Optimization of Routing and ResourceAllocation in Communication Networks
HDR Defence Presented by
Fen ZhouLISITE, Institut Superieur d’Electronique de
Paris (ISEP)LIA, University of Avignon (UAPV)
Jury Members:Prof. Chadi Assi Concordia University ReviewerProf. David Coudert INRIA, Sophia Antipolis ReviewerProf. Abdelhamid Mellouk LiSSi, University of Paris 12 ReviewerProf. Marcelo Dias de Amorim LIP6, CNRS/Sorbonne University ExaminerProf. Abderrahim Benslimane LIA, University of Avignon PresidentProf. Nathalie Mitton INRIA, Lille ExaminerProf. Abderrezak Rachedi LIGM, University of Marne-la-Vallee Examiner
Avignon, Sept. 26th, 2018
Outline
Outline
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 2 / 99
Curriculum Vitae
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 3 / 99
Curriculum Vitae
Curriculum Vitae
2004 - 2007 Master on TelecommunicationsNorthwestern Polytechnic University, China
2007 - 2010 PhD on Optical NetworkingIRISA, INSA of Rennes, France
2010 - 2012 Post-doc on Content Delivery NetworksIMT Atlantique (ex Telecom Bretagne)
09/2012 - 09/2018 Associate Professor on NetworkingLIA lab, CERIUniversity of Avignon
09/2018 - present Associate Professor on NetworkingLISITE labInstitut Superieur d’electronique de Paris (ISEP)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 4 / 99
Curriculum Vitae
ResumeResponsibilities + Awards
Awards: PEDR 2016-2020; IEEE senior member, etc
Responsibles: Master RISM; axis FR Agorantic
Conference organisations: ICNC, WCSP, Wimob, Netgcoop, MoWnet
Project coordinations: 5 Eiffel+CSC scholarships, regional projet, Sino-French project...
ResearchRouting, resource allocation, survivability and security in networking
Routing optimization in ITS
Advising: PhD (10), interns (6)
Publications: journals (25), conferences (44)
Teaching
1600h, 3rd year engineer, L2/L3/M1/M2
Networking, multimedia, CISCO, graph theory
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 5 / 99
Introduction
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 6 / 99
Introduction
Communication Networks
https://reseaux.orange.fr/cartes-de-couverture/fibre-optique
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 7 / 99
Introduction
Communication Networks
Tx
Servers
Rx
Services
… …
Optical fiber
https://reseaux.orange.fr/cartes-de-couverture/fibre-optique
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 7 / 99
Introduction
Communication Networks
Tx
Servers
Rx
Services
… …
Optical fiber
https://reseaux.orange.fr/cartes-de-couverture/fibre-optique
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 7 / 99
Introduction
Studied Problem in Communication Networks
Routing and Resource Allocation
Routing: path, tree, etc.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 8 / 99
Introduction
Studied Problem in Communication Networks
Routing and Resource Allocation (RRA)
Routing
Resource allocation: spectrum, battery, bandwidth, capacity etc.
12.5GHz for one subcarrier
1 2 3 4 … …
Frequency Slot (FS)
320… …
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 9 / 99
Introduction
Optimization of Routing and Resource Allocation
Challenges
Coupled together
NP-Hard problems
Optimization techniques required
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 10 / 99
Introduction
Optimization techniques
Integer Linear Programming
Optimal solution
High computation complexity
Heuristics and Approximation Algorithms
Feasible solution, approximation ratio
Low computation complexity
Large-scale optimization: Column Generation
Near-optimal solution
Relatively low computation complexity
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 11 / 99
Introduction
RRA in Communication Networks
Routing and Resource allocation
Optimization techniques:
ILP, heuristic, approximation algorithm, column generation
Elastic Optical Networks (EONs)
Content Delivery Networks (CDNs)
Wireless Sensor Networks (WSNs)
Datacenter Networks (DCNs)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 12 / 99
Delivery of Multiple Video Channels in Telco-CDNs
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 13 / 99
Delivery of Multiple Video Channels in Telco-CDNs
MotivationOTT content providers: twitch, ustream, second screen video...
