Buffer Sizing for Congested Internet Links Amogh Dhamdhere, Hao Jiang and Constantinos Dovrolis

1. Buffer Sizing for Congested Internet Links Amogh Dhamdhere, Hao Jiang and Constantinos Dovrolis (amogh,hjiang,dovrolis)@cc.gatech.edu Networking and Telecommunications Group, College of Computing, Georgia Tech.

2. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraints • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

3. Motivation • Router buffers are important in packet networks • Absorb rate variations of incoming traffic • Prevent packet losses during traffic bursts • Increasing buffer space increases the utilization of the link and decreases the loss rate • Increasing buffer also increases queuing delays ! • So smaller buffers are desirable • Fundamental Question: What is the minimum buffer requirement to satisfy constraints on the utilization, loss rate and queuing delay ? Amogh Dhamdhere IEEE Infocom 2005

4. Rules of Thumb • Some router vendors suggest 500ms of buffering. • Why 500ms ? • Bandwidth Delay Product rule: Capacity of link times the “typical” RTT (B = CT) • Which RTT should we use ? • Many TCP flows with different RTTs ? • How do different types of flows (large vs small) affect the buffer requirement ? • Several variants of this rule • e.g. Capacity times link delay Amogh Dhamdhere IEEE Infocom 2005

5. Related Work • Approaches based on queuing models e.g. M/M/1/k • TCP is not open-loop. TCP flows are reactive • Modeling Internet traffic is difficult • “Stanford” model (Appenzeller et al. Sigcomm 2004) • Buffer requirement for full utilization decreases with square root of N • Did not consider the loss rate at the link • Assumed that flows are completely desynchronized • Applicable when the number of flows is large • Morris (1997 and 2000) • Buffer proportional to the number of flows (B = 6*N) • Considered all flows active at the link Amogh Dhamdhere IEEE Infocom 2005

6. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraints • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

7. Our Objectives • Full utilization: • The average utilization of the link should be at least % when the offered load is sufficiently high • Maximum loss rate: • The loss rate p should not exceed , typically 1-2% for a saturated link • Minimum queuing delays: • High queuing delay causes higher transfer latencies and jitter • Also increases cost and power consumption • Should satisfy utilization and loss rate constraints with minimumamount of buffering possible • All of these objectives may not be feasible ! Amogh Dhamdhere IEEE Infocom 2005

8. Traffic Classes • Locally Bottlenecked Persistent (LBP) TCP flows • Large TCP flows limited by losses at the target link • Loss rate p is equal to the loss rate at the target link • Remotely Bottlenecked Persistent (RBP) TCP flows • Large TCP flows limited by losses at target link and other links • Loss rate is greater than loss rate at target link • Window Limited Persistent TCP flows • Large TCP flows, throughput limited by the advertised window • Short TCP flows and non-TCP traffic Amogh Dhamdhere IEEE Infocom 2005

9. Assumption • Key Assumption: LBP flows account for most of the traffic at the target link (80-90 %) • In this case, we can ignore the buffering requirement of non-LBP flows • non-LBP flows also contribute to the utilization and loss rate at the target link • Contribution is small if fraction of non-LBP traffic is small • Our model is applicable in links where this assumption holds • Edge links and links in access networks are candidates Amogh Dhamdhere IEEE Infocom 2005

10. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraints • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

11. TCP Window Dynamics • Saw-tooth behavior of TCP • Padhye (1998) • TCP throughput can be approximated by • Average window size is independent of RTT • Valid when loss rate is small Amogh Dhamdhere IEEE Infocom 2005

12. Util. Constraint - Multiple TCP Flows • heterogeneous LBP flows with RTTs • Consider initially the worst-case scenario: Global Loss Synchronization. • All flows decrease windows simultaneously in response to losses. • We derive that • As a bandwidth-delay product • Where is the harmonic mean of the RTTs Amogh Dhamdhere IEEE Infocom 2005

13. Util. Constraint - Multiple TCP Flows • is called the effective RTT of the flows • Influenced more by smaller values • Intuition: • Flows with smaller RTTs have larger portion of their window in the bottleneck buffer • Hence have larger influence on the required buffer • Flows with large RTTs have larger portion of their window “on the wire” • Practical Implication: • A few connections with very large RTTs cannot significantly influence the buffer requirement, as long as most flows have small RTTs Amogh Dhamdhere IEEE Infocom 2005

14. Partial Synchronization Model • In practice, flows are not completely synchronized • Loss Burst Length: Number of packets lost by flows during a congestion event • Empirical observation: Loss burst length increases almost linearlywith i.e. • A simple probabilistic argument gives us, • Partial loss synchronization reduces the buffer requirement. Amogh Dhamdhere IEEE Infocom 2005

15. Validation • ns2 simulations. • Heterogeneous flows, % • Partial synchronization model accurately predicts the buffer requirement. • Deterministic model overestimates the buffer requirement ! Amogh Dhamdhere IEEE Infocom 2005

16. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraint • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

17. Utilization and Loss Rate • End-user perceived service is poor when the loss rate is more than 5-10% • Particularly for short and interactive flows • Results by Morris (1997) • High variability in the completion times of short transfers • Some “unlucky” flows suffer repeated losses and timeouts • The buffer size controls the loss rate • Upper bound the loss rate to . Assume is 1% Amogh Dhamdhere IEEE Infocom 2005

