1. EE384Y: Packet Switch Architectures
Part II
Sizing Router Buffers
(Recent work by Guido Appenzeller)
Nick McKeown
Professor of Electrical Engineering
and Computer Science, Stanford University

2. How much Buffer does a Router need?
Universally applied rule-of-thumb:
A router needs a buffer size:
2T is the round-trip propagation time (or just 250ms)
C is the capacity of the outgoing link
Background
Mandated in backbone and edge routers.
Appears in RFPs and IETF architectural guidelines.
Has major consequences for router design.
Comes from dynamics of TCP congestion control.
Villamizar and Song: “High Performance TCP in ANSNET”, CCR, 1994.
Based on 2 to 16 TCP flows at speeds of up to 40 Mb/s.

3. Example 10Gb/s linecard or router Memory technologies
Requires 300Mbytes of buffering.
Read and write new packet every 32ns.
Memory technologies
SRAM: require 80 devices, 1kW, $2000.
DRAM: require 4 devices, but too slow.
Problem gets harder at 40Gb/s
Hence RLDRAM, FCRAM, etc.

4. TCP TCP adapts to congestion
Sender sends packets, receiver sends ACKs
Sending rate is controlled by Window W
At any time, only W unacknowledged packets may be outstanding
W is adjusted for each packet (in CA mode):
If ACK received: W = W+1/W (W=W+1 for each W packets)
If packet is lost: W = W/2 (W halved in case of loss)
The sending rate of TCP is:

5. For every W ACKs received,
Single TCP Flow Router with large enough buffers for full link utilization t
Window size
Buffer size and RTT
For every W ACKs received,
send W+1 packets B
Source
Dest
C’ > C C

6. Over-buffered Link

7. Under-buffered Link

8. Buffer = Rule-of-thumb
Interval magnified
on next slide

9. Microscopic TCP Behavior When sender pauses, buffer drains
one RTT
Drop

10. Origin of rule-of-thumb
Before and after reducing window size, the sending rate of the TCP sender is the same
Inserting the rate equation we get
The RTT is part transmission delay T and part queuing delay B/C . We know that after reducing the window, the queueing delay is zero. 

11. Rule-of-thumb Rule-of-thumb makes sense for one flow
Typical backbone link has > 20,000 flows
Does the rule-of-thumb still hold?
Answer:
If flows are perfectly synchronized, then Yes.
If flows are desynchronized then No.

12. Buffer size is height of sawtootht

13. If flows are synchronizedt
Aggregate window has same dynamics
Therefore buffer occupancy has same dynamics
Rule-of-thumb still holds.

14. Two TCP Flows Two TCP flows can synchronize

15. If flows are not synchronized
Aggregate window has less variation
Therefore buffer occupancy has less variation
The more flows, the smaller the variation
Rule-of-thumb does not hold.

16. If flows are not synchronized
Probability
Distribution B
Buffer Size

17. Quantitative Model
Model congestion window of a flow as random variable
model as
where
For many de-synchronized flows
We assume congestions windows are independent
All congestion windows have the same probability distribution
Now central limit theorem gives us queue length distribution

18. Required buffer size
Simulation

19. Required buffer size
99.9%
99.5% 2×
98.0%

20. Small buffers help short flows Average flow completion times of 14 packet flows that share a congested bottleneck link with long-lived flows.

21. Experiments with backbone router GSR 12000, OC3 Line Card
TCP
Flows
Router Buffer
Link Utilization
Pkts
RAM
Model
Sim
Exp
100
0.5 x
1 x
2 x
3 x 64
129
258
387
1Mb
2Mb
4Mb
8Mb
96.9%
99.9%
100%
94.7%
99.3%
99.8%
94.9%
98.1%
99.7%
400 32
128
192
512kb
99.2%
99.5%
Thanks: Experiments conducted by Paul Barford and Joel Sommers, U of Wisconsin

22. What about Short Flows?
So far we assumed long flows in congestion avoidance mode.
What if traffic is mainly short flows in slow-start?
Answer: Behavior is different, but
In mixes of flows, long flows drive buffer requirements
Required buffer for short flows is independent of line speed and RTT (same for 1Mbit/s or 40 Gbit/s)

23. A single, short-lived TCP flow Flow length 62 packets, RTT ~140 ms32
Flow Completion Time (FCT) 16 8 4
fin ack received
syn 2
RTT

24. Modelling TCP Flows vs. independent bursts
Inter-Burst Arrival Time is greater than buffer size
Therefore, we assume bursts are independent.
Poisson arrivals of flows
Arrivals of length Lflow (the flow length in packets)
Poisson arrivals of bursts
Four different poisson arrival processes of lengths 2,4,...

25. The M/G/1 Model TCP traffic is modelled as an M/G/1 arrival process:
poisson arrivals of jobs
with an arrival rate of
Average queue length in jobs is:
This gives us an average queue length in packets of
Let's see if this works in practice...

26. Average Queue length

27. Queue Distribution
To determine the required buffer, we need the queue distribution.
Or at least the tail end of the queue distribution
Buffer B Q
Packet Loss
P(Q = x)
For M/G/1 queues there is no general solution for the queue distribution.
We did two things (details are in the paper):
Use M/G/1 processor sharing model (bad)
Use Frank Kelly's effective bandwidth (good)

28. In Summary Buffer size is dictated by long TCP flows.
10Gb/s linecard with 200,000 x 56kb/s flows
Rule-of-thumb: Buffer = 2.5Gbits
Requires external, slow DRAM
Becomes: Buffer = 6Mbits
Can use on-chip, fast SRAM
Completion time halved for short-flows
40Gb/s linecard with 40,000 x 1Mb/s flows
Rule-of-thumb: Buffer = 10Gbits
Becomes: Buffer = 50Mbits