On the Ergodicity and Stability of the Sequence $w_{n + 1} = f(w_n ,\xi _n )$: Applications to Communication Networks
Alexandr Alekseevich Borovkov · Theory of Probability and Its Applications · 1989
Next article On the Ergodicity and Stability of the Sequence $w_{n + 1} = f(w_n ,\xi _n )$: Applications to Communication NetworksA. A. BorovkovA. A. Borovkovhttps://doi.org/10.1137/1133094PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. A. Borovkov, Asymptotic Methods in Queueing Theory, Nauka, 1980, (In Russian.) 0479.60006 Google Scholar[2] A. A. Borovkov, Asymptotic methods in queuing theory, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons Ltd., Chichester, 1984xi+292 85f:60134 Google Scholar[3] A. A. Borovkov, Convergence of distributions of functionals and sequences defined on the whole axis, Trudy Mat. Inst. Steklov, 78 (1972), 41–65, (In Russian.) Google Scholar[4] L. Kleinrock, Queueing systems, II: Computer Applications, John Wiley, New York, 1976, 360–414 0361.60082 Google Scholar[5] N. Abramson, The throughput of packet broadcasting channels, IEEE Trans. Comm., 25 (1977), 117–128 10.1109/TCOM.1977.1093713 CrossrefGoogle Scholar[6] Guy Favolle, , Erol Gelenbe and , Jacques Labetoulle, Stability and optimal control of the packet switching broadcast channel, J. Assoc. Comput. Mach., 24 (1977), 375–386 56:3975 CrossrefGoogle Scholar[7] Michael J. Fergusson, On the control, stability, and waiting time in a slotted ALOHA random-access system, IEEE Trans. Comm., COM-23 (1975), 1306–1311 10.1109/TCOM.1975.1092743 55:2292 CrossrefGoogle Scholar[8] B. S. Tsybakov and , V. A. Mikhailov, Ergodicity of a synchronous ALOHA system, Problemy Peredachi Informatsii, 15 (1979), 73–87, (In Russian.) Google Scholar[9] Guy Favolle, , Philippe Flajolet, , Micha Hofri and , Philippe Jacquet, Analysis of a stack algorithm for random multiple-access communication, IEEE Trans. Inform. Theory, 31 (1985), 244–254 10.1109/TIT.1985.1057014 86g:94015 CrossrefGoogle Scholar[10] Bruce Hajek, Stochastic approximation methods for decentralized control of multiaccess communications, IEEE Trans. Inform. Theory, 31 (1985), 176–184 10.1109/TIT.1985.1057025 86j:94026 0563.94003 CrossrefGoogle Scholar[11] Guy Favolle, , Philippe Flajolet and , Micha Hofri, On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel, Adv. in Appl. Probab., 18 (1986), 441–472 87g:68008 CrossrefGoogle Scholar[12] A. G. Pakes, Some conditions for ergodicity and recurrence of Markov chains, Operations Res., 17 (1969), 1058–1061 41:4664 0183.46902 CrossrefGoogle Scholar[13] J. Lamperti, Criteria for the recurrence or transcience of stochastic processes, I, J. Math. Anal. Appl., 1 (1960), 314–330 10.1016/0022-247X(60)90005-6 0099.12901 CrossrefGoogle Scholar[14] Hans Fölmer, Martingale criteria for stochastic stabilityProbability theory (Papers, VIIth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1976), Banach Center Publ., Vol. 5, PWN, Warsaw, 1979, 89–96, Polish Scientific Publications 81c:93088 0412.60049 CrossrefGoogle Scholar[15] A. A. Borovkov, Wahrscheinlichkeitstheorie, Birkhäuser Verlag, Basel, 1976xi+264 53:14561 Google Scholar Next article FiguresRelatedReferencesCited ByDetails Markov renewal theory for stationary (m+1)-block factors: convergence rate resultsStochastic Processes and their Applications, Vol. 98, No. 1 | 1 Mar 2002 Cross Ref Treelike queueing networks: asymptotic stationarity and heavy trafficThe Annals of Applied Probability, Vol. 8, No. 2 | 1 May 1998 Cross Ref Stationary solutions of stochastic recursions describing discrete event systemsStochastic Processes and their Applications, Vol. 68, No. 2 | 1 Jun 1997 Cross Ref Limit theorems for recursive algorithmsJournal of Computational and Applied Mathematics, Vol. 56, No. 1-2 | 1 Dec 1994 Cross Ref Asymptotic stationarity of multichannel queuesAdvances in Applied Probability, Vol. 25, No. 01 | 1 July 2016 Cross Ref Asymptotic stationarity of multichannel queuesAdvances in Applied Probability, Vol. 25, No. 1 | 1 July 2016 Cross Ref Stationary solutions of stochastic recursions describing discrete event systemsProceedings of 1994 33rd IEEE Conference on Decision and Control Cross Ref Volume 33, Issue 4| 1989Theory of Probability & Its Applications595-765 History Submitted:09 December 1986Published online:28 July 2006 InformationCopyright © 1988 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133094Article page range:pp. 595-611ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics