file fragmentation over an unreliable network - bachelor thesis · 2009-10-06 · bachelor thesis...
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![Page 1: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/1.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
File Fragmentation over an UnreliableNetwork
Bachelor Thesis
Martin [email protected]
Royal Institute of Technology
September 7, 2009
![Page 2: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/2.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Imagine yourself playing an action game
![Page 3: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/3.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
There is always a risk of getting caught, which increasesby time
![Page 4: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/4.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
AcknowledgmentsIf you get caught, you have to start over where you lastsaved
But saving very frequently would cost too much time
![Page 5: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/5.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
AcknowledgmentsIf you get caught, you have to start over where you lastsaved
But saving very frequently would cost too much time
![Page 6: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/6.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Basic model
A file is sent over an unreliable network
Large files are more likely to be corrupted than small
If a file is corrupted, the whole file needs to be resent
![Page 7: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/7.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Basic model
A file is sent over an unreliable network
Large files are more likely to be corrupted than small
If a file is corrupted, the whole file needs to be resent
![Page 8: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/8.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Basic model
A file is sent over an unreliable network
Large files are more likely to be corrupted than small
If a file is corrupted, the whole file needs to be resent
![Page 9: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/9.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Large files are likely to be corrupted
![Page 10: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/10.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Basic model
To prevent file losses and heavy-tailes, large files can befragmented
Smaller fragments are less likely to be corrupted
![Page 11: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/11.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Basic model
To prevent file losses and heavy-tailes, large files can befragmented
Smaller fragments are less likely to be corrupted
![Page 12: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/12.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Fragmentation prevents corruption
![Page 13: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/13.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Packets however, carry an overhead
This makes too small packet sizes inefficient
![Page 14: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/14.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Thesis
What is the optimal fragment size?
![Page 15: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/15.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Mathematical model
xi + φ denotes the packet size (xi data size, φ overheadsize)
Transmission will succeed if Ai ≥ xi + φ (Ai randomvariable with distribution f)
![Page 16: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/16.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Mathematical model
xi + φ denotes the packet size (xi data size, φ overheadsize)
Transmission will succeed if Ai ≥ xi + φ (Ai randomvariable with distribution f)
![Page 17: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/17.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Expected transmission time
J =M−1∑i=0
xi + φ
F̄ (xi + φ)=
M−1∑i=0
h(xi ) F̄ (x) = P(Ai > x) (1)
Want to minimize J over M and xi
![Page 18: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/18.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Expected transmission time
J =M−1∑i=0
xi + φ
F̄ (xi + φ)=
M−1∑i=0
h(xi ) F̄ (x) = P(Ai > x) (1)
Want to minimize J over M and xi
![Page 19: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/19.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
The KKT condition for (1) is
h′(xi ) =1
F̄ (xi + φ)+ (xi + φ)
f (xi + φ)(F̄ (xi + φ)
)2 = λ
M−1∑i=0
xi = L (2)
Lemma
If the failure rate (failure risk) f (x)/F̄ (x) is increasing:
The optimization over xi is convex
The solution is x∗i = x∗ for all i (packet sizes are equal)
![Page 20: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/20.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
The KKT condition for (1) is
h′(xi ) =1
F̄ (xi + φ)+ (xi + φ)
f (xi + φ)(F̄ (xi + φ)
)2 = λ
M−1∑i=0
xi = L (2)
Lemma
If the failure rate (failure risk) f (x)/F̄ (x) is increasing:
The optimization over xi is convex
The solution is x∗i = x∗ for all i (packet sizes are equal)
![Page 21: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/21.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
The KKT condition for (1) is
h′(xi ) =1
F̄ (xi + φ)+ (xi + φ)
f (xi + φ)(F̄ (xi + φ)
)2 = λ
M−1∑i=0
xi = L (2)
Lemma
If the failure rate (failure risk) f (x)/F̄ (x) is increasing:
The optimization over xi is convex
The solution is x∗i = x∗ for all i (packet sizes are equal)
![Page 22: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/22.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
