zbMATH — the first resource for mathematics

Digital bifurcation analysis of Internet congestion control protocols. (English) Zbl 1453.93141
93C62 Digital control/observation systems
93C83 Control/observation systems involving computers (process control, etc.)
93B70 Networked control
93B52 Feedback control
Full Text: DOI
[1] Ahmad Sharbafi, M. & Yazdanpanah, M. J. [2011] “ IDFC: A new approach to control bifurcation in TCP/RED,” J. Netw. Comput. Appl.34, 2042-2050.
[2] Al-Bahadili, H. [2012] Simulation in Computer Network Design and Modeling: Use and Analysis, 1st edition (IGI Global, Hershey, PA).
[3] Alpcan, T. & Basar, T. [2005] “ A globally stable adaptive congestion control scheme for internet-style networks with delay,” IEEE/ACM Trans. Netw.13, 1261-1274.
[4] Andreychenko, A., Mikeev, L., Spieler, D. & Wolf, V. [2011] “ Parameter identification for Markov models of biochemical reactions,” Computer Aided Verification, (Springer), pp. 83-98.
[5] Athuraliya, S., Low, S. H., Li, V. H. & Yin, Q. [2001] “ REM: Active queue management,” IEEE Netw.15, 48-53.
[6] Azadegan, M., Beheshti, M. T. H. & Tavassoli, B. [2013] “ Design of state feedback controller based on state-dependent delay modeling for congestion control in internet,” 2013 American Control Conf. (IEEE), pp. 2728-2732.
[7] Baccelli, F. & McDonald, D. R. [2008] “ A stochastic model for the throughput of non-persistent TCP flows,” Perform. Eval.65, 512-530.
[8] Barnat, J., Chaloupka, J. & Van De Pol, J. [2011] “ Distributed algorithms for SCC decomposition,” J. Logic Comput.21, 23-44. · Zbl 1210.68131
[9] Barnat, J., Beneš, N., Brim, L., Demko, M., Hajnal, M., Pastva, S. & Šafránek, D. [2017] “ Detecting attractors in biological models with uncertain parameters,” CMSB 2017 (Springer), pp. 44-56. · Zbl 1416.92068
[10] Bartocci, E., Bortolussi, L., Nenzi, L. & Sanguinetti, G. [2015] “ System design of stochastic models using robustness of temporal properties,” Theoret. Comput. Sci.587, 3-25. · Zbl 1327.68147
[11] Belta, C., Yordanov, B. & Gol, E. A. [2017] Formal Methods for Discrete-Time Dynamical Systems, , Vol. 89 (Springer). · Zbl 1409.93003
[12] Beneš, N., Brim, L., Demko, M., Pastva, S. & Šafránek, D. [2016a] “ A model checking approach to discrete bifurcation analysis,” FM 2016 (Springer), pp. 85-101. · Zbl 1427.68159
[13] Beneš, N., Brim, L., Demko, M., Pastva, S. & Šafránek, D. [2016b] “ Parallel SMT-based parameter synthesis with application to piecewise multi-affine systems,” ATVA 2016 (Springer), pp. 192-208. · Zbl 1427.68159
[14] Beneš, N., Brim, L., Demko, M., Hajnal, M., Pastva, S. & Šafránek, D. [2017] “ Discrete bifurcation analysis with Pithya,” CMSB 2017 (Springer), pp. 319-320. · Zbl 1416.92068
[15] Beneš, N., Brim, L., Pastva, S., Šafránek, D., Troják, M., Červený, J. & Šalagovič, J. [2018] “ Fully automated attractor analysis of cyanobacteria models,” 2018 22nd Int. Conf. System Theory, Control and Computing (ICSTCC), pp. 354-359.
[16] Beneš, N., Brim, L., Pastva, S. & Šafránek, D. [2019a] “ Parallel parameter synthesis algorithm for hybrid CTL,” Sci. Comput. Program.185, 102321. · Zbl 07120145
[17] Beneš, N., Brim, L., Pastva, S. & Šafránek, D. [2019b] “ Digital bifurcation analysis of TCP dynamics,” Tools and Algorithms for the Construction and Analysis of Systems (Springer, Cham), pp. 339-356. · Zbl 07120145
[18] Braden, B., Clark, D., Crowcroft, J., Davie, B., Deering, S., Estrin, D., Floyd, S., Jacobson, V., Minshall, G., Partridge, C., Peterson, L., Ramakrishnan, K., Shenker, S., Wroclawski, J. & Zhang, L. [1998] “Recommendations on queue management and congestion avoidance in the Internet,” RFC 2309, RFC Editor, doi:10.17487/RFC2309, https://www. rfc-editor.org/rfc/rfc2309.txt.
