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
9/20/2018
NTG Seminar

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 ?
9/20/2018
NTG Seminar

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 ?
9/20/2018
NTG Seminar

5. Previous work Approaches based on queuing theory (e.g. M|M|1|B)
Assume a certain input traffic model, service model and buffer size
Loss probability for M|M|1|B system is given by
p=ρB(1- ρ)/(1- ρB+1)
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 = 6*N)
Did not specify which flows to count in N
Objective: limit loss rate
High loss rate causes unfairness and poor application performance
9/20/2018
NTG Seminar

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 !
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

9. Stanford Model (cont’)
Buffer for full utilization is given by B = CT / √N
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
9/20/2018
NTG Seminar

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
Don’t want to sound like a broken record, but…
WHAT ABOUT THE LOSS RATE ?
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

12. What are the objectives ?
Network layer vs. application layer objectives
Network’s perspective: Utilization, loss rate, queuing delay
User’s perspective: Per-flow throughput, fairness etc.
Stanford Model: Focus on utilization & queueing delay
Can lead to high loss rate (> 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?
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

14. Which flows to count ? N: Number of “long” flows at the link
“Long” flows show TCP’s 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 ?
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

16. Traffic model (cont’) Open-loop TCP traffic: Closed-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 > 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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

18. Why worry about loss rate?
The Stanford model gives very small buffer if N is large
E.g., CT=200 packets, N=400 flows: B=10 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:
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

21. Simulation results – Loss rate
CT=250 packets, N=200 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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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?
9/20/2018
NTG Seminar

24. Persistent connections and mice
Application layer throughput for B=18 (Stanford buffer) and larger buffer B=500
Two flow categories: Large (>100KB) and small (<100KB)
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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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
9/20/2018
NTG Seminar

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 ?
9/20/2018
NTG Seminar

30. Thank You !
9/20/2018
NTG Seminar