The KKT condition for (1) is
h′(xi ) =1
F̄ (xi + φ)+ (xi + φ)
f (xi + φ)(F̄ (xi + φ)
)2 = λ
M−1∑i=0
xi = L (2)
Lemma
If the failure rate (failure risk) f (x)/F̄ (x) is increasing:
The optimization over xi is convex
The solution is x∗i = x∗ for all i (packet sizes are equal)
![Page 23: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/23.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
Seek minimizer M∗ by inserting x∗ = L/M into (1):
J = MLM + φ
F̄(
LM + φ
) = LLM + φ
LM F̄
(LM + φ
) := L·g(
L
M
)(3)
Lemma
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing, g(x) is unimodal
![Page 24: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/24.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
Seek minimizer M∗ by inserting x∗ = L/M into (1):
J = MLM + φ
F̄(
LM + φ
) = LLM + φ
LM F̄
(LM + φ
) := L·g(
L
M
)(3)
Lemma
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing, g(x) is unimodal
![Page 25: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/25.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Minimizing J
Seek minimizer M∗ by inserting x∗ = L/M into (1):
J = MLM + φ
F̄(
LM + φ
) = LLM + φ
LM F̄
(LM + φ
) := L·g(
L
M
)(3)
Lemma
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing, g(x) is unimodal
![Page 26: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/26.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
![Page 27: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/27.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
![Page 28: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/28.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Bounding x∗
Definition
a := argminx
(g(x))
Theorem
If L > a:
a
2≤ a
1 + a/L≤ x∗(L) ≤ min
(2a,
a
1− a/L
)
Corollary
limL→∞
x∗(L) = a
![Page 29: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/29.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Bounding x∗
Definition
a := argminx
(g(x))
Theorem
If L > a:
a
2≤ a
1 + a/L≤ x∗(L) ≤ min
(2a,
a
1− a/L
)
Corollary
limL→∞
x∗(L) = a
![Page 30: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/30.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Bounding x∗
Definition
a := argminx
(g(x))
Theorem
If L > a:
a
2≤ a
1 + a/L≤ x∗(L) ≤ min
(2a,
a
1− a/L
)
Corollary
limL→∞
x∗(L) = a
![Page 31: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/31.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Bounding x∗
Definition
a := argminx
(g(x))
Theorem
If L > a:
a
2≤ a
1 + a/L≤ x∗(L) ≤ min
(2a,
a
1− a/L
)
Corollary
limL→∞
x∗(L) = a
![Page 32: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/32.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Conclusion
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing,
Constant fragmentation is optimal
The fragment sizes are unique
If the file size and distribution f are known, the file canbe pre-fragmented
For large filesizes L, the optimal fragment size isindependent of L
![Page 33: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/33.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Conclusion
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing,
Constant fragmentation is optimal
The fragment sizes are unique
If the file size and distribution f are known, the file canbe pre-fragmented
For large filesizes L, the optimal fragment size isindependent of L
![Page 34: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/34.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Conclusion
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing,
Constant fragmentation is optimal
The fragment sizes are unique
If the file size and distribution f are known, the file canbe pre-fragmented
For large filesizes L, the optimal fragment size isindependent of L
![Page 35: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/35.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Conclusion
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing,
Constant fragmentation is optimal
The fragment sizes are unique
If the file size and distribution f are known, the file canbe pre-fragmented
For large filesizes L, the optimal fragment size isindependent of L
![Page 36: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/36.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Conclusion
Under the assumption that the failure rate f (x)/F̄ (x) isincreasing,
Constant fragmentation is optimal
The fragment sizes are unique
If the file size and distribution f are known, the file canbe pre-fragmented
For large filesizes L, the optimal fragment size isindependent of L
![Page 37: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/37.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Acknowledgments
Steven H. Low, Jayakrishnan Nair (Caltech) andLachlan Andrew (Swinburne)
Henrik Sandberg and Karl Henrik Johansson (KTH)
![Page 38: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/38.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Acknowledgments
Steven H. Low, Jayakrishnan Nair (Caltech) andLachlan Andrew (Swinburne)
Henrik Sandberg and Karl Henrik Johansson (KTH)
![Page 39: File Fragmentation over an Unreliable Network - Bachelor Thesis · 2009-10-06 · Bachelor Thesis Martin Andreasson mandreas@kth.se Royal Institute of Technology September 7, 2009](https://reader033.vdocuments.us/reader033/viewer/2022052803/5f7c124b64c914325f1eedc4/html5/thumbnails/39.jpg)
File Fragmentationover an Unreliable
Channel
Martin [email protected]
Introduction
Model and method
Conclusion
Acknowledgments
Acknowledgments
Steven H. Low, Jayakrishnan Nair (Caltech) andLachlan Andrew (Swinburne)
Henrik Sandberg and Karl Henrik Johansson (KTH)