EECS%20122:%20Introduction%20to%20Computer%20Networks%20Transport%20Analysis

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EECS 122 Introduction to Computer Networks
Transport Analysis

• Computer Science Division
• Department of Electrical Engineering and Computer
  Sciences
• University of California, Berkeley
• Berkeley, CA 94720-1776

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Outline

• Exponential averaging and its applications
• Retransmission timeout (RTO) computation
• Littles Theorem (revisited)

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Exponential Averaging

• Let X1, X2, , XN be a series of measurements
• Then average value Ai after the i-th measurement
  is computed as
• Ai a Ai-1 (1 - a ) Xi
• where a is a constant between 0 and 1
• Note that (assuming A0 0)
• Ai a N-1 (1 - a) X1 a N-2 (1 - a) X2 (1
  - a) XN
• What is the role of a? What does a control?

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Exponential Averaging Example

• X constant A converges to X

X
A

iteration
1
2
3
4
5
6
7
8
9
10
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Exponential Averaging Example

• Maintaining queue size in RED

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Exponential Averaging Example

• RTT estimation in TCP
• Measure RTT for each packet/ACK pair
• Compute average of RTT as
• EstRTT a x EstRTT (1 - a ) x RTT
• a is 0.9 (or 0.8)

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Moving Window Average

• Let X1, X2, , XN be a series of measurements
• Then average value Ai after the i-th measurement
  is computed as
• Ai (Xi-1 Xi-2 Xi-w)/W
• where W is the window size
• How do exponential averaging and moving window
  averaging compare?

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Outline

• Exponential averaging and its applications
• Retransmission timeout (RTO) computation
• Littles Theorem (revisited)

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Retransmission Timeout (RTO) Computation The
Problem
1
1
Timeout
RTT
RTT
1
Timeout
1
Timeout too long ? inefficiency
Timeout too short ? duplicate packets
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RTO Computation Original Algorithm

• Measure RTT for each packet/ACK pair, then
  perform
• EstRTT a x EstRTT (1 - a ) x RTT, where
  a is 0.9 (or 0.8)
• RTO 2 x EstRTT

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RTO Computation Jacobson/Karels Algorithm

• Measure RTT for each packet/ACK pair, then
  perform
• Err RTT - EstRTT
• EstRTT EstRTT (1 a ) x Err
  (Note equivalent to
  EstRTT a x EstRTT (1 - a ) x RTT)
• DevRTT (1 - b ) x DevRTT b x Err
• RTO EstRTT 4 DevRTT
• where a 0.9 and b 1/8
• DevRTT represents the mean of the deviation (like
  standard deviation) of the RTT
• Why do we need DevRTT?

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RTO Computation Karn/Partridge Algorithm

• Add the following two considerations to
  Jacobson/Karels algorithm
• EstRTT is updated only when an ACK is received
  before the timeout expires. Why?
• If a packet timeouts, double EstRTT. Why?

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Outline

• Exponential averaging and its applications
• Retransmission timeout (RTO) computation
• Littles Theorem (revisited)

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Littles Theorem

• Assume a system (e.g., a queue) at which packets
  arrive at rate a(t)
• Let d(i) be the delay of packet i , i.e., time
  packet i spends in the system
• What is the average number of packets in the
  system?

d(i) delay of packet i
a(t) arrival rate
system

• Intuition
• Assume arrival rate is a 1 packet per second
  and the delay of each packet is s 5 seconds
• What is the average number of packets in the
  system?

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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
time
T
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S area
time
T
Average occupancy S/T
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
S area
time
T
S S(1) S(2) S(N) P(d(1) d(2)
d(N))
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
S area
time
T
S/T (P(d(1) d(2) d(N)))/T
((PN)/T) ((d(1) d(2) d(N))/N)
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
a(i)
S(N-1)
d(N-1)
x(t)
S area
time
T
Average occupancy (average arrival rate) x
(average delay)