Buffer Sizing for Congested Internet Links

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

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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraints
• Parameter estimation and simulation results

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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 ?

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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

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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
  6N)
• Considered all flows active at the link

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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraints
• Parameter estimation and simulation results

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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 minimum amount of buffering
  possible
• All of these objectives may not be feasible !

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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

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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

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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraints
• Parameter estimation and simulation results

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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

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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

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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

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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.

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Validation

• ns2 simulations.
• Heterogeneous flows,
• Partial synchronization model accurately predicts
  the buffer requirement.
• Deterministic model overestimates the buffer
  requirement !

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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraint
• Parameter estimation and simulation results

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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

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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

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Flow Proportional Queueing

• First proposed by Morris (2000)
• Dont 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
  

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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

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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

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Integrated Model - Validation

• Simulations using ns2.
• Heterogeneous flows, varied from 1 to 200.
• Utilization and loss constraint
  

Utilization constraint
Loss rate constraint
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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraints
• Parameter estimation and simulation results

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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

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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.

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Results Loss Rate
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Results Loss Rate
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Results Loss Rate
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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.

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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.

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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.

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• Thank You !

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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).

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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.

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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.

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Outline

• Motivation and related work
• Objectives and traffic model
• The utilization constraint alone
• Utilization and loss rate constraints
• Parameter estimation and simulation results

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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.