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Modeling TCP in Small-Buffer Networks

Modeling TCP in Small-Buffer Networks. Mark Shifrin and Isaac Keslassy. Technion (Israel). Problem. How much buffering do routers need?. Why Does Buffer Size Matter?. Buffers are costly. Today’s buffers: 1/2 board space 1/3 power consumption Small buffers: On chip buffers

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Modeling TCP in Small-Buffer Networks

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  1. Modeling TCP in Small-Buffer Networks Mark Shifrin and Isaac Keslassy Technion (Israel)

  2. Problem How much buffering do routers need?

  3. Why Does Buffer Size Matter? • Buffers are costly. • Today’s buffers: • 1/2 board space • 1/3 power consumption • Small buffers: • On chip buffers • Higher density • Lower cost • Scalability [N. McKeown, Stanford]

  4. How much Buffer does a Router need? • Universally applied rule-of-thumb: • A router needs a buffer size: • 2Tis the round-trip propagation time (or just 250ms) • C is the capacity of the outgoing link • Background • Mandated in backbone and edge routers. • Appears in RFPs and IETF architectural guidelines. • Has major consequences for router design. • Comes from dynamics of TCP congestion control. • Villamizar and Song: “High Performance TCP in ANSNET”, CCR, 1994. • Based on 2 to 16 TCP flows at speeds of up to 40 Mb/s.

  5. Synchronized Flows • Aggregate window has same dynamics • Therefore buffer occupancy has same dynamics • Rule-of-thumb still holds. t

  6. Many TCP Flows Probability Distribution Buffer Size B 0

  7. Stanford Model [Appenzeller et al., ’04 | McKeown and Wischik, ’05 | McKeown et al., ‘06] • Assumption 1: TCP Flows modeled as i.i.d.  total window W has Gaussian distribution • Assumption 2: Queue is the only variable part queue has Gaussian distribution: Q=W-CONST usesmaller bufferthan in rule of thumb

  8. Impact on Router Design • 40Gb/s linecard with 1,000,000 flows • Rule of thumb: Buffer = 10Gbits • Requires external, slow DRAM • Stanford model: Buffer = 10Mbits • Can use on-chip, fast SRAM • Delays halved for short-flows

  9. Motivation In a small-buffer world… • Assumption 1: TCP Flows modeled as i.i.d.  total window W has Gaussian distribution • Assumption 2: Queue is the only variable part queue has Gaussian distribution: Q=W-CONST OK Queue is small  negligible? Gaussian part is… on the lines!

  10. Contributions • Distribution models for: • Lines • Arrival rates to queues • Queue sizes • Packet loss rates • General closed-loop model for small-buffer networks • Result: queues are not the only variable part in the network

  11. Model Development Flow li1 pdf total arrival rate Q pdf packet loss l1i arrival rates cwnd

  12. Model of li1 li1 pdf packet loss cwnd

  13. Bursty Model of Window Distribution B dest. source li5 li3 li1 li4 li6 li2 rtti=tp1i+tp2i+tp3i+tp4i+tp5i+tp6i • Common Approach 1: Uniform packet distribution. l1(t)i = wi(t)* tpi1/rtti. • Approach 2: Bursty Packet Distribution

  14. Bursty Model of Window Distribution • Assumption: All packets in a flow move in a single burst • Conclusion 1: All packets belonging to an arbitrary flow i are present almost always on the same link. • Conclusion 2: The probability of burst of flow ibeing present on the certain link is equal to the ratio of its propagation latency to the total rtti.

  15. Simulation Results

  16. Model Development Flow li1 pdf total arrival rate l1i arrival rates cwnd

  17. Rate Transmission Derivation The objective is to find the pdf of the number of packets sent on some link i, ri, in a time unit δt. Assumptions: The rate on each one of the links in L1 is statistically independent We assume that the transmissions are bursty. We assume that the rate is proportional to the distribution of l1i and to the ratio δt/tp1i.

  18. Arrival rate of a single flow B δt source li2 li1 li1*δt/tp1i tp1i We find the arrival distribution for every flow in δt msec.

  19. Total Rate • Result: • Proof based on the Lindeberg condition. • Generalizes Central Limit Theorem for non-identically distributed components • Holds if the share of each flow comparatively to the sum is negligible as the number of the flows grows. • Argument for the proof: cwnd is limited by maximum value  same for l1i andri.

  20. Instantaneous Rate Model - Results Probability Total arrival rate – number of packets per δt

  21. Model Development Flow li1 pdf total arrival rate Q pdf packet loss l1i arrival rates cwnd

  22. PDF for Q • To find the queue size distribution: • Run Markov Chain simulation (compared with [Tran-Gia and Ahmadi, ‘88]) • Use samples of R for the transitions • Packet lossp is derived from the queue size distribution.

  23. PDF of Q Probability Q state – 0 to 585 packets

  24. Fixed Point Solution: p=f(p) li1 pdf total arrival rate Q pdf packet loss l1i arrival rates cwnd

  25. Packet loss - results • Model gives about 10%-25% of discrepancy. • Case 1: Measured: p=2.7%, Model: p=3% • Case 2: Measured: p=0.8%, Model: p=0.98% • Case 3: Measured: p=1.4%, Model: p=1.82% • Case 4: Measured: p=0.452%, Model: p=0.56%

  26. The Gaussian distributions L4 L2 L5 L6 L1 W NS2 simulation of 500 flows with different propagation times

  27. Are these lines really Gaussian?

  28. Summary • Introduced general closed-loop model for small-buffer networks • Proved wrong the usual assumption that queues are the only variable part in the network

  29. Thank you.

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