Transcript slides ppt

Buffer sizes for large multiplexers:
TCP queueing theory and
instability analysis
Gaurav Raina
Damon Wischik
Mark Handley
Cambridge
UCL
UCL
Sizing router buffers SIGCOMM 2004
Guido Appenzeller Isaac Keslassy
Stanford University
Stanford University
Nick McKeown
Stanford University
Abstract. All Internet routers contain buffers to hold packets during times of congestion. Today, the size of
the buffers is determined by the dynamics of TCP's congestion control algorithm. In particular, the goal is
to make sure that when a link is congested, it is busy 100% of the time; which is equivalent to making sure
its buffer never goes empty. A widely used rule-of-thumb states that each link needs a buffer of size B =
RTT*C, where RTT is the average round-trip time of a flow passing across the link, and C is the data rate
of the link. For example, a 10Gb/s router linecard needs approximately 250ms*10Gb/s = 2.5Gbits of
buffers; and the amount of buffering grows linearly with the line-rate. Such large buffers are challenging
for router manufacturers, who must use large, slow, off-chip DRAMs. And queueing delays can be long,
have high variance, and may destabilize the congestion control algorithms. In this paper we argue that the
rule-of-thumb (B = RTT*C) is now outdated and incorrect for backbone routers. This is because of the
large number of flows (TCP connections) multiplexed together on a single backbone link. Using theory,
simulation and experiments on a network of real routers, we show that a link with N flows requires no
more than B = (RTT*C)/N, for long-lived or short-lived TCP flows. The consequences on router design
are enormous: A 2.5Gb/s link carrying 10,000 flows could reduce its buffers by 99% with negligible
difference in throughput; and a 10Gb/s link carrying 50,000 flows requires only 10Mbits of buffering,
which can easily be implemented using fast, on-chip SRAM.
http://tiny-tera.stanford.edu/~nickm/papers/index.html
Queue simulations
Simulate a queue
• fed by N flows, each of rate x pkts/sec (x=0.95 then 1.05 pkts/sec)
• served at rate NC (C=1 pkt/sec)
• with buffer size N1/2B (B=3 pkts)
90
80
70
30
queue
size
arrival
rate x
20
20
10
10
60
60
50
50
40
40
30
30
20
20
10
10
1
1
1
1
0.5
0.5
0.5
0.5
20
40
60
N=50
80
20
40
60
N=100
80
20
40
60
N=500
80
20
40
60
N=1000
80
time
Fixed-Point Models for the End-to-End
Performance Analysis of IP Networks ITC 2000
RJ Gibbens, SK Sargood, C Van Eijl, FP Kelly,
H Azmoodeh, RN Macfadyen, NW Macfadyen
Statistical Laboratory, Cambridge; and BT, Adastral Park
Abstract. This paper presents a new approach to modeling end-to-end performance for IP
networks. Unlike earlier models, in which end stations generate traffic at a constant rate, the
work discussed here takes the adaptive behaviour of TCP/IP into account. The approach is
based on a fixed-point method which determines packet loss, link utilization and TCP
throughput across the network. Results are presented for an IP backbone network, which
highlight how this new model finds the natural operating point for TCP, which depends on
route lengths (via round-trip times and number of resources), end-to-end packet loss and the
number of user sessions.
http://www.statslab.cam.ac.uk/~frank/PAPERS/fpmee.html
Fixed-point analysis
traffic intensity x/C
0.5
1
1.5
2
-1
C*RTT=4 pkts
log10 of
pkt loss
probability
-2
-3
C*RTT=20 pkts
-4
C*RTT=100 pkts
Fluid-based Analysis of a Network of AQM Routers
Supporting TCP Flows with an Application to RED
SIGCOMM 2000
Vishal Misra
UMass Amherst
Wei-Bo Gong
UMass Amherst
Don Towsley
UMass Amherst
Abstract. In this paper we use jump process driven Stochastic Differential Equations to model the
interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show
how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved
numerically. Our solution methodology scales well to a large number of flows. As an application, we model
and solve a system where RED is the AQM policy. Our results show excellent agreement with those of
similar networks simulated using the well known ns simulator. Our model enables us to get an in-depth
understanding of the RED algorithm. Using the tools developed in this paper, we present a critical analysis
of the RED algorithm. We explain the role played by the RED configuration parameters on the behavior of
the algorithm in a network. We point out a flaw in the RED averaging mechanism which we believe is a
cause of tuning problems for RED. We believe this modeling/solution methodology has a great potential in
analyzing and understanding various network congestion control algorithms.
