a framework for network survivability characterization soung c. liew and kevin w. lu ieee journal on...
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3 OUTLINE 1. Introduction 2. Survivability of a Centralized Ring Network under Link Failures 3. General Procedure for Finding Survivability Function 4. Finding Survivability Function for a Network 5. ConclusionsTRANSCRIPT
A Framework for Network Survivability CharacterizationSoung C. Liew and Kevin W. LuIEEE Journal on Selected Areas in Communications, January 1994 (ICC, 1992)
Wendy Wen
OPlab, IM, NTU
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OUTLINE1. Introduction2. Survivability of a Centralized Ring
Network under Link Failures3. General Procedure for Finding
Survivability Function4. Finding Survivability Function for a
Network5. Conclusions
3
OUTLINE1. Introduction2. Survivability of a Centralized Ring Network
under Link Failures3. General Procedure for Finding Survivability
Function4. Finding Survivability Function for a Network5. Conclusions
4
Objective This paper attempts to formulate a general
framework that both includes and extends the existing definitions for network survivability.
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Survivability Function The probability that a fraction s of the nodes are
connected to the central node.
S : network survivability, which is a random variable e : sample point E : sample space, E = {e} Pe: probability of each e Se: probability of nodes connected to the central node
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Advantage A number of different quantities of interest can be
derived from the function. E[S] , s* , sr , p0
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OUTLINE1. Introduction2. Survivability of a Centralized Ring Network
under Link Failures3. General Procedure for Finding Survivability
Function4. Finding Survivability Function for a Network5. Conclusions
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1. S = fraction of nodes connected to the central node under
2. All links are bidirectional. 3. The number of Node is very large. 4. link failures = n
A link failure is equally likely to be located anywhere.The locations of the n failures are independent.
n ≧2
Assumption
self-healing
s = Con.
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Objective Derive the corresponding survivability
function:
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Derivation (1) Dividing into many
small segments, each of length △s.
Size of the sample space is
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Derivation (2) Each of these sample points is equally likely,
Ns : the number of ways to make n cuts that result in
a survivability of s.
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Derivation (3): Find Ns 1. n(n-1) ways of choosin
g two cuts to be Cl and Cr
2. s/ s△ ways of putting the two adjacent cuts, from Cl to Cr
3. Ways of the remaining (n-2) cuts is .
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Derivation (4)
By definition,
Remind that,
Derivation (6): Find ps(S) Let Nc be the r.v. associated with the numbe
r of cuts.
where δ(x) is the impulse function
總和定理
Pr of n=0 and n=1
Pr of n≧2
P[S=s | n] , from eq.12
1, x=00, otherwise
δ(x) =
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Derivation (7): Find ps(S) Let MGF of Nc is
Then,
Assume Poisson distribution,
Thus,
pdf of Poisson
MGF of Poisson
P(N=0)
P(N=1)
P(N 2)=mgf≧ (2)(1-s)
Fr.eq. 17:
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OUTLINE1. Introduction2. Survivability of a Centralized Ring Network
under Link Failures3. General Procedure for Finding Survivability
Function4. Finding Survivability Function for a Network5. Conclusions
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Procedure1. Specify disaster type2. Define “goodness” of networks3. List the sample points {e}, or all
combinations of events 4. Determine the survivability Se
5. Determine or assign probability of each event e
6. Calculate survivability function
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Step 1. Specify disaster type Different disaster types may have different
effects on networks. severe thunderstorm cable cut
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Step 2. Define “goodness” of networks We may obtain results depending on the fe
atures of the network for which we are calculating survivability. the number of subscribers connected to a centr
al node the revenue collected by the network operator
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Step 3. List all combinations ofevents Sample space may simply be too large. It maybe can only be done effectively by a
computer.
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Step 4. Determine Se
This calculation will depend on our definition of survivability.
If as example above, then we would need an efficient algorithm.
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Step 5. Determine Pe This should be based on past observations
or experience. If the disaster happens so rarely, one will n
eed to use one’s judgement when assigning probabilities.
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Step 6. Calculate survivability function By summing the probabilities of all sample
points with the same survivability.
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OUTLINE1. Introduction2. Survivability of a Centralized Ring Network
under Link Failures3. General Procedure for Finding Survivability
Function4. Finding Survivability Function for a Network5. Conclusions
27
24 nodes 26 links the number associated
with each link is its length 69 DS3 fiber-optic
transmission systems between 29 node pairs
Assumption
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Table I. DS3 demands between nodes of n network.
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4
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Step 1. Specify disaster type Hurricanes
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Step 2. Define “goodness” of networks Total number of surviving DS3’s under link f
ailures
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Step 3. List all combinations ofevents Localized disasters: the network survivability can
be easily found.
Hurricane: 226 = 67,108,864 possible combinations of link failures.
Assume that more than four link failures are highly unlikely.
179011495026003252626
4
26
3
26
2
26
1 CCCC
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Step 4. Determine Se
For each event e, the survivability is Se = (surviving DS3’s) / 69
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Step 5. Determine Pe (1) Assume that,
link failures are independent probability of a link failure is proportional to its l
ength
ε: to reflect the extent of damage expected of the hurricane,
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Step 5. Determine Pe (2) Probabilities of single, double, triple, and
quadruple link failures are:
Pr of a link failure Pr of the others
Pr of two link failures Pr of the others
Pr of three link failures Pr of the others
Pr of four link failures Pr of the others
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Step 6. Calculate survivability function (1)
For illustration, we condense all survivability within the intervals,
(0.02i -0.1 , 0.02i +0.1] i=1, 2 ,..., 50
Show survivability functions for ρ= 0.1 and ρ= 0.2.
Remind that,
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ρ = 0.1E [ S ] ≈ 0.923S* ≈ 0.28S10 ≈ 0.8Po ≈ 0
ρ = 0.2E [ S ] ≈ 0.822S* ≈ 0.28S10 ≈ 0.72Po ≈ 0
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When increasing ρ from 0.1 to 0.2, P(s=1) : decreases from 0.341 to 0.11 E[S] : decreases from 0.923 to 0.822 S10 : decreases from 0.8 to 0.72 S* : unchanged
Step 6. Calculate survivability function (2)
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Step 6. Calculate survivability function (3) Although the worst-case survivability is 0.2
8, it corresponds to two events of quadruple link failures links 3-6, 5-6, 6-7 and 6-8 links 3-6, 5-6, 6-7 and 8-15
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97
2510
links 3-6, 5-6, 6-7, 6-897
25
8
links 3-6, 5-6, 6-7, 8-15
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OUTLINE1. Introduction2. Survivability of a Centralized Ring Network
under Link Failures3. General Procedure for Finding Survivability
Function4. Finding Survivability Function for a Network5. Conclusions
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Conclusions Network survivability is characterized by a
survivability function.
Various quantities of interest can be derived from the survivability function.
This framework provides a unified and practical approach to analyzing and designing highly survivable communications networks.
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The End
Thank you for your listening~
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Fig. 1. A ring network with node failures due to a thunderstorm
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Table II. DS3’s lost due to link failures of a network.
3+2
3+ 2+4
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4
46Fig. 6. A network for survivability characterization.
max li
2.18max10 il
126.03.22.181][min min lfailslP i
min li
12.182.181][max max lfailslP i