Abstract
Using probabilistic scaling methods, we extend the square root law of TCP to schemes which may not be of the AIMD type. Our results offer insight in the relationship between throughput and loss rate, and the time scale on which losses take place. Similar results are shown to hold in scenarios where dependencies between losses occur.
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Altman, E., Avrachenkov, K., Barakat, C., & Núñez Queija, R. (2002). State-dependent M/G/1 type queueing analysis for congestion control in data networks. Computer Networks, 39, 789–808.
Altman, E., Avrachenkov, K., Barakat, C., Kherani, A. A., & Prabhu, B. (2005a). Analysis of MIMD congestion control algorithm for high speed networks. Computer Networks, 48, 972–989.
Altman, E., Avrachenkov, K., Barakat, C., Kherani, A. A., & Prabhu, B. (2005b). Performance analysis and stochastic stability of congestion control protocols. In: Proceedings of IEEE Infocom, Miami, USA.
Bansal, D., & Balakrishnan, H. (2001). Binomial congestion control algorithms. In: Proceedings of IEEE Infocom, Anchorage, USA.
Dumas, V., Guillemin, F., & Robert, P. (2002). A Markovian analysis of additive-increase multiplicative-decrease algorithms. Advances in Applied Probability, 34, 85–111.
Ethier, S., & Kurtz, T. (1986). Markov processes: characterization and convergence. New York: Wiley.
Floyd, S. (1991). Connections with multiple congested gateways in packet-switched networks part 1: One-way traffic. Computer Communications Review, 21(5), 23–30.
Floyd, S. (2002). Highspeed TCP for large congestion windows. http://www.icir.org/floyd/papers/draft-floyd-tcp-highspeed-01.txt.
Gamarnik, D., & Zeevi, A. (2006). Validity of heavy traffic steady-state approximation in generalized Jackson networks. Annals of Applied Probability, 16, 56–90.
Gibbens, R. J., Sargood, S. K., Van Eijl, C., Kelly, F. P., Azmoodeh, H., Macfadyen, R. N., & Macfadyen, N. W. (2000). Fixed-point models for the end-to-end performance analysis of IP networks. In: 13th ITC specialist seminar: IP traffic measurement, modeling and management, Monterey, CA.
Guillemin, F., Robert, P., & Zwart, B. (2004). AIMD algorithms and exponential functionals. Annals of Applied Probability, 14, 90–117.
Jacobson, V. (1988). Congestion avoidance and control. In: Proceedings of SIGCOMM ’88.
Kelly, T. (2003). Scalable TCP: Improving performance in Highspeed wide area networks. Computer Communications Review, 32, 83–91.
Kelly, F. P., Maulloo, A. K., & Tan, D. K. H. (1998). Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society, 49, 237–252.
Massoulie, L. (2007). Structural properties of proportional fairness: stability and insensitivity. Annals of Applied Probability, 17(3), 809–839.
Mathis, M., Semke, J., Mahdavi, J., & Ott, T. J. (1997). The macroscopic behavior of the TCP congestion avoidance algorithm. Computer Communication Review 27, 67–82.
Maulik, K., & Zwart, B. (2006). Tail asymptotics for exponential functionals of Levy processes. Stochastic Processes and their Applications, 116, 156–177.
Meyn, S., & Tweedie, R. (1994). Markov chains and stochastic stability. http://decision.csl.uiuc.edu/~meyn/pages/book.html.
Ott, T. J. (2005). Transport protocols in the TCP paradigm and their performance. Telecommunication Systems, 30, 351–385.
Ott, T. J., & Swanson, J. (2006). Asymptotic behavior of a generalized TCP congestion avoidance algorithm. Preprint; see http://front.math.ucdavis.edu/math.PR/0608476.
Padhye, J., Firoiu, V., Towsley, D., & Kurose, J. (2000). Modeling TCP reno performance: a simple model and its empirical validation. IEEE/ACM Transactions on Networking, 8, 133–145.
Paxson, V. (1999). End-to-end Internet packet dynamics. IEEE/ACM Transactions on Networking, 7, 277–292.
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Maulik, K., Zwart, B. An extension of the square root law of TCP. Ann Oper Res 170, 217–232 (2009). https://doi.org/10.1007/s10479-008-0437-8
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DOI: https://doi.org/10.1007/s10479-008-0437-8