Open Issues in Buffer Sizing

1
Open Issues in Buffer Sizing

• Amogh Dhamdhere
• Constantine Dovrolis
• College of Computing
• Georgia Tech

2
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Buffer sizing for bounded loss rate (Infocom05)

3
Motivation

• Router buffers are crucial elements of packet
  networks
• Absorb rate variations of incoming traffic
• Prevent packet losses during traffic bursts
• Increasing the router buffer size
• Can increase link utilization (especially with
  TCP traffic)
• Can decrease packet loss rate
• Can also increase queuing delays

4
Common operational practices

• Major router vendor recommends 500ms of buffering
• Implication buffer size increases proportionally
  to link capacity
• Why 500ms?
• Bandwidth Delay Product (BDP) rule
• Buffer size B link capacity C x typical RTT T
  (B CxT)
• What does typical RTT mean?
• Measurement studies showed that RTTs vary from
  1ms to 10sec!
• How do different types of flows (TCP elephants vs
  mice) affect buffer requirement?
• Poor performance is often due to buffer size
• Under-buffered switches high loss rate and poor
  utilization
• Over-buffered DSL modems excessive queuing delay
  for interactive apps

5
Previous work

• Approaches based on queuing theory (e.g. MM1B)
• Assume a certain input traffic model, service
  model and buffer size
• Loss probability for MM1B system is given by
• TCP is not open-loop TCP flows react to
  congestion
• There is no universally accepted Internet traffic
  model
• Morris Flow Proportional Queuing (Infocom 00)
• Proposed a buffer size proportional to the number
  of active TCP flows (B 6N)
• Did not specify which flows to count in N
• Objective limit loss rate
• High loss rate causes unfairness and poor
  application performance

6
TCP window dynamics for long flows

• TCP-aware buffer sizing must take into account
  TCP dynamics
• Saw-tooth behavior
• Window increases until packet loss
• Single loss results in cwnd reduction by factor
  of two
• Square-root TCP model
• TCP throughput can be
• approximated by
• Valid when loss rate p is
• small (less than 2-5)
• Average window size is
• independent of RTT

Loss Rate
RTT
7
Origin of BDP rule

• Consider a single flow with RTT T
• Window follows TCPs saw-tooth behavior
• Maximum window size CT B
• At this point packet loss occurs
• Window size after packet loss (CT B)/2
• Key step Even when window size is minimum, link
  should be fully utilized
• (CT B)/2 CT which means B CT
• Known as the bandwidth delay product rule
• Same result for N homogeneous TCP connections

8
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Buffer sizing for bounded loss rate (BSCL)

9
Stanford Model - Appenzeller et al.

• Objective Find the minimum buffer size to
  achieve full utilization of target link
• Assumption Most traffic is from TCP flows
• If N is large, flows are independent and
  unsynchronized
• Aggregate window size distribution tends to
  normal
• Queue size distribution also tends to normal
• Flows in congestion avoidance (linear increase of
  window between successive packet drops)
• Buffer for full utilization is given by
• N is the number of long flows at the link
• CT Bandwidth delay product

10
Stanford Model (cont)

• If link has only short flows, buffer size depends
  only on offered load and average flow size
• Flow size determines the size of bursts during
  slow start
• For a mix of short and long flows, buffer size is
  determined by number of long flows
• Small flows do not have a significant impact on
  buffer sizing
• Resulting buffer can achieve full utilization of
  target link
• Loss rate at target link is not taken into
  account

11
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Buffer sizing for bounded loss rate (BSCL)

12
What are the objectives ?

• Network layer vs. application layer objectives
• Networks perspective Utilization, loss rate,
  queuing delay
• Users perspective Per-flow throughput, fairness
  etc.
• Stanford Model Focus on utilization queueing
  delay
• Can lead to high loss rate (gt 10 in some cases)
• BSCL Both utilization and loss rate
• Can lead to large queuing delay
• Buffer sizing scheme that bounds queuing delay
• Can lead to high loss rate and low utilization
• A certain buffer size cannot meet all objectives
• Which problem should we try to solve?