User-generated live video traffic: exploding
Telco-CDN: tight resource and deployment constraint
Problem: How to manage live video traffic? (CNG projet, thesis of Jiayi Liu)
links to IXP Telco-CDN linksentrypointsedge servers
s1 s2
s3
1
2
3
4
56
78 9
10
11 12 13
Figure 1: Topology of a French Telco-CDN
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 14 / 99
Delivery of Multiple Video Channels in Telco-CDNs
MotivationOTT content providers: twitch, ustream, second screen video...
User-generated live video traffic: exploding
Telco-CDN: tight resource and deployment constraint
Problem: How to manage live video traffic? (CNG projet, thesis of Jiayi Liu)
links to IXP Telco-CDN linksentrypointsedge servers
s1 s2
s3
1
2
3
4
56
78 9
10
11 12 13
Figure 1: Topology of a French Telco-CDNF. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 14 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Multi-channel video delivery problemDescription
Teleco-CDNs G(V,E), entrypoints si ∈ S ⊂ V
Video channels i ∈ I, channel importance πi
Deliver channel i ∈ I from si to subscribing edge-servers Vi ⊂ V with rateless coding
Multi-tree overlay Fi: one distinct unit of rateless codes per tree
ConstraintsEdge-server capacity constraint (cv).∑
i∈I
∑T∈Fi
deg+T (v) ≤ cv,∀v ∈ V (1)
Rateless codes constraint K.
∀i ∈ I, ∀v ∈ Vi, |Fi(v)| ≥ K (2)
QoS (delay) constraint H.
∀i ∈ I, ∀T ∈ Fi,∀v ∈ T,∑
e∈SPT (v)
de ≤ H (3)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 15 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Multi-channel video delivery problemDescription
Teleco-CDNs G(V,E), entrypoints si ∈ S ⊂ V
Video channels i ∈ I, channel importance πi
Deliver channel i ∈ I from si to subscribing edge-servers Vi ⊂ V with rateless coding
Multi-tree overlay Fi: one distinct unit of rateless codes per tree
ConstraintsEdge-server capacity constraint (cv).∑
i∈I
∑T∈Fi
deg+T (v) ≤ cv,∀v ∈ V (1)
Rateless codes constraint K.
∀i ∈ I, ∀v ∈ Vi, |Fi(v)| ≥ K (2)
QoS (delay) constraint H.
∀i ∈ I, ∀T ∈ Fi,∀v ∈ T,∑
e∈SPT (v)
de ≤ H (3)F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 15 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Multi-channel video delivery problem
Objectives
Main: Max overall importance of the delivered video channels, i.e.,∑i∈I
Ri × πi
2nd: Min traffic load, i.e., number of links in the overlay
Telco-CDNlinks to IXP Telco-CDN links
entrypointsedge servers
s1 s2
s3
12
3
4
5 67
8 910
11 12 13
Example of a multi-tree overlayEntrypoint s1; subscribingedge-servers: 10 and 12, delay H = 2,and rateless codes parameter K = 2,upload capacity c8 = 2
s1
8
10 12
s1
9
12
s1
7
10
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 16 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Multi-channel video delivery problem
Objectives
Main: Max overall importance of the delivered video channels, i.e.,∑i∈I
Ri × πi
2nd: Min traffic load, i.e., number of links in the overlay
Telco-CDNlinks to IXP Telco-CDN links
entrypointsedge servers
s1 s2
s3
12
3
4
5 67
8 910
11 12 13
Example of a multi-tree overlayEntrypoint s1; subscribingedge-servers: 10 and 12, delay H = 2,and rateless codes parameter K = 2,upload capacity c8 = 2
s1
8
10 12
s1
9
12
s1
7
10
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 16 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Overlay construction: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
ILP formulationsSOP-ILPs: ILP-Overlay + ILP-Bandwidth→ Suboptimal.ci
v: capacity reserved by edge server v ∈ V for forest Fi:∑i∈I
civ × Ri ≤ cv, ∀v (4)
JOP-ILP (overlay construction + bandwidth allocation)→ Optimal.Lik
uv ∈ 0, 1: Is 1 if arc (u, v) is used in T ik, 0 otherwise.∑i∈I
∑k∈1,...,Wi
∑u∈N+(v)
Likvu ≤ cv, ∀v (5)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 17 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Overlay construction: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
ILP formulationsSOP-ILPs: ILP-Overlay + ILP-Bandwidth→ Suboptimal.ci
v: capacity reserved by edge server v ∈ V for forest Fi:∑i∈I
civ × Ri ≤ cv, ∀v (4)
JOP-ILP (overlay construction + bandwidth allocation)→ Optimal.Lik
