1. A Stochastic Model for TCP with Stationary Random Losses
Jiang Wu

2. 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

3. 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

4. Inter-loss time in LAN

5. Inter-loss time in MAN

6. Inter-loss time in WAN

7. Some correlation coefficients

8. 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

9. TCP Model

10. Solution

11. Throughput and Loss Rate

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

13. Limitation
RTT is not a constant
TCP model is simplified

14. 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