Initialization and Disconnect for ARQ Protocols MasterSlave Protocol

1
Initialization and Disconnect for ARQ Protocols
(Master-Slave Protocol)
B?A link free of data
Initiating
Disconnecting
Initiating
Up
Down
INIT
DISC
INIT
Node A
Node B
ACKI
ACKD
ACKI
Up
Down
A?B link free of data
2
Discussion of Master-Slave Protocol

• Is it possible to abort the initialization before
  receiving ACKI?
• Normal response mode of HDLC
• SETM ? INIT
• DISC ? DISC
• ACK ? ACKI ACKD
• Unnumbered frame
• Figure 2.44 on page 106

3
A Balanced Protocol for Link Initialization

• Why we need a balanced protocol?
• Essential idea use two Master-Slave Protocols
• To simplify synchronization INIT or DISC
  contains ACKI or ACKD
• A link is up when A?B link is up and B?A link is
  up
• Initialize ARQ at the beginning of an up period

4
A Balanced Protocol
B?A link free of data
Up
Down
INIT ACKD
DISC ACKI
INIT ACKI
ACKI
ACKD
Node A
Node B
ACKI
DISC ACKD
INIT ACKI
INIT ACKD
Down
Up
A?B link free of data
5
Discussion Link Initialization in the Presence
of Node Failure

• Piggyback ACK
• Three-way Handshake
• Correctness proof
• Difficulty in the presence of node failure
• State information

6
Problem Caused by Node Failure
Data
Data
Data
Fail
Fail
INIT
SN0
INIT
INIT
SN0
SN1
Node A
Node B
ACKI
ACKI
RN1
ACKI
Data
RN0
RN0
Packet out
0
7
Review of Probability Theory

• The basic model is a repeatable experiment
• An experiment a procedure and observations
• Model
• An outcome of an experiment
• Sample space of an experiment
• Event

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Axioms of Probability

• Terminology mapping to Set Theory
• Element, Set, Universal Set
• A probability measure P? s.t.
• Axiom 1 For any event A, PA ? 0
• Axiom 2 PS 1
• Axiom 3 For any countable mutually exclusive
  events A1, A2, ?
• PA1?A2?? PA1 PA2 ?

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Random Variable (RV)

• A random variable (RV) consists of an experiment
  with P? defined on a sample space S, and a
  function ? that assigns a real number to each
  outcome in the sample space of the experiment.
• Toss a fair dice. The RV X is the number of spots
  that appears on the side facing up.

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• SXxii?i1,2,3,4,5,6 PXXxi1/6. Note
  that PX(x)PXXxi?0,1 and for all x that ?
  PX(x)1
• Discrete RV
• Probability Mass Function (PMF)
• PMF of the discrete RV X is PX(x)PXx
• Cumulative Distribution Function (CDF)
• The CDF of RV X is FX(x)PX?x
• Probability Density Function (PDF)
• The PDF of a continuous RV X is fX(x)dFX(x)/dx

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Mean Value (Expected Value)

• Mean value of RV X
• EX ?X ? xPX(x)
• x?SX
• Properties of mean value
• X Y are RVs, ? ? are constants
• If Y X ?, then EY EX ?
• If Y ?X, then EY ?EX

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Variance

• Variance of RV X
• VarX E(X??X)2 EX2 (EX)2
• Standard Deviation ?Xsqrt(VarX)
• Properties of variance
• X Y are RVs, ? ? are constants
• If Y X ?, then VarY VarX
• If Y ?X, then VarY ?2VarX

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Sum of Two RVs

• YX1X2
• Mean value of Y is EY EX1 EX2
• Variance of Y is
• VarY VarX1 VarX2 2CovX1, X2
• CovX1, X2 E(X1??X1)(X2??X2)

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Moment Generating Function (MGF)

• MGF of RV X is
• ?X(s)EesX
• ?X(s) ? PX(x)esx if X is a discrete RV
• x?SX
• ?X(s)?esxfX(x)dx if X is a continuous RV
• All of the moment of X can be obtained by
  successively differentiating (s)

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Use MGF to Calculate EX

• ?X(s)d?X(s)/ds ?PX(x)xesx
• x?SX
• ?X(s)?s0?PX(x)x
• x?SX
• EX ?X(s)?s0

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Use MGF to Calculate VarX

• ?X(s)d2?X(s)/ds2 ?PX(x)x2esx
• x?SX
• ?X(s)??X(s)2?s0?PX(x)x2
• x?SX
• VarX?X(s)??X(s)2?s0

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MGF of Two RVs

• If YX1X2 and X1,X2 are independent RVs, then
  the MGF of Y is
• ?Y(s)?X1(s)?X2(s)

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Bernoulli RV (1)

• Experiment with outcome success (denoted as 1)
  or failure (denoted as 0)
• Using CRC to detect error of a received frame.
  With probability p, the frame is detected as a
  correct or error-free frame. Let X be the number
  of error-free frames in one detection. What is
  PX(x)?

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Bernoulli RV (2)

• ? 1?p x0
• PX(x) ? p x1
• ? 0 otherwise
• Question compute EX and VarX using
  definition and MGF ?X(s)1?p pes
• EX ?X(s)?s0p
• VarX?X(s)??X(s)2?s0p?p2

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Geometric RV (1)

• Study the case that independent trails are
  performed until a success occurs.
• X equals the number of frames received up to and
  including the first one that CRC detects an
  error-free frame. What is PX(x)?

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Geometric RV (2)

• PX(x) ? p(1?p)x?1 x1,2,3,?
• ? 0 otherwise
• ?X(s)pes/1?(1?p)es
• EX ?X(s)?s01/p
• VarX?X(s)??X(s)2?s0(1?p)/p2