uv ∈ 0, 1: Is 1 if arc (u, v) is used in T ik, 0 otherwise.∑i∈I
∑k∈1,...,Wi
∑u∈N+(v)
Likvu ≤ cv, ∀v (5)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 17 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Overlay construction: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
ILP formulationsSOP-ILPs: ILP-Overlay + ILP-Bandwidth→ Suboptimal.ci
v: capacity reserved by edge server v ∈ V for forest Fi:∑i∈I
civ × Ri ≤ cv, ∀v (4)
JOP-ILP (overlay construction + bandwidth allocation)→ Optimal.Lik
uv ∈ 0, 1: Is 1 if arc (u, v) is used in T ik, 0 otherwise.∑i∈I
∑k∈1,...,Wi
∑u∈N+(v)
Likvu ≤ cv, ∀v (5)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 17 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Delivery Overlay: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
HeuristicsSOP1-heu: two-step optimizationHeu-Overlay for all first, then Heu1-Bandwidth (sorting πi)
SOP2-heu: two-step optimizationHeu-Overlay for all first, then Heu2-Bandwidth (knapsack and bin packing)
JOP-heu: Divide and ConquerRecursive overlay construction + Bandwidth allocation:
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 18 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Delivery Overlay: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
HeuristicsSOP1-heu: two-step optimizationHeu-Overlay for all first, then Heu1-Bandwidth (sorting πi)
SOP2-heu: two-step optimizationHeu-Overlay for all first, then Heu2-Bandwidth (knapsack and bin packing)
JOP-heu: Divide and ConquerRecursive overlay construction + Bandwidth allocation:
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 18 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Delivery Overlay: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
HeuristicsSOP1-heu: two-step optimizationHeu-Overlay for all first, then Heu1-Bandwidth (sorting πi)
SOP2-heu: two-step optimizationHeu-Overlay for all first, then Heu2-Bandwidth (knapsack and bin packing)
JOP-heu: Divide and ConquerRecursive overlay construction + Bandwidth allocation:
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 18 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Proposed Solutions
Problem Decomposition
Delivery Overlay: capacity-and-delay-bounded min-cost forest
Bandwidth allocation: multi-dimension knapsack
HeuristicsSOP1-heu: two-step optimizationHeu-Overlay for all first, then Heu1-Bandwidth (sorting πi)
SOP2-heu: two-step optimizationHeu-Overlay for all first, then Heu2-Bandwidth (knapsack and bin packing)
JOP-heu: Divide and ConquerRecursive overlay construction + Bandwidth allocation:
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 18 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Heuristic vs. Optimal
Table 1: Heuristic Solutions vs MILP Solutions: 6 channelsvideo bit-rate JOP-ILP SOP-ILP JOP-heu SOP1-heu SOP2-heu
Profit ratio512 kbps 100% 100% 100% 100% 100%
1024 kbps 100% 90.7% 100% 100% 100%1536 kbps 100% 76.7% 100% 100% 100%2048 kbps 100% 67.4% 100% 93% 76.7%
Number of delivered channels512 kbps 6 6 6 6 6
1024 kbps 6 4.5 6 6 61536 kbps 6 3.5 6 6 62048 kbps 6 3.5 6 5 5
Ratio of used capacity512 kbps 12.7% 12.8% 14% 13.8% 13.8%
1024 kbps 21.7% 16.5% 23.7% 23.3% 23.3%1536 kbps 30.8% 18.1% 33.2% 32.7% 32.7%2048 kbps 40.4% 21.2% 42.6% 36% 34.3%
Average computing time (Seconds)2048 kbps 749.5 228 0.3 < 0.1 0.3
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 19 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Results of Heuristics in French CDN - 1
40 60 80 1000.5
0.6
0.7
0.8
0.9
1
number of video channels
profi
trat
io
JOP-heu SOP1-heu SOP2-heu
(a) profit ratio vs. channels
40 60 80 100
40
60
80
100
number of video channelsde
liver
edvi
deo
chan
nels
JOP-heu SOP1-heu SOP2-heu
(b) delivered channels vs. channels
Figure 2: Simulation Results in a French Telco-CDN
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 20 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Results of Heuristic in French CDN - 2
40 60 80 1000
0.2
0.4
0.6
0.8
1
number of video channels
ratio
ofus
edca
paci
ty
JOP-heu SOP1-heu SOP2-heu