ftp://gaia.cs.umass.edu/pub/Misra00_AQM.ps.gz
Stability/instability of fluid model
arrival
rate x/C
1.4
1.2
0.8
0.6
20
40
60
80
100
20
40
60
80
100
1.4
1.2
0.8
0.6
• For some values of C*RTT,
the differential equation is stable
• For others it is unstable and there are oscillations
(i.e. the flows are partially synchronized)
• When it is unstable,
we can calculate the amplitude of the oscillations
time
Instability plot
traffic intensity x/C
0.5
1
1.5
2
-1
C*RTT=4 pkts
log10 of
pkt loss
probability
-2
-3
C*RTT=20 pkts
-4
C*RTT=100 pkts
Illustration: 20 flows
Standard TCP, single bottleneck link, no AQM
service=60 pkts/sec/flow, RTT=200 ms, #flows=20
B=20 pkts
(Kelly rule)
B=54 pkts
(Stanford rule)
B=240 pkts
(rule of thumb)
Illustration: 200 flows
Standard TCP, single bottleneck link, no AQM
service=60 pkts/sec/flow, RTT=200 ms, #flows=200
B=20 pkts
(Kelly rule)
B=170 pkts
(Stanford rule)
B=2,400 pkts
(rule of thumb)
Illustration: 2000 flows
Standard TCP, single bottleneck link, no AQM
service=60 pkts/sec/flow, RTT=200 ms, #flows=2000
B=20 pkts
(Kelly rule)
B=537 pkts
(Stanford rule)
B=24,000 pkts
(rule of thumb)
Some more stable alternatives
Rule of thumb, no AQM buffer = bandwidth*delay
or Stanford rule buffer = bandwidth*delay / sqrt(#flows)
b25
b100
b400
-1
-2
Rule of thumb with RED
-3
buffer=bandwidth*delay*{¼,1,4}
-4
0.5
b10
1
1.5
b20
b50
-1
-2
Kelly rule, no AQM
-3
buffer={10,20,50} pkts
-4
0.5
b50
1
1.5
b1000
-1
-2
Kelly rule, no AQM, ScalableTCP
p -3
-4
buffer={50,1000} pkts
-5
-6
0.5
1
1.5
Scalable TCP: improving performance in
highspeed wide area networks SIGCOMM CCR 2003
Tom Kelly
CERN -- IT division
Abstract. TCP congestion control can perform badly in highspeed wide area networks because of its slow
response with large congestion windows. The challenge for any alternative protocol is to better utilize
networks with high bandwidth-delay products in a simple and robust manner without interacting badly with
existing traffic. Scalable TCP is a simple sender-side alteration to the TCP congestion window update
algorithm. It offers a robust mechanism to improve performance in highspeed wide area networks using
traditional TCP receivers. Scalable TCP is designed to be incrementally deployable and behaves identically
to traditional TCP stacks when small windows are sufficient. The performance of the scheme is evaluated
through experimental results gathered using a Scalable TCP implementation for the Linux operating system
and a gigabit transatlantic network. The preliminary results gathered suggest that the deployment of
Scalable TCP would have negligible impact on existing network traffic at the same time as improving bulk
transfer performance in highspeed wide area networks.
http://www-lce.eng.cam.ac.uk/~ctk21/scalable/
Higher utilization
b10
b20
• A fixed buffer cannot give
high utilization over all values
of C*RTT
-1
-2
-3
-4
0.5
1
1.5
r 0.8
r 0.9
r 0.95
r 0.99
-1
-2
p
b50
-3
-4
0.5
1
r
1.5
• By choosing
B=c1+c2*log(C*RTT)/log(r)
we get utilization r
[Towsley]