[19] Brim, L., Češka, M., Dražan, S. & Šafránek, D. [2013] “ Exploring parameter space of stochastic biochemical systems using quantitative model checking,” Computer Aided Verification (Springer), pp. 107-123.
[20] Brim, L., Češka, M., Demko, M., Pastva, S. & Šafránek, D. [2015a] “ Parameter synthesis by parallel coloured CTL model checking,” CMSB 2015 (Springer), pp. 251-263.
[21] Brim, L., Demko, M., Pastva, S. & Šafránek, D. [2015b] “ High-performance discrete bifurcation analysis for piecewise-affine dynamical systems,” HSB 2015 (Springer), pp. 58-74. · Zbl 1412.92115
[22] Chen, X., Wong, S.-C., Tse, C. K. & Trajković, L. [2009] “ Detrended fluctuation analysis of the TCP-RED algorithm,” Int. J. Bifurcation and Chaos19, 4237-4245.
[23] Clarke, E. M., Henzinger, T. A., Veith, H. & Bloem, R. [2018] Handbook of Model Checking, 1st edition (Springer International). · Zbl 1390.68001
[24] Ding, D.-W., Zhu, J. & Luo, X.-S. [2008] “ Hybrid control of bifurcation and chaos in stroboscopic model of internet congestion control system,” Chinese Phys. B17, 105-110.
[25] Ding, D., Zhu, J. & Luo, X. [2009] “ Hopf bifurcation analysis in a fluid flow model of internet congestion control algorithm,” Nonlin. Anal.: Real World Appl.10, 824-839. · Zbl 1167.34334
[26] Feng, W.-C., Kandlur, D., Saha, D. & Shin, K. [1999] “ A self-configuring RED gateway,” Proc. IEEE INFOCOM (IEEE), pp. 1320-1328.
[27] Feng, W.-C., Shin, K. G., Kandlur, D. D. & Saha, D. [2002] “ The BLUE active queue management algorithms,” IEEE/ACM Trans. Netw.10, 513-528.
[28] Firoiu, V. & Borden, M. [2000] “ A study of active queue management for congestion control,” Proc. IEEE INFOCOM 2000. Conf. Computer Communications. Nineteenth Ann. Joint Conf. IEEE Computer and Communications Societies (IEEE), pp. 1435-1444.
[29] Floyd, S., Gummadi, R., Shenker, S. et al. [2001] “Adaptive red: An algorithm for increasing the robustness of red’s active queue management,” available at: http://www.icir.org/floyd, August 2001.
[30] Floyd, S. [2000] “Recommendation on using the gentle variant of red,” www.icir.org/floyd/red/gentle.html.
[31] Floyd, S. & Jacobson, V. [1993] “ Random early detection gateways for congestion avoidance,” IEEE/ACM Trans. Netw.1, 397-413.
[32] Gaeta, R., Sereno, M. & Manini, D. [2003] “ Stochastic petri nets models for the performance analysis of TCP connections supporting finite data transfer,” Proc. 2nd Int. Workshop on Quality of Service in Multiservice IP Networks, QoS-IP 2003 (Springer), pp. 372-391. · Zbl 1021.68636
[33] Gao, Y. & Hou, J. C. [2003] “ A state feedback control approach to stabilizing queues for ECN-enabled TCP connections,” IEEE INFOCOM 2003. Twenty-second Ann. Joint Conf. IEEE Computer and Communications Societies (IEEE Cat. No. 03CH37428) (IEEE), pp. 2301-2311.
[34] Gettys, J. & Nichols, K. [2011] “ Bufferbloat: Dark buffers in the Internet,” Queue9, 40-54.
[35] Ha, S., Rhee, I. & Xu, L. [2008] “ Cubic: A new TCP-friendly high-speed TCP variant,” ACM SIGOPS Operating Syst. Rev.42, 64-74.
[36] Halper, R. D., Harder, E. J., Hunt, B. R. & Yorke, J. A. [2009] “ Stability of TCP dynamics in large data networks,” SIAM J. Appl. Dyn. Syst.8, 146-159. · Zbl 1167.37048
[37] Hamadneh, N., Murray, D., Dixon, M. & Cole, P. [2011] “ Weighted RED (WTRED) strategy for TCP congestion control,” Int. Conf. Informatics Engineering and Information Science (Springer), pp. 421-434.