(a) capacity ratio vs. channels
500 1,000 1,500 2,000 2,5000.5
0.6
0.7
0.8
0.9
1
video bitrate (kbps)pr
ofitr
atio
JOP-heu SOP1-heu SOP2-heu
(b) profit ratio vs. bit-rate
Figure 3: Simulation Results-2 in a French Telco-CDN
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 21 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Results of Heuristics in French CDN - 3
500 1,000 1,500 2,000 2,500
40
60
80
100
120
video bitrate (kbps)
deliv
ered
vide
och
anne
ls
JOP-heu SOP1-heu SOP2-heu
(a) delivered channels vs. bit-rate
500 1,000 1,500 2,000 2,5000
0.2
0.4
0.6
0.8
1
video bitrate (kbps)ra
tioof
used
capa
city
JOP-heu SOP1-heu SOP2-heu
(b) capacity ratio vs. bit-rate
Figure 4: Simulation Results in a French Telco-CDN
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 22 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Computation Time of Heuristic
40 60 80 1000
2
4
6
8
10
number of video channels
com
putin
gtim
e(s
econ
ds)
JOP-heu SOP1-heu SOP2-heu
(a) Computing time in French-CDN (16nodes)
Figure 5: Average Computing Time (seconds) on Real-Scale Systems: 30 ∼ 105channels, video bitrate 2048 kbps
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 23 / 99
Delivery of Multiple Video Channels in Telco-CDNs
Summary of Video Delivery in Telco-CDNs
Joint optimization of Video Delivery
Delivery of multiple video channels in Telco-CDNs
Joint optimization vs. two-step optimization
JOP serves 1/3 more channels, and also time-efficient
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 24 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 25 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Wireless Sensor Networks (WSNs)
Applications
Environment monitoring: forest, pollution etc.
Health monitoring
Habitat monitoring
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 26 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Data Collection and Transmission
Data Gathering Tree
Data collection in each time slot
Data transmission: many-to-one communications
Tree optimization: maximize lifetime
s
1
32
54
Figure 6: An example of a data-gathering tree
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 27 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Motivations
LiteratureOnly heuristic algorithms are proposed
Only simple energy consumption model is considered
Exact solution is missing except exhaustive search
Either routing or data aggregation is proposed for improving network lifetime
This workThree data aggregation techniques
Exact solution using MILP formulations
Joint optimal routing and data aggregation
Gain on network lifetime
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 28 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Maximum-Lifetime Data-Gathering Tree
Data Gathering Tree
Static sensor nodes: wireless + limited battery
Single sink: sensors report data to the sink in each time slot
Data aggregations
Data collection tree
Maximize network lifetime of tree (the number of time slots)
s
Figure 7: Data collection using a WSN
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 29 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Maximum-Lifetime Data-Gathering Tree
Sensor Lifetime (number of time slots)
Emission energy unit et /packet
Reception energy unit er/packet
Computing equation
LTv =
Ev
ntv · et + nr
v · er (6)
Network Lifetime (number of time slots)
The time duration until the first sensor node is out of battery,i.e., L = min
v∈VLT
v
Critical for full monitoring in WSNs
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 30 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Data Aggregation Techniques
Aggregation Modes
Full Aggregation Mode (FAM)
No Aggregation Mode (NAM)
Hybrid-Aggregation Mode (HAM) using Compressive Sensing
Figure 8: Comparison of different data compression methods
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 31 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Energy Consumption Model
Sensor Lifetime
LTv =
Ev
ntv · et + nr
v · er (7)
Full Aggregation Mode (FAM)
Statistical queries: sum, max, ...
