Abstract
Fluid models of IP networks have been recently proposed, to break the scalability barrier of traditional performance evaluation approaches, both simulative (e.g., ns-2) and analytical (e.g., queues and Markov chains). Fluid models adopt a deterministic description of the average source and network dynamics through a set of (coupled) ordinary differential equations that are solved numerically, obtaining estimates of the time-dependent behavior of the IP network.
The most attractive property of fluid models resides in the fact that they are scalable, i.e., their complexity is independent of the number of TCP flows and of link capacities. In this paper we provide a theoretical investigation of the origins of the scalability of fluid models. We show that the set of differential equations defining the network dynamics under both drop-tail and AQM buffering exhibits a nice invariance property, that allows an equivalence relation to be established among different systems. The validity of the invariance property is verified in realistic network scenarios with ns-2 simulations.
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References
F. Baccelli, D. Hong, “Interaction of TCP Flows as Billiards”, IEEE Infocom 2003, San Francisco, CA, March 2003.
F. Baccelli, D. Hong, “Flow Level Simulation of Large IP Networks”, IEEE Infocom 2003, SanFrancisco, CA, March 2003.
S. Misra, W.B. Gong, D. Towsley, “Fluid-Based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED”, ACM SIGCOMM 2000, Stockholm, Sweden, August 2000.
C.V. Hollot, V. Misra, D. Towsley, W.B. Gong, “On the Design of Improved Controllers for AQM Routers Supporting TCP Flows”, IEEE Infocom 2001, Anchorage, Alaska, USA, April 2001.
Y. Liu, F.Lo Presti, V. Misra, D. Towsley, “Fluid Models and Solutions for Large-Scale IP Networks”, ACM Sigmetrics 2003, San Diego, CA, June 2003.
C.V. Hollot, V. Misra, D. Towsley, W.B. Gong, “A Control Theoretic Analysis of RED”, IEEE Infocom 2001, Anchorage, Alaska, USA, April 2001.
S. Deb, S. Shakkottai, R. Srikant, “Stability and Convergence of TCP-like Congestion Controllers in a Many-Flows Regime”, IEEE Infocom 2003, San Francisco, CA, March 2003.
S. Shakkottai, R. Srikant, “How Good are Deterministic FluidModels of Internet Congestion Control?” IEEE INFOCOM 2002, New York, June 2002.
P. Tinnakornsrisuphap, A. Makowski, “Limit Behavior of ECN/RED Gateways Under a Large Number of TCP Flows”, IEEE Infocom 2003, San Francisco, CA, March 2003.
F. Baccelli, D.R. McDonald, J. Reynier, “A Mean-Field Model for Multiple TCP Connections through a Buffer Implementing RED”, Performance Evaluation, vol. 49 n. 1/4, pp. 77–97, 2002.
M. Ajmone Marsan, M. Garetto, P. Giaccone, E. Leonardi, E. Schiattarella, A. Tarello, “Using Partial Differential Equations to Model TCP Mice and Elephants in Large IP Networks”, Infocom 2004, Hong Kong, March 2004.
M. Ajmone Marsan, G. Carofiglio, M. Garetto, P. Giaccone, E. Leonardi, E. Schiattarella, A. Tarello, “Of Mice and Models”, QoS IP 2005, Catania, February 2005.
S. Floyd, V. Jacobson, “Random Early Detection Gateways for Congestion Avoidance”, IEEE/ACM Transactions on Networking, vol. 1, n. 4, pp. 397–413, August 1993.
R. Pan, B. Prabhakar, K. Psounis, D. Wischik, “SHRiNK: A method for scalable performance prediction and efficient network simulation”, IEEE Infocom 2003, San Francisco, CA, March 2003
R. Pan, B. Prabhakar, K. Psounis, M. Sharma, “A study of the applicability of a scaling hypothesis”, in Proc. ASCC 2002, Singapore, September 2002
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Marsan, M.A. et al. (2006). On the Scalability of Fluid Models of IP Networks Loaded by Long-lived TCP Flows. In: Nejat Ince, A., Topuz, E. (eds) Modeling and Simulation Tools for Emerging Telecommunication Networks. Springer, Boston, MA . https://doi.org/10.1007/0-387-34167-6_6
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DOI: https://doi.org/10.1007/0-387-34167-6_6
Publisher Name: Springer, Boston, MA
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