13
Saturable/congestible links

• A link is saturable when offered load is
  sufficient to fully utilize it, given large
  enough buffer
• A link may not be saturable at all times
• Some links may never be saturable
• Advertised-window limitation, other bottlenecks,
  size-limited
• Small buffers are sufficient for non-saturable
  links
• Only needed to absorb short term traffic bursts
• Stanford model applicable when N is large
• Backbone links are usually not saturable due to
  over-provisioning
• Edge links are more likely to be saturable
• But N may not be large for such links

14
Which flows to count ?

• N Number of long flows at the link
• Long flows show TCPs saw-tooth behavior
• Short flows do not exit slow start
• Does size matter?
• Size does not indicate slow start or congestion
  avoidance behavior
• If no congestion, even large flows do not exit
  slow start
• If highly congested, small flows can enter
  congestion avoidance
• Should the following flows be included in N ?
• Flows limited by congestion at other links
• Flows limited by sender/receiver socket buffer
  size
• N varies with time. Which value should we use ?
• Min ? Max ? Time average ?

15
Which traffic model to use ?

• Traffic model has major implications on buffer
  sizing
• Early work considered traffic as exogenous
  process
• Not realistic. The offered load due to TCP flows
  depends on network conditions
• Stanford model considers mostly persistent
  connections
• No ambiguity about number of long flows (N)
• N is time-invariant
• In practice, TCP connections have finite size and
  duration, and N varies with time
• Open-loop vs closed-loop flow arrivals

16
Traffic model (cont)

• Open-loop TCP traffic
• Flows arrive randomly with average size S,
  average rate l
• Offered load lS, link capacity C
• Offered load is independent of system state
  (delay, loss)
• The system is unstable if lS gt C
• Closed-loop TCP traffic
• Each user starts a new transfer only after the
  completion of previous transfer
• Random think time between consecutive transfers
• Offered load depends on system state
• The system can never be unstable

17
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Buffer sizing for bounded loss rate (BSCL)

18
Why worry about loss rate?

• The Stanford model gives very small buffer if N
  is large
• E.g., CT200 packets, N400 flows B10 packets
• What is the loss rate with such a small buffer
  size?
• Per-flow throughput and transfer latency?
• Compare with BDP-based buffer sizing
• Distinguish between large and small flows
• Small flows that do not see losses limited only
  by RTT
• Flow size k segments
• Large flows depend on both losses RTT

19
Simulation setup

• Use ns-2 simulations to study the effect of
  buffer size on loss rate for different traffic
  models
• Heterogeneous RTTs (20ms to 530ms)
• TCP NewReno with SACK option
• BDP 250 packets (1500 B)
• Model-1 persistent flows mice
• 200 infinite connections active for whole
  simulation duration
• mice flows - 5 of capacity, size between 3 and
  25 packets, exponential inter-arrivals

20
Simulation setup (cont)

• Flow size distribution for finite size flows
• Sum of 3 exponential distributions Small files
  (avg. 15 packets), medium files (avg. 50 packets)
  and large files (avg. 200 packets)
• 70 of total bytes come from the largest 30 of
  flows
• Model-2 Closed-loop traffic
• 675 source agents
• Think time exponentially distributed with average
  5 s
• Time average of 200 flows in congestion avoidance
• Model-3 Open-loop traffic
• Exponentially distributed flow inter-arrival
  times
• Offered load is 95 of link capacity
• Time average of 200 flows in congestion avoidance

21
Simulation results Loss rate

• CT250 packets, N200 for all traffic types
• Stanford model gives a buffer of 18 packets
• High loss rate with Stanford buffer
• Greater than 10 for open loop traffic
• 7-8 for persistent and closed loop traffic
• Increasing buffer to BDP or small multiple of BDP
  can significantly decrease loss rate

Stanford buffer
22
Per-flow throughput

• Transfer latency flow-size / flow-throughput
• Flow throughput depends on both loss rate and
  queuing delay
• Loss rate decreases with buffer size (good)
• Queuing delay increases with buffer size (bad)
• Major tradeoff Should we have low loss rate or
  low queuing delay ?
• Answer depends on various factors
• Which flows are considered Long or short ?
• Which traffic model is considered?