[38] Hespanha, J. P. [2005] “ A model for stochastic hybrid systems with application to communication networks,” Nonlin. Anal.: Th. Meth. Appl.62, 1353-1383. · Zbl 1131.90322
[39] Hespanha, J. P. [2006] “ 8,” Stochastic Hybrid Modeling of On-Off TCP Flows (CRC Press), pp. 191-219.
[40] Ho, C. Y.-F., Ling, B. W.-K. & Iu, H. H. [2010] “ Symbolic dynamical model of average queue size of random early detection algorithm,” Int. J. Bifurcation and Chaos20, 1415-1437. · Zbl 1193.68063
[41] Hollot, C. V., Misra, V., Towsley, D. & Gong, W.-B. [2001a] “A control theoretic analysis of RED,” Proc. IEEE INFOCOM 2001. Conf. Computer Communications. Twentieth Ann. Joint Conf. IEEE Computer and Communications Society (IEEE), pp. 1510-1519.
[42] Hollot, C. V., Misra, V., Towsley, D. & Gong, W.-B. [2001b] “On designing improved controllers for AQM routers supporting TCP flows,” Proc. IEEE INFOCOM 2001. Conf. Computer Communications. Twentieth Ann. Joint Conf. IEEE Computer and Communications Society (Cat. No. 01CH37213) (IEEE), pp. 1726-1734.
[43] Issariyakul, T. & Hossain, E. [2010] Introduction to Network Simulator NS2 (Springer).
[44] Khoshnevisan, L., Liu, X. & Salmasi, F. R. [2019] “ Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure,” Chaos Solit. Fract.118, 255-273. · Zbl 1442.93014
[45] Kunniyur, S. & Srikant, R. [2001] “ Analysis and design of an adaptive virtual queue (avq) algorithm for active queue management,” ACM SIGCOMM Comput. Commun. Rev.31, 123-134.
[46] La, R. J. [2004] “ Instability of a tandem network and its propagation under RED,” IEEE Trans. Autom. Contr.49, 1006-1011. · Zbl 1365.90036
[47] Liu, Y., Lo Presti, F., Misra, V., Towsley, D. & Gu, Y. [2003] “ Fluid models and solutions for large-scale IP networks,” ACM SIGMETRICS Perform. Evaluat. Rev.31, 91-101.
[48] Liu, M., Zhang, H. & Trajkovic, L. [2005] “ Stroboscopic model and bifurcations in TCP/RED,” 2005 IEEE Int. Symp. Circuits and Systems (IEEE), pp. 2060-2063.
[49] Liu, M., Marciello, A., di Bernardo, M. & Trajkovic, L. [2006] “ Discontinuity-induced bifurcations in TCP/RED communication algorithms,” 2006 IEEE Int. Symp. Circuits and Systems (IEEE), pp. 2632-2636.
[50] Liu, F., Guan, Z.-H. & Wang, H. O. [2010] “ Controlling bifurcations and chaos in TCP-UDP-RED,” Nonlin. Anal.: Real World Appl.11, 1491-1501. · Zbl 1188.93049
[51] McLendon, W. III, Hendrickson, B., Plimpton, S. J. & Rauchwerger, L. [2005] “ Finding strongly connected components in distributed graphs,” J. Parall. Distrib. Comput.65, 901-910. · Zbl 1082.68086
[52] Milnor, J. [1985] “ On the concept of attractor,” Commun. Math. Phys.99, 177-195. · Zbl 0595.58028
[53] Misra, V., Gong, W.-B. & Towsley, D. [2000] “ Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED,” ACM SIGCOMM Computer Communication Review (ACM), pp. 151-160.
[54] Nga, J., Iu, H. H., Ling, B. W.-K. & Lam, H.-K. [2008] “ Analysis and control of bifurcation and chaos in average queue length in TCP/RED model,” Int. J. Bifurcation and Chaos18, 2449-2459.
[55] Ott, T. J., Lakshman, T. & Wong, L. H. [1999] “SRED: Stabilized RED,” IEEE INFOCOM’99. Conf. Computer Communications. Proc. Eighteenth Ann. Joint Conf. IEEE Computer and Communications Societies. The Future is Now (Cat. No. 99CH36320) (IEEE), pp. 1346-1355.
