission, 40:3 (2004), 243–253  mathnet  crossref  mathscinet  zmath
    9. A. A. Nazarov, Yu. D. Odyshev, “Analysis of a Communication Network with the Adaptive ALOHA Protocol for a Finite Number of Stations under Overload”, Problems Inform. Transmission, 36:3 (2000), 272–281  mathnet  mathscinet  zmath
    10. Ephremides, A, “Information theory and communication networks: An unconsummated union”, IEEE Transactions on Information Theory, 44:6 (1998), 2416  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы передачи информации Problems of Information Transmission
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