Abstract
A model for a random access network controlled by a static conflict warning protocol is designed as a single-server queueing system with a retrial buffer. The domain of stable operation of the system, whose state probability distribution remains constant in a large time interval, is determined under asymptotic conditions. The mean stable operation time of the system is determined and shown to be large, almost infinite, for certain traffic intensities.
Similar content being viewed by others
REFERENCES
Shvarts, M., Seti svyazi: protokoly, modelirovanie i analiz, Ch. I, II(Communication Networks: Protocols, and Analysis. Parts I and II), Moscow: Nauka, 1992.
Falin, G.I., Instability of Synchronized Aloha System, Probl. Peredachi Inf., 1990, no. 1, pp. 76–82.
Tsybakov, B.S. and Bakirov, V.L., The Stability of a Network with Packet Commutation and Its Application in a Unified Approach to Designing Synchronous and Asynchronous Radio Networks with Aloha Algorithm, Probl. Peredachi Inf., 1988, no. 2, pp. 70–85.
Nazarov, A.A. and Shokhor, S.L., Ergodicity of Markov Chains with Homogeneous String Graphs and Its Application to Analysis of Existence Conditions for Stationary States in Networks under Multiple Random Access Dynamic Protocols, Probl. Peredachi Inf., 2001, no. 2, pp. 3–16.
Nazarov, A.A. and Shokhor, S.L., Controlled Asynchronous Multiple Access in Satellite Communication Networks with Conflict Warning, Probl. Peredachi Inf., 2000, no. 1, pp. 77–89.
Nazarov, A.A. and Odyshev, Yu.A., Communication Networks under Synchronous Aloha Protocol for Heavy Traffic Intensities, Avtomat. Vychisl. Tekh.,2001, no. 1, pp. 77–84.
Nazarov, A.A. and Odyshev, Yu.A., Communication Networks under Adaptive Aloha Protocol for a Finite Number of Stations under Overloads, Probl. Peredachi Inf., 2000, no. 3, pp. 83–93.
Kuznetsov, D.Yu. and Nazarov, A.A., Communication Networks with a Finite Number of Subscriber Stations Controlled by Adaptive Multiple Random Access Protocols under Overloads, Avtomat. Telemekh., 1999, no. 12, pp. 99–113.
Kuznetsov, D.Yu. and Nazarov, A.A., Non-Markov Communication Network Models with Adaptive Multiple Random Access Protocols, Avtom. Telemekh., 2001, no. 5, pp. 124–146.
Nazarov, A.A. and Yurevich, N.M., Networks with Static and h-Persistent Multiple Random Access Protocol, Avtomat. Vychisl. Tekh., 1995, no. 1, pp. 68–78.
Nazarov, A.A., Stable Operation of Unstable Communication Networks under Random Access Protocol, Probl. Peredachi Inf., 1997, no. 2, pp. 101–111.
Nazarov, A.A., Asimptoticheskii analiz markoviziruemykh sistem(Asymptotic Analysis of Markovizable Systems), Tomsk: Tomsk. Gos. Univ., 1991.
Barucha-Reid, A.T., Elements of Theory of Markov Processes and Their Application, New York: McGraw-Hill, 1960. Translated under the title Elementy teorii markovskikh protsessov i ikh prilozheniya, Moscow: Nauka, 1969.
El'sgol'ts, L.E., Differentsial'nye uravneniya i variatsionnoe ischislenie(Differential Equations and Variational Calculus), Moscow: Nauka, 1965.
Gikhman, I.I. and Skorokhod, A.V., Stokhasticheskie differentsial'nye uravneniya(Stochastic Differential Equations), Kiev: Naukova Dumka, 1968.
Lavrent'ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo(Methods of the Theory of Functions of a Complex Variable), Moscow: Nauka, 1973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Margolis, N.Y., Nazarov, A.A. Unstable Random Access Networks under a Static Conflict Warning Protocol. Automation and Remote Control 65, 1240–1249 (2004). https://doi.org/10.1023/B:AURC.0000038726.35872.22
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000038726.35872.22