1. Amogh Dhamdhere, Hao Jiang and Constantinos Dovrolis
Buffer Sizing for Congested Internet Links
Amogh Dhamdhere, Hao Jiang and Constantinos Dovrolis
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
11/19/2018
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 ?
11/19/2018
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
11/19/2018
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
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

6. Outline Objectives and traffic model Motivation and related work
The utilization constraint alone
Utilization and loss rate constraints
Parameter estimation and simulation results
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

7. Our Objectives Full utilization: Maximum loss rate:
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 minimum amount of buffering possible
All of these objectives may not be feasible !
11/19/2018
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
11/19/2018
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
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

10. Outline The utilization constraint alone Motivation and related work
Objectives and traffic model
The utilization constraint alone
Utilization and loss rate constraints
Parameter estimation and simulation results
11/19/2018
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
11/19/2018
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
11/19/2018
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
11/19/2018
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 linearly with i.e.
A simple probabilistic argument gives us,
Partial loss synchronization reduces the buffer requirement.
11/19/2018
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 !
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

16. Outline Utilization and loss rate constraint
Motivation and related work
Objectives and traffic model
The utilization constraint alone
Utilization and loss rate constraint
Parameter estimation and simulation results
11/19/2018
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%
11/19/2018
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
11/19/2018
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
11/19/2018
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 all flows active at the link
Increasing RTTs may violate delay constraint
In that case, choose the minimum buffer that can satisfy utilization and loss constraints
11/19/2018
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
11/19/2018
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
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

23. Outline Parameter estimation and simulation results
Motivation and related work
Objectives and traffic model
The utilization constraint alone
Utilization and loss rate constraints
Parameter estimation and simulation results
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

24. Parameter Estimation Flow Classification: Number of LBP flows:
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
11/19/2018
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.
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

26. Results – Loss Rate
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

27. Results – Loss Rate
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

28. Results – Loss Rate
11/19/2018
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.
11/19/2018
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.
11/19/2018
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.
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005

32. Thank You !
11/19/2018
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).
11/19/2018
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.
11/19/2018
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.
11/19/2018
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
11/19/2018
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.
11/19/2018
Amogh Dhamdhere
IEEE Infocom 2005