[56] Pokhrel, S. R. & Williamson, C. [2018] “ Modeling compound TCP over WIFI for IOT,” IEEE/ACM Trans. Netw.26, 864-878.
[57] Raina, G. & Wischik, D. [2005] “ Buffer sizes for large multiplexers: TCP queueing theory and instability analysis,” Next Generation Internet Networks, 2005 (IEEE), pp. 173-180.
[58] Raina, G., Manjunath, S., Prasad, S. & Giridhar, K. [2015] “ Stability and performance analysis of compound TCP with REM and drop-tail queue management,” IEEE/ACM Trans. Netw.24, 1961-1974.
[59] Ranjan, P. & Abed, E. H. [2002] “ Bifurcation analysis of TCP-RED dynamics,” Proc. 2002 American Control Conf. (IEEE Cat. No. CH37301) (IEEE), pp. 2443-2448.
[60] Ranjan, P., Abed, E. H. & La, R. J. [2004] “ Nonlinear instabilities in TCP-RED,” IEEE/ACM Trans. Netw.12, 1079-1092.
[61] Ranjan, P. & Abed, E. [2006] “ Nonlinear dynamical models for internet protocols,” IFAC Proc. Vol.39, 297-302.
[62] Reif, J. H. [1985] “ Depth-first search is inherently sequential,” Inform. Process. Lett.20, 229-234. · Zbl 0572.68051
[63] Schoenen, R., Sediq, A. B., Yanikomeroglu, H., Senarath, G. & Chao, Z. [2011] “ Fairness analysis in cellular networks using stochastic petri nets,” 2011 IEEE 22nd Int. Symp. Personal, Indoor and Mobile Radio Communications (IEEE), pp. 1983-1988.
[64] Shakkottai, S. & Srikant, R. [2002] “ How good are deterministic fluid models of internet congestion control?,” Proc. Twenty-First Ann. Joint Conf. IEEE Computer and Communications Societies (IEEE), pp. 497-505.
[65] Sullivan, D. & Williams, R. [1976] “ On the homology of attractors,” Topology15, 259-262. · Zbl 0332.58011
[66] Tan, K., Song, J., Zhang, Q. & Sridharan, M. [2006] “ A compound TCP approach for high-speed and long distance networks,” Proc. IEEE INFOCOM 2006. 25th IEEE Int. Conf. Computer Communications (IEEE), pp. 1-12.
[67] Tarjan, R. E. [1972] “ Depth-first search and linear graph algorithms,” SIAM J. Comput.1, 146-160. · Zbl 0251.05107
[68] Tinnakornsrisuphap, P. & La, R. J. [2006] “ Asymptotic behavior of heterogeneous TCP flows and RED gateway,” IEEE/ACM Trans. Netw.14, 108-120.
[69] Torres, R., Border, J., Choquette, G., Xu, J. & Jong, J.-H. [2012] “ Congestion control using RED and TCP window adjustment,” MILCOM 2012-2012 IEEE Military Communications Conf. (IEEE), pp. 1-6.
[70] Wang, X. & Eun, D. Y. [2007] “ Local and global stability of TCP-newReno/RED with many flows,” Comput. Commun.30, 1091-1105.
[71] Xu, Y.-D., Wang, Z.-Y. & Wang, H. [2005] “ Ared: A novel adaptive congestion controller,” 2005 Int. Conf. Machine Learning and Cybernetics (IEEE), pp. 708-714.
[72] Xu, W., Cao, J. & Xiao, M. [2015] “ Bifurcation analysis of a class of \((n+1)\)-dimension internet congestion control systems,” Int. J. Bifurcation and Chaos25, 1550019-1-17. · Zbl 1309.34139
[73] Yanfie, F., Fengyuan, R. & Chuang, L. [2003] “ Design a pid controller for active queue management,” Proc. Eighth IEEE Symp. Computers and Communications. ISCC 2003 (IEEE), pp. 985-990.
[74] Zhang, H. [2004] “A discrete-time model of TCP with active queue management, PhD thesis, Simon Fraser University, Applied Sciences: School of Engineering Science.
[75] Zhang, C., Yin, J., Cai, Z. & Chen, W. [2010] “ Rred: Robust red algorithm to counter low-rate denial-of-service attacks,” IEEE Commun. Lett.14, 489-491.
[76] Zheng, B. & Atiquzzaman, M. [2008] “ A framework to determine the optimal weight parameter of red in next-generation internet routers,” Int. J. Commun. Syst.21, 987-1008.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.