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

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

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

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

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

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

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.

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).

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

Comparison of Throughputs (Cont)

Analysis of TD period

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,…. ∞

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, …∞

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

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

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

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

No Packets are lost

One or more packets are lost in a round

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

Exponential BackOff

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

Comparison of Send Rates Approximate model proposed in [9]

Comparison of Send Rates

Comparison of Throughputs

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.

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

Questions/Comments