18. Relation between loss rate and N • homogeneous LBP flows at the target link. Link capacity C, flow RTTs T • Assume that the flows saturate the link and their throughput is given by • p is proportional to the square of • Hence to maintain loss rate at less than • But this requires admission control • Such schemes not deployed yet Amogh Dhamdhere IEEE Infocom 2005

19. Flow Proportional Queueing • First proposed by Morris (2000) • Don’t limit • Increase RTTs to decrease loss rate • Increase RTT by increasing buffer, which increases queuing delay • Solving for B gives • Where • Practically, packets for , and packets for Amogh Dhamdhere IEEE Infocom 2005

20. Flow Proportional Queueing (contd.) • Intuition: • packets per flow, either in buffer (B term) or “on the wire” ( term) • Differences with Morris’ FPQ scheme • Morris did not take into account the term • Set arbitrarily to 6 packets • Applied the rule for allflows active at the link • Increasing RTTs may violate delay constraint • In that case, choose the minimum buffer that can satisfy utilization and loss constraints Amogh Dhamdhere IEEE Infocom 2005

21. Integrated Model • Separate results for utilization and loss rate constraints • Satisfy the most stringent of the two requirements • B for utilization decreases with , while B for loss rate increases with • : Crossover point • Called the BSCL formula Amogh Dhamdhere IEEE Infocom 2005

22. Integrated Model - Validation • Simulations using ns2. • Heterogeneous flows, varied from 1 to 200. • Utilization % and loss constraint % Utilization constraint Loss rate constraint Amogh Dhamdhere IEEE Infocom 2005

23. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraints • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

24. Parameter Estimation • Flow Classification: • Zhang et al. (2002): Classify TCP flows based on rate limiting factors • Number of LBP flows: • LBP flows: all rate reductions due to packet losses at target link • RBP flows: Some rate reductions due to losses elsewhere • Effective RTT: • Jiang et al. (2002): Passive algorithm to measure TCP Round Trip Times from packet traces • Loss Synchronization: • Measure loss burst length from trace or use approximation Amogh Dhamdhere IEEE Infocom 2005

25. Evaluation - Setup • ns2 simulations. • Multi-level tree topology with wide range of RTTs (20ms to 550ms). • Target link capacity 50Mbps. • varied from 1 to 400. • 20 RBP flows, 10 window limited flows. • Mice flows with average size 14 packets, exponential inter-arrivals. • Non-LBP traffic (R) is varied between 5% and 20% of C. Amogh Dhamdhere IEEE Infocom 2005

26. Results – Loss Rate Amogh Dhamdhere IEEE Infocom 2005

27. Results – Loss Rate Amogh Dhamdhere IEEE Infocom 2005

28. Results – Loss Rate Amogh Dhamdhere IEEE Infocom 2005

29. Results – Loss Rate • BSCL can bound loss rate close to the target, if R is less than 10%. • Accuracy decreases as fraction of non-LBP traffic increases. • Stanford model and the rule of thumb cannot bound loss rate. Amogh Dhamdhere IEEE Infocom 2005

30. Results - Utilization • For a large number of flows, all three schemes achieve full utilization. • For smaller number of flows, BSCL sometimes leads to underutilization. • Due to the probabilistic nature of loss synchronization. Amogh Dhamdhere IEEE Infocom 2005

31. Summary • Derived a buffer sizing formula (BSCL) for congested links, taking into account both utilization and loss rate of the target link. • Applicable for links in which 80-90% of the traffic comes from large locally bottlenecked TCP flows. • Account for the effects of heterogeneous RTTs and partial loss synchronization. • Validated the results through simulations. Amogh Dhamdhere IEEE Infocom 2005

32. Thank You ! Amogh Dhamdhere IEEE Infocom 2005

33. Parameter estimation - • Distinguishing between LBP and RBP flows: • Intuition: For a LBP flow, rate reduction should be preceded by a loss at the target link. • For RBP flows, rate reduction will not always be accompanied by a loss at the target link (due to losses in other links). Amogh Dhamdhere IEEE Infocom 2005

34. Why is Buffer Size Important ? • Router buffer size affects: • Utilization of the link. • Loss rate of the link. • Fairness among TCP connections. • Results by Morris (1997): • A very small buffer can lead to underutilization. • Loss rate increases as the square of N. Amogh Dhamdhere IEEE Infocom 2005

35. Partial Synchronization Model (contd.) • Consider a congestion event with the average loss-burst length . • A simple probabilistic argument gives us, • Remarks: • For global loss synchronization, and the buffer requirement becomes B = CT. • Partial loss synchronization reduces the buffer requirement. • For heterogeneous connections, replace T with the effective RTT. Amogh Dhamdhere IEEE Infocom 2005

36. Outline • Motivation and related work • Objectives and traffic model • The utilization constraint alone • Utilization and loss rate constraints • Parameter estimation and simulation results Amogh Dhamdhere IEEE Infocom 2005

37. Results - Loss Rate • BSCL can bound loss rate close to the target, if R is less than 10%. • Accuracy decreases as fraction of non-LBP traffic increases. • Stanford model and the rule of thumb cannot bound loss rate. Amogh Dhamdhere IEEE Infocom 2005