Complex Dynamics in the Delayed Stochastic AIMD/RED System
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Abstract
In the paper, we explore the stochastic bifurcation of the the heterogeneous delayed AIMD/RED system according to the qualitative changes in Invariant measure and stationary probability density of system response. Some new criteria ensuring stability and stochastic bifurcation are obtained.
Keywords
Equilibrium Point Invariant Measure Hopf Bifurcation Transmission Control Protocol Stochastic Stability
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References
- 1.Jacobson, V.: Congestion avoidance and control. ACM Computer Communication Review 18, 314–329 (1988)CrossRefGoogle Scholar
- 2.Kelly, P.: Models for a self-managed Internet. Philos. Trans. Roy. Soc. A 358, 2335–2348 (2000)MATHCrossRefGoogle Scholar
- 3.Hollot, M., Misra, V., Towsley, D., Gong, W.: Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Transactions on Automatic Control 47, 945–959 (2002)MathSciNetCrossRefGoogle Scholar
- 4.Athuraliya, S., Low, S., Yin, Q.: REM: Active queue management. IEEE Network 15, 48–53 (2001)CrossRefGoogle Scholar
- 5.Wang, L., Cai, L., Liu, X., Shen, X.: Stability and TCP-friendliness of AIMD/RED systems with feedback delays. Computer Networks 51, 4475–4491 (2007)CrossRefGoogle Scholar
- 6.Floyd, S., Jacobson, V.: Random early detection gateways for congestion avoidance. IEEE/ACM Transations on Networking 1, 397–413 (1993)CrossRefGoogle Scholar
- 7.Huang, Z., Yang, Q., Cao, J.: The stochastic stability and bifurcation behavior of an Internet congestion control model. Math. Comput. Modelling 54, 1954–1965 (2011)CrossRefGoogle Scholar
- 8.Li, C., Chen, G., Liao, X.: Hopf bifurcation in an Internet congestion control model. Chaos, Solitons & Fractals 19, 853–862 (2004)MathSciNetMATHCrossRefGoogle Scholar
- 9.Misra, V., Gong, W., Towsley, D.: Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED. Computer Communication Review 30, 151–160 (2000)CrossRefGoogle Scholar
- 10.Kelly, P.: Fairness and stability of end-to-end congestion control. Eur. J. Control 9, 149–165 (2003)CrossRefGoogle Scholar
- 11.Srikant, R.: The Mathematics of Internet Congestion Control. Birkhäuser (2004)Google Scholar
- 12.Zheng, Y., Wang, Z.: Stability and Hopf bifurcation of a class of TCP/AQM networks. Nonlinear Analysis: RWA 3, 1552–1559 (2010)CrossRefGoogle Scholar
- 13.Hale, J., Lunel, S.: Introduction to Functional Differential Equations. Springer, New York (1993)MATHGoogle Scholar
- 14.Arnold, L.: Random Dynamical Systems. Springer, New York (1998)MATHGoogle Scholar
- 15.Namachchivaya, N.: Stochastic bifurcation. Appl. Math. Comput. 38, 101–159 (1990)MathSciNetMATHCrossRefGoogle Scholar
- 16.Zhu, W.: Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation. Science Press, Beijing (2003)Google Scholar
- 17.Khasminskii, R.: On the principle of averaging for It\(\hat{\hbox{o}}\) stochastic differential equations. Kybernetika(Prague) 4, 260–279 (1968)MathSciNetGoogle Scholar
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