A Stochastic Model for TCP with Stationary Random Losses

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Presentation transcript:

A Stochastic Model for TCP with Stationary Random Losses Jiang Wu

Outline Introduction The models Performance analysis Conclusion TCP Congestion Control Packet loss pattern The models TCP transmission rate evolution A general model for packet losses Performance analysis Throughput calculation Result to particular loss processes Conclusion

Transmission rate X(t) TCP TCP congestion control An additive-increase multiplicative-decrease strategy for congestion control in the Internet Packet losses for congestion detection Packet losses Transmission rate X(t) Time t

Inter-loss time in LAN

Inter-loss time in MAN

Inter-loss time in WAN

Some correlation coefficients

The model for losses Consider the loss events as a point process Denote by the times between losses Notation: Average inter-loss time: Correlation functions: Covariance functions: Normalized functions: Sn-1 Sn Sn+1 Time t

TCP Model

Solution

Throughput and Loss Rate

Result to Particular Loss Process Deterministic losses: (square root formula) Poisson loss process: General renewal process:

Limitation RTT is not a constant TCP model is simplified

References [1] Van Jacobson. Congestion avoidance and control. SIGCOMM 88, August 1988. [2] Mark Allman, Vern Paxson, andW. Stevens. TCP congestion control. RFC2581, April 1999. [3] Matthew Mathis, Jeffrey Semke, Jamshid Mahdavi. The Macroscopic Behavior of TCP Congestion Avoidance Algorithm. Computer Communications Review, volume 27, number 3, July 1997. [4] Jitendra Padhye, Victor Firoiu, Don Towsley, and Jim Kurose. Modeling TCP throughput: A simple model and its empirical validation. In SIGCOMM 98, September 1998. [5] Eitan Altman, Konstantin Avrachenkov. A Stochastic Model of TCP/IP with Stationary Random Losses. ACM SIGCOMM Computer Communication Review, Volume 30, Issue 4, October 2000