LTv =
Ev
et + dTv · er (8)
dTv is the number of incoming links of sensor v in
tree T . In Fig. 9, dT1 = 2 for node 1 in FAM
s
1
32
54
Figure 9: A data-gathering tree
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 32 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Energy Consumption Model
Sensor Lifetime
LTv =
Ev
ntv · et + nr
v · er (9)
No Aggregation Mode (NAM)
No compression: Pictures, air parameters fordifferent regions, etc
LTv =
Ev
et + f Tv · (et + er)
(10)
f Tv denotes the number of sensors using v as a relay
to report data to s (including all descendants ofsensor v). In Fig. 10, f T
1 = 4 for node 1 in NAM
s
1
32
54
Figure 10: A data-gathering tree
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 33 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Energy Consumption Model
Sensor Lifetime
LTv =
Ev
ntv · et + nr
v · er (11)
Hybrid-Aggregation Mode (HAM)
Compressive Sensing (partial compression): oceandata
LTv =
Ev
minf Tv + 1, k · et + f T
v · er(12)
Let f Tv be the number of data units received from
the incoming links of sensor v. In Fig. 11, ifk = 4, then f T
1 = 4 for node 1.
s
1
32
54
Figure 11: A data-gathering tree
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 34 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Problem: Maximum-Lifetime Data-Gathering Tree
Given parameters
WSN topology G(V,E) and wireless transmission range
et and er
Data aggregation modes (FAM, NAM, HAM)
Energy consumption model
Objective
Find a data collection tree from sensors to the sink
Maximize network lifetime: max L
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 35 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Problem: Maximum-Lifetime Data-Gathering Tree
Challenges
NP-Hard
Different aggregation modes
Non-linear relationship between lifetime and the number of transmitted and receivedmessages in Eq. (13)
LTv =
Ev
ntv · et + nr
v · er (13)
Maximizing network lifetime (gathering tree)
Three MILP formulations
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 36 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Simulation Configurations
Parameters and ToolsInitial energy 1 J
Emitting energy et=6.4 µJ
Receiving energy et=12.8 µJ
100×100 m2 grid with an interval of 10 m
C++ and IBM ILOG CPLEX 12.2
EvaluationsNetwork lifetime vs. Number of sensors
Network lifetime vs. Transmission range
Network lifetime vs. Compression factor k
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 37 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Topologies
Sensors on the grid (100×100 m2)
Configuration I: Sink in the center
Configuration II: Sink at a corner
10
10
s
s
(I) Sink in the center (II) Sink at one corner
10
10
Figure 12: WSN grid topology with different sink positions
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 38 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Topologies
Sensors on the grid (100×100 m2)
Configuration I: Sink in the center
Configuration II: Sink at a corner
10
10
s
s
(I) Sink in the center (II) Sink at one corner
10
10
Figure 12: WSN grid topology with different sink positions
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 38 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Numerical Results
Results for Configuration I
20 25 30 35 40 450
2
4
6
8·104
number of sensor nodes (transmission range = 10)
netw
ork
lifet
ime
(min
utes
)
FAMNAM
HAM (k=2)HAM (k=3)
(a) Lifetime vs. # Sensors
10 15 20 25 30 35 40 450
2
4
6
8·104
transmission range (number of sensor nodes = 49)
netw
ork
lifet
ime
(min
utes
)
FAMNAM
HAM (k=2)HAM (k=3)
(b) Lifetime vs. Range
1 2 3 4 50
2
4
6
8·104
compressing factor k (transmission range =10)
netw
ork
lifet
ime
(min
utes
)
HAM (n=25)HAM (n=36)
(c) Lifetime vs. k
Figure 13: Simulation Results for Configuration I (sink at the center)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 39 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Data Accuracy vs. k
Table 2: Performance Evaluation of HAM (25 sensors, and sink node in center)
Metrics k = 1 k = 2 k = 3 k = 4 k = 5Lifetime 52083 26041 17361 13020 10416
Maximum Delay 10 10 10 8 6Data Accuracy 25% 36% 52% 72% 80%
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 40 / 99
Maximizing Lifetime for Data Collection in Wireless Sensor Networks
