Open Issues in Router Buffer Sizing

1
Open Issues in Router 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
• Summary and future work

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
• So the million dollar question is
• How much buffer should a router have ?

4
Motivation (cont)

• Some recent results suggest that small buffers
  are sufficient to achieve full utilization
• The loss rate is not considered !
• Other results propose larger buffers to achieve
  full utilization and a bounded loss rate
• Why these contradictory results ?
• Different assumptions, applicability of these
  models ?
• Is there a single answer to the buffer sizing
  problem ?
• NO !
• Is that answer a very small buffer ?
• NO !

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
• p?B(1- ?)/(1-
  ?B1)
• 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
Previous work (cont)

• BSCL (Dhamdhere et al. Infocom 2005)
• Proposed a buffer sizing formula to achieve full
  utilization and a bounded loss rate
• Applicable to congested edge links
• Proposes a buffer proportional to the number of
  active large flows
• Can lead to a large queuing delay !

7
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Summary and future work

8
Stanford Model - Appenzeller et al.

• Objective Find the minimum buffer size to
  achieve full utilization of target link
• Assumptions
• Most traffic is from long TCP flows
• Long flows are in congestion avoidance for most
  of their lifetime (follow the TCP throughput
  equation)
• The number of flows is large enough that flows
  are independent and unsynchronized
• Aggregate window size distribution tends to
  normal
• Queue size distribution also tends to normal

9
Stanford Model (cont)

• Buffer for full utilization is given by B CT /
  vN
• N is the number of long flows at the link
• CT Bandwidth delay product
• 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

10
Stanford Model (cont)

• More recent results (Wischik, McKeown et al.
  05)
• Sacrifice some utilization to make buffers
  smaller
• Of the order of 20 packets
• If TCP sources are paced, even smaller buffers
  are sufficient
• O(log W) where W is the TCP window size
• Pacing makes the sources less bursty
• Pacing can occur automatically, due to slow
  access links and fast backbone links

Dont want to sound like a broken record, but
WHAT ABOUT THE LOSS RATE ?
11
Outline

• Motivation and previous work
• The Stanford model for buffer sizing
• Important issues in buffer sizing
• Simulation results for the Stanford model
• Summary and future work

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 (Infocom 05) 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 is targeted at backbone links
• 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
• Stanford model requires large N

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
• Summary and future work

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
Why the different loss rate trends ?

• Open loop traffic
• The offered load does not depend on the buffer
  size
• Possible to decrease loss rate to zero with
  sufficient buffer size
• Loss rate decreases quickly with buffer size
• Closed loop traffic
• Larger buffer leads to smaller loss rate, flows
  complete faster, and new flows arrive faster
• Loss rate decreases slowly with buffer size

23
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?

24
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

25
Why the difference between large and small flows ?

• Persistent flows Larger buffer is better
• Mice flows Smaller buffer is better
• Reason Different effect of packet loss
• Persistent flows
• Large congestion window halved due to packet loss
• Take longer to reach original window Decreased
  throughput
• Mice flows
• Congestion windows never become very large
• Quickly return to original window, especially
  with a smaller buffer
• For persistent flows, the tradeoff is in favor of
  low loss rate, while for mice it is in favor of
  low queuing delay

26
Variability of per-flow throughputs

• Large buffer reduce the variability of throughput
  for persistent flows
• Two reasons
• All RTTs increased by a constant (the queuing
  delay)
• Smaller loss rate decreases the chance of a flow
  getting unlucky and seeing repeated losses
• In our simulations, the RTT increase accounts for
  most of the variability reduction
• Why is variability important ?
• For N persistent connections, we have a zero-sum
  game
• If one flow gets high throughput, some other must
  be losing

27
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
• Smaller difference in per-flow loss rate
• Reason Loss rate decreases slowly with buffer
  size

28
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

29
Summary and Future Work

• The buffer size required at a router depends on
  multiple factors
• The provisioning objective
• The model which the input traffic follows
• The nature of flows that populate that link
  (large vs small)
• Very small buffers proposed in recent work can
  cause a large loss rate and harm application
  performance
• Most work so far has focused on network layer
  performance
• What is the optimal buffer when some application
  layer performance metric is considered ?

30
Thank You !
31
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

32
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
33
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