1. Fluid-based analysis of TCP and RED Rajarshi Gupta WebTP Group April 3, 2000

2. Paper being Presented z“Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED” yAQM = Active Queue Management zAuthors yVishal Misra yDon Towsley yet al. (?) zWork in progress, early Preprint

3. Previous Work zRecall ”Stochastic Differential Equation Modeling and Analysis of TCP-Windowsize Behavior”, Vishal Misra, Wei-Bo Gong, Don Towsley zPresented at Performance’99, Istanbul, Turkey, October’99 zftp://gaia.cs.umass.edu/pub/Misra99-TCP-Stochastic.ps.gz zPresented by RG @ WebTP 11/08/99

4. Key Ideas of Old Paper zConsider network as source of losses and sources as recipient of these signals zModel loss arrival as independent Poisson process zUse Stochastic Differential Equations + Queuing Theory to estimate Rate zCompare with existing data and analytical model (Padhye - SIGCOMM’98)

5. Themes of Current Paper zUse SDE to model COMPLETE system yTCP characteristic yAction of AQM routers (RED) zEvaluate solution of system of equations zCorollary: RED is bad ! zSuggested improvements to RED filtering mechanisms

6. Assumptions zModel of complete system yPkt losses no longer independent parameter yTCP window size depends on RTT and RED pkt discard function yPkt loss is function of Q estimate and Q lengths yQ length is a function of window sizes zPkt losses to flow i are described by Poisson process {N i (t)} with rate i (t) zRTT R i (t) = A i (t) + q(t)/C

7. TCP Window Size zWindow size defined by zTaking expectations z Here E[x] =  x z Approximation used was E[f(x)]  f(E[x]) z Hence, 1

8. Pkt Loss Function zRED discards zLet x be exponentially weighted MA sampled every  seconds z Converting to DE and sampling z Comparing coefficients and taking expectations 2

9. Behavior of q zDifferential version of Lindley’s equation z-1 q(t) C is pkt servicing zW i / R i (q) is arrival of pkts from TCP flow i z Then, z For a bottlencked Q, q(t)>0 w.p. 1 z Hence, 3

10. Building Entire System zWe have, z N+2 coupled equations z N+2 unknowns (  x,  q,  W i ) z Solve numerically z These values can yield yR y yetc 1 3 2

11. Extensions to a Network zGeneralize yvariables to vectors yvectors to matrices zSubscript v denotes a specific router z Then, z 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

12. Further Complications zTimeout losses zSlow-Start zAggregation of identical flows ySame route and same RTT zDifferent variations of TCP

13. Application: RED zCompare the system with a network with RED as the AQM policy in routers zNetwork simulated using ns zDifferential equation solver done in Matlab zRED updates estimate every arrival zHere, choose  v = 1/C v where C v is the link capacity in pkts/sec

14. Topology z Two RED routers z S2 goes through both z S1, S3 use only Q1 z S4, S5 use only Q2 z Symmetric case (both Q capacities 5 MB/s) z Asymmetric case (Q1 = 5 MB/s, Q2 = 2.5 MB/s)

15. DiffEq Model works well (1/4)

16. DiffEq Model works well (2/4)

17. DiffEq Model works well (3/4)

18. DiffEq Model works well (4/4)

19. Effect of Packet Size (1/2)

20. Effect of Packet Size (2/2)

21. Effect of value of 

22. Flaws in RED zIf a busy state is followed by long silence, RED does not notice the silence zWhen there are rapid arrivals, average queue size closely follows instantaneous value zDiscontinuity in drop function also bad and should be eradicated

23. Suggestions for RED zAdaptive nature of sampling interval is harmful and leads to oscillations zOscillations caused by many factors like pkt size, link bw, load level etc zNeed to incorporate an appropriate sampling interval  in the sampling mechanism zTrying to design a better filter with nicer capabilities (Claims to be nearly there ;-)

24. Contributions zAn improved methodology of TCP modelling yAnalytical yComputationally efficient yModels the complete system yMatches well with simulation zDemonstrates inefficiencies of RED under certain circumstances yWorking on improved averaging mechanism