1. A Stochastic Model of TCP Reno Congestion Avoidance and Control
Jitendra Padhye
Victor Firoiui Don Towsley
Presented by Group 2

2. Agenda Introduction Goals Issues Discussed
Significance of the paper/Relation to Coursework
Stochastic Model
Previous Work - What’s different ?
Issues not Addressed
Related Work
Questions/Comments

3. Group 2 - Members Bijendra Vishal Domin Lee Guoqiang Shu Hannafi Tjan
Lei Chai
Jilani Sarmad Syed
Juan Torres
Rohit Shenai
Wissam El Riachy
Yaoyao Gu

4. Tasks/Responsibilities
Report
What issues does the paper address ?
Task 2
What is the significance of the paper ?
How is the paper related to the course work?
Task 3
Solutions to the Issues mentioned
Task 4
How does the paper differ from its previous work?
Task 5
What related issues do the paper not address
Task 6
Presentation

5. Introduction – TCP Reno
Most modern TCPs are “Reno”
Reno refined four key mechanisms of TCP
slow start
Congestion Avoidance
Fast Retransmit
Fast Recovery

6. Goals Validate the previous model
Analyze the performance of bulk transfer TCP flows using more precise, stochastic analysis
Compare the results from the approximate (previous) model and new and more precise model
Provide both an approximate formula and more accurate stochastic model for the steady state throughput of a bulk transfer TCP flow

7. Issues Discussed Use of a finite state Markov Chain Comparisons
For more precise and stochastic analysis
Probability transition matrix
Comparisons
To validate the approximate (previous) model
Send rate
Throughputs

8. Significance of this paper
Addresses achievements and weaknesses of previous work in the area.
Develops a stochastic approach to the problem to validate a previous and less complicated model.
Extends the knowledge of the topic by developing a random (real) model for TCP congestion avoidance.

9. Relation to Course Work ????
Paper uses many of the TCP characteristics learned in class, (i.e. window size increment when no losses present).
Connection oriented nature of TCP (concept learned in class) is clearly seen because a round finishes when one or more ACKs are received, and repeated versions of ACKs (at the sender) tell   that a package or more was lost (retransmission needed).

10. Impact of Packet Losses
Packet and ACK transmissions preceding a loss indication

11. Comparison of Throughputs (Cont)

12. Analysis of TD period

13. Stochastic Model
To model the behavior of TCP in terms of rounds, the following random variables are defined
Wi is window size for round i, i= 0,…∞
Ci allows to model the increment of window by one every two rounds during no-loss period.
Li is the number of packets lost in the (i-1)st round, i = 0,…. ∞

14. Stochastic Model (Continued)
Ti denotes whether the connection is in a timeout state in round i, i=0,…. ∞
Ri denotes the duration of round i, i = 0,.. ∞ RTT denotes the RoundTrip Time To denotes the base timeout value
Ni denotes the number of packets in round i, i = 0, …∞
Mi denotes the number of packets transmitted in round i, i = 0, …∞

15. Stochastic Model (Continued)
The sequence of random variables
is finite state Markov chain with probability transition matrix
Set S is defined as the set consisting of the states of irreducible sub-chains and over which the following probability could be defined

16. Conditional Expectations
Let and denote two successive states in the sequence
Let
conditional expectations is defined as

17. Steady State – Send Rate (SR)
For t >0, Nt = Number of packets transmitted in the interval [0, t] Mt = Number of packets received
The long term steady state send rate of a TCP connection is defined as

18. Steady State –Throughput
The long term steady state throughout of a TCP connection is defined as

19. No Packets are lost

20. One or more packets are lost in a round

21. One or more packets are lost in a ‘short round’

22. Exponential BackOff

23. Previous Work - What’s different ?
A simple approximate model was proposed earlier
SIGCOMM 98
Predict steady SR as a function of loss rate and RTT
This paper uses more precise Markov-Chain model
Result matches the approximation of previous paper
Verifies the previous results
Difference from other works (e.g. [Ott])
Model as many as 6 backoff (26 * TO)
Do not model slow start phase
Do not model fast retransmit

24. Comparison of Send Rates
Approximate model proposed in [9]

25. Comparison of Send Rates

26. Comparison of Throughputs

27. Related Issues not Addressed
Bulk transfer is analyzed
Short lived flows like HTTP or Real time traffic may behave differently and may not be captured the model which is presented in the paper.
Only stochastic analysis is done that has the following shortcomings
Transition probabilities from one state to another is assumed to be constant which in real traffic may vary over time.
Transition probabilities are determined by present state, not by history
Other characteristic of TCP like fast recovery and non delayed ACKs are modeled.

28. Related Works Approaches to analyze TCP connection
Deterministic analysis of steady state
Stochastic analysis of the steady state
This paper
Fluid queuing model
Algebraic computation
Refined models of losses

29. Questions/Comments