Fluid-based analysis ofTCP and RED

Rajarshi GuptaWebTP GroupApril 3, 2000

Paper being Presented

“Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED” AQM = Active Queue Management

Authors Vishal Misra Don Towsley et al. (?)

Work in progress, early Preprint

Previous Work

Recall ”Stochastic Differential Equation Modeling and Analysis of TCP-Windowsize Behavior”, Vishal Misra, Wei-Bo Gong, Don Towsley

Presented at Performance’99, Istanbul, Turkey, October’99

ftp://gaia.cs.umass.edu/pub/Misra99-TCP-Stochastic.ps.gz

Presented by RG @ WebTP 11/08/99

Key Ideas of Old Paper

Consider network as source of losses and sources as recipient of these signals

Model loss arrival as independent Poisson process

Use Stochastic Differential Equations + Queuing Theory to estimate Rate

Compare with existing data and analytical model (Padhye - SIGCOMM’98)

Themes of Current Paper

Use SDE to model COMPLETE system TCP characteristic Action of AQM routers (RED)

Evaluate solution of system of equations

Corollary: RED is bad !Suggested improvements to RED

filtering mechanisms

Assumptions

Model of complete system Pkt losses no longer independent parameter TCP window size depends on RTT and RED pkt

discard function Pkt loss is function of Q estimate and Q

lengths Q length is a function of window sizes

Pkt losses to flow i are described by Poisson process {Ni (t)} with rate i (t)

RTT Ri (t) = Ai (t) + q(t)/C

TCP Window Size

Window size defined by

Taking expectations

Here E[x] =x

Approximation used was E[f(x)] f(E[x])

Hence,

1

Pkt Loss Function

RED discards

Let x be exponentially weighted MA sampled every seconds

Converting to DE and sampling

Comparing coefficients and taking expectations

2

Behavior of q

Differential version of Lindley’s equation

-1q(t)C is pkt servicing

Wi / Ri (q) is arrival of pkts from TCP flow i

Then,

For a bottlencked Q, q(t)>0 w.p. 1

Hence,

3

Building Entire System

We have, N+2 coupled equations

N+2 unknowns (x,q,Wi )

Solve numericallyThese values can

yield R etc

1

3

2

Extensions to a Network

Generalize variables to vectors vectors to matrices

Subscript v denotes a specific router

Then,

Replacing the old system of equations

is same (for |V| routers)

1

2

3

So we get a total of N+2|V| unknowns to solve numerically

Further Complications

Timeout lossesSlow-Start

Aggregation of identical flows Same route and same RTT

Different variations of TCP

Application: RED

Compare the system with a network with RED as the AQM policy in routers

Network simulated using nsDifferential equation solver done in Matlab

RED updates estimate every arrivalHere, choose v = 1/Cv where Cv is the link

capacity in pkts/sec

Topology

Two RED routersS2 goes through bothS1, S3 use only Q1S4, S5 use only Q2Symmetric case (both

Q capacities 5 MB/s)Asymmetric case (Q1

= 5 MB/s, Q2 = 2.5 MB/s)

DiffEq Model works well (1/4)

DiffEq Model works well (2/4)

DiffEq Model works well (3/4)

DiffEq Model works well (4/4)

Effect of Packet Size (1/2)

Effect of Packet Size (2/2)

Effect of value of

Flaws in RED

If a busy state is followed by long silence, RED does not notice the silence

When there are rapid arrivals, average queue size closely follows instantaneous value

Discontinuity in drop function also bad and should be eradicated

Suggestions for RED

Adaptive nature of sampling interval is harmful and leads to oscillations

Oscillations caused by many factors like pkt size, link bw, load level etc

Need to incorporate an appropriate sampling interval in the sampling mechanism

Trying to design a better filter with nicer capabilities (Claims to be nearly there ;-)

Contributions

An improved methodology of TCP modelling Analytical Computationally efficient Models the complete system Matches well with simulation

Demonstrates inefficiencies of RED under certain circumstances Working on improved averaging mechanism