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Modeling TCP-Vegas under On/Off traffic

Modeling TCP-Vegas under On/Off traffic. Fifth Workshop on MAthematical performance Modeling and Analysis (MAMA) San Diego, June 10-11, 2003. Talk by Jörgen Olsén Joint work with Adam Wierman and Takayuki Osogami. Goal of paper.

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Modeling TCP-Vegas under On/Off traffic

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  1. Modeling TCP-Vegas under On/Off traffic Fifth Workshop on MAthematical performance Modeling and Analysis (MAMA) San Diego, June 10-11, 2003 Talk by Jörgen Olsén Joint work with Adam Wierman and Takayuki Osogami

  2. Goal of paper • Model multiple TCP-Vegas sources sending On/Off traffic • Predict TCP-network operating point in a bottleneck network • link utilization • per source throughput • per source goodput • loss rate • Only use network topology and statistical traffic characteristics as input

  3. Main contributions • Model of TCP-Vegas On/Off traffic sources that includes packet loss and network delay • Accurate predictions of network operating point for TCP-Vegas On/Off sources from primary network parameters • Framework allows easy comparisons of different TCP flavors within the same network • Model validated withhigh accuracy against ns-simulations

  4. TCP-Vegas - mechanisms Slow-start • Slow-start • If no packets are lost, the window size is doubled every second RTT until slow-start threshold is reached (Reno doubles every single RTT) • Vegas queries delay. Exits slow-start early if delay too high. (Reno only uses slow-start threshold)

  5. TCP-Vegas - mechanisms Congestion avoidance • Congestion avoidance • Vegas strives to avoid loss by adjusting the congestion window in response to observed network delay (Reno only uses loss to infer congestion) • Little delay  window increased by 1 packet • Moderate delay  window size maintained • Much delay  window decreased by 1 packet

  6. TCP-Vegas - mechanisms Fast Retransmit / Fast Recovery • Fast Retransmit / Fast Recovery • If loss still occurs Vegas implements Reno-like Fast Retransmit / Fast Recovery to recover from “moderate” loss • Window size adjusted W  3W/4 (Reno adjusts to W/2)

  7. TCP-Vegas - mechanisms Timeout • Timeout • If less than three duplicate ACKs are received Vegas times out • After timeout window reset to initial size and slow-start occurs • Consecutive timeouts doubles timeout length (exponential back-off)

  8. High-level methodology Aggregated load l Network TCP Source Loss and Delay Separate the models of the TCP source and the network and allow interaction via feedback • Fundamental relationship: • Network loss and delay depends on load • TCP-Vegas adjusts load in response to observed loss and delay • Use a fixed-point method

  9. TCP Transport level model Assume the network model has delivered • PW( k ): probability of dropping k packets among W sent • P( Nb ≤ j ): probability for ≤ j packets in bottleneck queue from each source • RTT: Propagation delay + Queuing delay Then, • Derive the TCP Markov chain and transition rates • Stationary solution to Markov chain determines throughput as function of packet loss rate and network delay

  10. TCP Transport level model • Continuous time Markov chain model of the source in busy state • A state consists of: • Current window size • Slow start threshold (Wt) • Active or loss recovery phase? • Transition rate depends on the RTT and packet loss rate.

  11. TCP-Vegas Markov Chain Slow-start – transition rates Below delay threshold: Transition to intermediate state from window size w: Pw(0) P(Nb≤) / RTT From intermediate state to doubling: Pw(0) P(Nb≤) / RTT Above delay threshold(exit to C.A): Transition to intermediate state from window size w: Pw(0) P(Nb>) / RTT From intermediate to congestion avoidance w+1: Pw(0) P(Nb>) / RTT • Slow Start • If no packets are lost, the window size is doubled every second RTT. • RTT is estimated. If the delay at the network is more than  packets we jump out of slow start to avoid loss. • Slow Start • If no packets are lost, the window size is doubled every second RTT.

  12. TCP-Vegas Markov Chain Congestion Avoidance – transition rates If no packets are lost: Increase:P(Nb<) Pw(0) / RTT Decrease:P(Nb>) Pw(0) / RTT Stay:P( <Nb< ) Pw(0) / RTT • Congestion Avoidance • If no packets are lost: • If the delay at the network is more than β packets we decrease our window by 1. • If the delay at the network is less than α packets we increase our window by 1. • Otherwise we maintain our window size.

