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Measurement and Modelling I:End-to-End Bandwidth Measurements
6.829 Lecture 11
October 10, 2002
Jacob Strauss
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End-to-End Measurements
Goal: Bandwidth-Aware Applications
Is a path fast enough? Which path is faster?
What is bandwidth?
Link Capacity: physical link speed (e.g. 100 Mbps Ethernet)
for link i, link capacity ci.
Path Capacity: minimum capacity link along a path
C= mini=0...n(ci)
Link Utilization: fraction of link capacity used over some time interval
0 ui 1
Available Bandwidth: minimum spare capacity along a path over some interval
A = mini=0...n(1 ui)ci
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Example Topology
C=10 Mbps, u=0.2C=100 Mbps, u=0.95
C=20 Mbps, u=0.5X
Y
Capacity from X to Y?
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Example Topology
C=10 Mbps, u=0.2C=100 Mbps, u=0.95
C=20 Mbps, u=0.5X
Y
Capacity from X to Y? C = 10Mbps
Available bandwidth from X to Y?
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Example Topology
C=10 Mbps, u=0.2C=100 Mbps, u=0.95
C=20 Mbps, u=0.5X
Y
Capacity from X to Y? C = 10Mbps
Available bandwidth from X to Y? A = 5Mbps
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Problem: Capacity Estimation
X Y
C1
C2
C3
How can we measure the path capacity between X and Y?
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Packet Pair on an unloaded path
X Y
tt
C1
C2
C3
Send two packets, of P bits each, back-to-back
Record the difference between arrival times, t.
Path Capacity is Pt
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Packet Pair Complications: Cross Traffic
X Y
t
C1
C2
C3
t
other packet
probe packet
t >P
C
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Packet Pair Complications: Multiple Queues
X Y
C1
C2
C3
t
other packet
probe packet
t
t nyu.ron.lcs.mit.edu
1
500B
500B
sen
tgap
b2b
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New Problem: Available Bandwidth Estimation
Can we use the same packet train to estimate A?
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New Problem: Available Bandwidth Estimation
Can we use the same packet train to estimate A?
No, but we can determine whether P/ > A or P/ < A
Later well build on this test to estimate A
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New Problem: Available Bandwidth Estimation
Can we use the same packet train to estimate A?
No, but we can determine whether P/ > A or P/ < A
Later well build on this test to estimate A
Basic idea: instead of just comparing wn+1 to wn, compare wn to
wn+1, wn+2, wn+3, . . .
Method: Plot evolution of wn versus n
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Pathload Delay Model
The packet train consists of K packets of size L sent at a constant
rate R.
Path consists ofH links, each with capacity Ci, available bandwidth
Ai, and queue length qki when the kth probe packet arrives
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Pathload Delay Model
The packet train consists of K packets of size L sent at a constant
rate R.
Path consists ofH links, each with capacity Ci, available bandwidth
Ai, and queue length qki when the kth probe packet arrives
The One-Way-Delay for probe k is:
Dk =Hi=1
L
Ci+
qkiCi
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Pathload Delay Model
The packet train consists of K packets of size L sent at a constant
rate R.
Path consists ofH links, each with capacity Ci, available bandwidth
Ai, and queue length qki when the kth probe packet arrives
The One-Way-Delay for probe k is:
Dk =Hi=1
L
Ci+
qkiCi
Dk Dk+1Dk =Hi=1
qkiCi
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Increasing Trends
If R > A, then Dk > 0 for k 1
If R A, then Dk = 0 for k 1
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Increasing Trends
If R > A, then Dk > 0 for k 1
If R A, then Dk = 0 for k 1
Intuition for a single link i with Ai < R:
Queue grows longer with each probe packet that arrives
qki = (L + uiCiT)C1T = (RAi)T > 0
For a single link with Ai R:
qki = 0
By induction, show that Dk > 0 when R > A
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Increasing Trends
If R > A, then Dk > 0 for k 1
If R A, then Dk = 0 for k 1
Intuition for a single link i with Ai < R:
Queue grows longer with each probe packet that arrives
qki = (L + uiCiT)C1T = (RAi)T > 0
For a single link with Ai R:
qki = 0
By induction, show that Dk > 0 when R > A
Plot Dk if Dk > 0 then R > A
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Complications
Ai not a constant
varies on both short and long time scales
Need to choose K and L carefully
Too short cant tell if Dk > 0
Too long flood link
Compromise use multiple trains
How did we choose R initially?
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Iterative Search for A
maintain two state variables: Rmax and Rmin.
always have Rmin A Rmax .
Pick a new R halfway between Rmax and Rmin
Test whether R A, update either Rmax or Rmin
Stop when Rmax and Rmin are close enough.
In practice the search is more complicated because the outcome of
testing R A is sometimes unsure
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Pathload Block Diagram
Timestamps
Filters
Estimates
Network
Packet Source
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Available Bandwidth isnt the full story
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.01 0.1 1 10 100
CDF
BTC / Pathload rate
BTC vs Pathload: 15 RON hosts -- one test per path
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Conclusion
Theres a lot you can learn with simple probes
packet pair packet trains regular interval, constant packet size
Just by looking at packet delay variations you can determine
Path Capacity
Common Packet Sizes
Available Bandwidth
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