23
Persistent connections and mice

• Application layer throughput for B18 (Stanford
  buffer) and larger buffer B500
• Two flow categories Large (gt100KB) and small
  (lt100KB)
• Majority of large flows get better throughput
  with large buffer
• Large difference in loss rates
• Smaller variability of per-flow throughput with
  larger buffer
• Majority of short flows get better throughput
  with small buffer
• Lower RTT and smaller difference in loss rates

24
Closed-loop traffic

• Per-flow throughput for large flows is slightly
  better with larger buffer
• Majority of small flows see better throughput
  with smaller buffer
• Similar to persistent case
• Not a significant difference in per-flow loss
  rate
• Reason Loss rate decreases slowly with buffer
  size

25
Open-loop traffic

• Both large and small flows get much better
  throughput with large buffer
• Significantly smaller per-flow loss rate with
  larger buffer
• Reason Loss rate decreases very quickly with
  buffer size

26
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Buffer sizing for bounded loss rate (BSCL)

27
Our buffer sizing objectives

• Full utilization
• The average utilization of the target link
  should be at least when
  the offered load is sufficiently high
• Bounded loss rate
• The loss rate p should not exceed , typically
  1-2 for a saturated link
• Minimum queuing delays and buffer requirement,
  given previous two objectives
• Large queuing delay causes higher transfer
  latencies and jitter
• Large buffer size increases router cost and power
  consumption
• So, we aim to determine the minimum buffer size
  that meets the given utilization and loss rate
  constraints

28
Why limit the loss rate?

• End-user perceived performance is very poor when
  loss rate is more than 5-10
• Particularly true for short and interactive flows
• High loss rate is also detrimental for large TCP
  flows
• High variability in per-flow throughput
• Some unlucky flows suffer repeated losses and
  timeouts
• We aim to bound the packet loss rate to 1-2

29
Traffic classes

• Locally Bottlenecked Persistent (LBP) TCP flows
• Large TCP flows limited by losses at target link
• Loss rate p is equal to loss rate at target link
• Remotely Bottlenecked Persistent (RBP) TCP flows
• Large TCP flows limited by losses at other links
• Loss rate is greater than loss rate at target
  link
• Window Limited Persistent TCP flows
• Large TCP flows limited by advertised window,
  instead of congestion window
• Short TCP flows and non-TCP traffic

30
Scope of our model

• Key assumption
• LBP flows account for most of the traffic at the
  target link (80-90 )
• Reason we ignore buffer requirement of non-LBP
  traffic
• Scope of our model
• Congested links that mostly carry large TCP
  flows, bottlenecked at target link

31
Minimum buffer requirement for full utilization
homogenous flows

• Consider a single LBP flow with RTT T
• Window follows TCPs saw-tooth behavior
• Maximum window size CT B
• At this point packet loss occurs
• Window size after packet loss (CT B)/2
• Key step Even when window size is minimum, link
  should be fully utilized
• (CT B)/2 gt CT which means B gt CT
• Known as the bandwidth delay product rule
• Same result for N homogeneous TCP connections

32
Minimum buffer requirement for full utilization
heterogeneous flows

• Nb heterogeneous LBP flows with RTTs Ti
• Initially, assume Global Loss Synchronization
• All flows decrease windows simultaneously in
  response to single congestion event
• We derive that
• As a bandwidth-delay product
• Te effective RTT is the harmonic mean of RTTs
• Practical Implication
• Few connections with very large RTTs cannot
  significantly increase buffer requirement, as
  long as most flows have small RTTs

33
Minimum buffer requirement for full utilization
(cont)

• More realistic model partial loss
  synchronization
• Loss burst length L(Nb) number of packets lost
  by Nb flows during single congestion event
• Assumption loss burst length increases almost
  linearly with Nb, i.e., L(Nb) a Nb
• a synchronization factor (around 0.5-0.6 in our
  simulations)
• Minimum buffer size requirement
• Fraction of flows that see losses in
  a congestion event
• M Average segment size
• Partial loss synchronization reduces buffer
  requirement