  13. TCP-Vegas Markov Chain Fast retransmit – transition rates To fast retransmit: Pfr/fr / RTT From fast retransmit back to congestion avoidance: 1 / RTT • Fast retransmit • If packets are lost but atleast 3 duplicate ACKs are received we fast retransmit. • Drop window by 1/4. • Fast retransmit probability Pfr/fr(w) quantified for different window sizes using “A Simulation based study” Fall & Floyd 96

  14. TCP-Vegas Markov Chain • Timeout • If too few duplicate ACKs are received Vegas times out • Timeout length T=RTT+4. Window set to inital winsize followed by slow-start • Timeout probability Pto quantified for different window sizes using “A Simulation based study” Fall & Floyd 96 Timeout – transition rates To timeout: Pto(w) / RTT From timeout back to slow-start: P1(0) / T

  15. TCP-Vegas Markov Chain Exponential backoff – transition rates From exponential backoff state k to k+1: [1-P1(0)] / 2kT From exponential backoff k back to slow-start: P1(0) / 2kT • Exponential backoff • If the first resent packet after a timeout is lost, the next timeout doubles in length to 2T • This exponential backoff continues up to maximum 64 T

  16. Modeling the sources Application web On/Off traffic Transport TCP mechanisms Network Link Physical Our TCP-Vegas source model mimics the structure of a network stack:

  17. Application level model • On/Off – transition rates • Idle to busy: • 1 / E[ Toff ] • Active states (slow-start, congestion avoidance ) to idle: • 1 / E[ Ton ] • On/Off model • Exponential time in the idle state E[ Toff ] • Exponential time in busy state E[ Ton ] • Each busy period starts with window size of one packet. Slow-start threshold Wt=Wmax/2 • Extensions: by increasing the state space • Arbitrary distributions can be approximated by hyper-exponential • File size distributions modeled using N = max file size classes

  18. High-level methodology - reminder Aggregated load l Network TCP Source Loss and Delay Separate the models of the TCP source and the network and allow interaction via feedback

  19. Modeling the network • We model the network using a single bottleneck link: • Queueing model to output the loss rate and delay distribution on the link given the throughput coming into the link. Offered traffic from TCP sources Server speed is the speed of the bottleneck link Buffer size of the bottleneck link

  20. Modeling the network • We will model the network using a single bottleneck link: • Queueing model to output the loss rate and delay distribution on the link given the throughput coming into the link. • But how should the bottleneck • link be modeled? • M/M/1/B • Mr/M/1/B • M/D/1/B • … Offered traffic from TCP sources Server speed is the speed of the bottleneck link Buffer size of the bottleneck link

  21. Fixed-point methodology Aggregated load l TCP Source Network l* - average load • Stationary distribution to Markov Chain pi • Per source load li = S wipi • Aggregate load from N sources l = Sli • Packet loss rate p • Delay distribution Dq p* - average loss rate Loss and Delay Find fixed-point (l*,p*, Dq*) { l* = f(p*,Dq*) (p*,Dq*) = g(l*)

  22. Validation: 100 sources, On/Off=5/1.5 sec.

  23. Related work Single source model - renewal theory model for TCP • Samios and Vernon ”Modeling the throughput of TCP-Vegas”, Sigmetrics, June 2003. Fixed-point methods - Markov Chain model for TCP • Casetti and Meo ”A new approach to model the stationary behavior of TCP connections”, INFOCOMM, March 2000. • Casetti and Meo ”An analytical framework for the performance evaluation of TCP Reno connections”, Computer Networks 37, 2001. • Wierman, Osogami, Olsén, ”A unified framework for modeling TCP-Vegas, TCP-SACK, and TCP-Reno”, Technical report, May 2003.

  24. Related work Fixed-point methods – square root of p-law for TCP and multiple bottlenecks • Gibbens et al. ”Fixed-point models for the end-to-end performance analysis of IP networks”, 13th ITC Special Seminar, Sep 2000. • Bu and Towsley ”Fixed point approximations for TCP behavior in an AQM network”, Sigmetrics, June2001. • Firoiu, Yeom, Zhang, ”A framework for practical performance evaluation and traffic engineering in IP networks”, IEEE ICT, June 2001.

  25. Contributions A step forward in the modeling of TCP-Vegas • Predicts operating point for Vegas in bottleneck network (Most previous work on Vegas have considered single sources) • Allows modeling loss, and Vegas delay sensitive slow-start & congestion avoidance phases. (Few previous analyses have allowed loss) • On/Off traffic (Previous models have focused on bulk transfer) Showed the extensibility of the framework • Added two new TCP flavors: Vegas and SACK, and extended Reno • Showed the plug and play of both network and source models by analyzing M/M/1/B, M/D/1/B and Mr/M/1/B queuing models

  26. Extensions The Source Model is extensible • Other application models (arbitrary On/Off time distributions and arbitrary file sizes) • Other flavors of TCP (modify Markov Chain) The Network Model is extensible • Wireless, DiffServ,… • Multiple-bottleneck networks • Multiple types of heterogeneous TCP sources

  27. Questions?

  28. Backup slides

  29. Vegas delay estimation Estimated throughput Number of back-logged packets Approximate by Queuing delay Every source tries to keep a≤Nb ≤ b packets backlogged in the network

  30. Network performance metrics M/M/1/B queuing model:

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