34
Validation (ns2 simulations)

• Heterogeneous flows (RTTs vary between 20ms
  530ms)
• Partial synchronization model accurate
• Global synchronization (deterministic) model
  overestimates buffer requirement by factor 3-5

35
Relation between loss rate and N

• Nb homogeneous LBP flows at target link
• Link capacity C, flows RTT T
• If flows saturate target link, then flow
  throughput is given by
• Loss rate is proportional to square of Nb
• Hence, to keep loss rate less than we must
  limit number of flows
• But this would require admission control (not
  deployed)

36
Flow Proportional Queuing (FPQ)

• First proposed by Morris (Infocom00)
• Bound loss rate by
• Increasing RTT proportionally to number of flows
• Solving for T gives
• Where and Tp RTTs propagation delay
• Set Tq ? C/B, and solve for B
• Window of each flow should be Kp packets,
  consisting of
• Packets in target link buffer (B term)
• Packets on the wire (CTp term)
• Practically, Kp6 packets for 2 loss rate, and
  Kp9 packets for 1 loss rate
  

37
Buffer size requirement for both full utilization
and bounded loss rate

• We previously showed separate results for full
  utilization and bounded loss rate
• To meet both goals, provide enough buffers to
  satisfy most stringent of two requirements
• Buffer requirement
• Decreases with Nb (full utilization objective)
• Increases with Nb (loss rate objective)
• Crossover point
• Previous result is referred to as the BSCL formula

38
Model validation

• Heterogeneous flows
• Utilization and loss constraint
  

Utilization constraint
Loss rate constraint
39
Parameter estimation

• Number of LBP flows
• With LBP flows, all rate reductions occur due to
  packet losses at target link
• RBP flows some rate reductions due to losses
  elsewhere
• Effective RTT
• Jiang et al. (2002) simple algorithms to measure
  TCP RTT from packet traces
• Loss burst lengths or loss synchronization
  factor
• Measure loss burst lengths from packet loss trace
  or use approximation L(Nb) a Nb

40
Results Bound loss rate to 1
41
Results Bound loss rate to 1
42
Per-flow throughput with BSCL

• BSCL can achieve network layer objectives of full
  utilization and bounded loss rate
• Can lead to large queuing delay due to larger
  buffer
• How does this affect application throughput ?
• BSCL loss rate target set to 1
• BSCL buffer size is 1550 packets
• Compare with the buffer of 500 packets
• BSCL is able to bound the loss rate to 1 target
  for all traffic models

43
Persistent connections and mice

• BSCL buffer gives better throughput for large
  flows
• Also reduces variability of per-flow throughputs
• Loss rate decrease favors large flows in spite of
  larger queuing delay
• All smaller flows get worse throughput with the
  BSCL buffer
• Increase in queuing delay harms small flows

44
Closed-loop traffic

• Similar to persistent traffic case
• BSCL buffer improves throughput for large flows
• Also reduces variability of per-flow throughputs
• Loss rate decrease favors large flows in spite of
  larger queuing delay
• All smaller flows get worse throughput with the
  BSCL buffer
• Increase in queuing delay harms small flows

45
Open-loop traffic

• No significant difference between B500 and
  B1550
• Reason Loss rate for open loop traffic decrease
  quickly
• Loss rate for B500 is already less than 1
• Further increase in buffer reduces loss rate to
  0
• Large buffer does not increase queuing delays
  significantly

46
Summary

• We derived a buffer sizing formula (BSCL) for
  congested links that mostly carry TCP traffic
• Objectives
• Full utilization
• Bounded loss rate
• Minimum queuing delay, given previous two
  objectives
• BSCL formula is applicable for links with more
  than 80-90 of traffic coming from large and
  locally bottlenecked TCP flows
• BSCL accounts for the effects of heterogeneous
  RTTs and partial loss synchronization
• Validated BSCL through simulations