Summary of Data Collection
Data gathering tree with maximum network lifetime
Joint routing and data aggregation
Three MILP formulations
Network Lifetime increases fivefold
Tradeoff between data accuracy and network lifetime
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 41 / 99
Distance Spectrum Assignment in Elastic Optical Networks
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 42 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Motivations
Elastic Optical Networks (EONs)
Huge bandwidth
Low latency
Spectrum flexibility
Figure 14: EONs
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 43 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Motivations
Spectrum resource in optical fibers
Narrow-band (12.5GHz or less) frequencies→ Frequency Slots (FS’)
Flexibility
Limited number of FSs
12.5GHz for one subcarrier
1 2 3 4 … …
Frequency Slot (FS)
320… …
Figure 15: EONs and FSF. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 44 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Distance Spectrum Allocation (DSA) in EONs
Guard Band (GB)
Two requests (lightpaths) with common links
Interference Mitigation for QoT
Physical layer security
Heterogeneous GB size→ Spectrum efficiency
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 45 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Distance Spectrum Allocation (Thesis of Haitao Wu)
Spectrum Conflicts
Inside a lightpath: Spectrum continuity
Inside a lightpath: Spectrum contiguity
Between lightpaths: Guard Band (GB) separation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 46 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Conflict Graph G(V,E)v ∈ V: Vertices set with each node representing a request (lightpath)
e = (vi, vj) ∈ E: (vi, vj) exists if lightpaths vi and vj share common links
s ∈ N+: Index of an FS
v ∈ V: Vertices set with each node representing a request (lightpath)
vwi : Number of FSs required by request i
wvi : Set of contiguous FSs assigent for request i
vbi , v
ai : Begin/end index of FS assigned for request i
de: Least guard band size for separating lightpaths vi and vj
Figure 16: DSA conflict graph G(V,E, vwi , dvivj).
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 47 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Conflict Graph G(V,E)v ∈ V: Vertices set with each node representing a request (lightpath)
e = (vi, vj) ∈ E: (vi, vj) exists if lightpaths vi and vj share common links
s ∈ N+: Index of an FS
v ∈ V: Vertices set with each node representing a request (lightpath)
vwi : Number of FSs required by request i
wvi : Set of contiguous FSs assigent for request i
vbi , v
ai : Begin/end index of FS assigned for request i
de: Least guard band size for separating lightpaths vi and vj
Figure 16: DSA conflict graph G(V,E, vwi , dvivj).F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 47 / 99
Distance Spectrum Assignment in Elastic Optical Networks
DSA ModelObjective: Minimize the maximum FS index assigned
Minimize maxs∈(∪
vi∈Vwvi
)(s) (DSA), (14)
ConstraintsBandwidth Requirement Constraint
|wvi | = vwi , ∀vi ∈ V, (15)
Spectrum Continuity Constraint: satisfied automatically
Spectrum Contiguity Constraint: wvi =vbi , v
bi + 1, ..., va
i − 1, vai
Spectrum Distance Constraint
distance(wvi ,wvj ) ≥ dvivj , ∀vivj ∈ E, (16)
where,distance(wvi ,wvj ) = min
s ∈ wvi t ∈ wvj
(|s− t| − 1).
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 48 / 99
Distance Spectrum Assignment in Elastic Optical Networks
DSA ModelObjective: Minimize the maximum FS index assigned
Minimize maxs∈(∪
vi∈Vwvi
)(s) (DSA), (14)
ConstraintsBandwidth Requirement Constraint
|wvi | = vwi , ∀vi ∈ V, (15)
Spectrum Continuity Constraint: satisfied automatically
Spectrum Contiguity Constraint: wvi =vbi , v
bi + 1, ..., va
i − 1, vai
Spectrum Distance Constraint
distance(wvi ,wvj ) ≥ dvivj , ∀vivj ∈ E, (16)
where,distance(wvi ,wvj ) = min
s ∈ wvi t ∈ wvj
(|s− t| − 1).
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 48 / 99
Distance Spectrum Assignment in Elastic Optical Networks
DSA Exampple: Input
Table 3: Four requests in a 4-cycle EON
Bandwidth Capacity RouteRequest R1 3 FS’ B-A-DRequest R2 2 FS’ C-B-ARequest R3 3 FS’ A-D-C-BRequest R4 1 FS C-B-A-D
Figure 17: Explicit routes for the above table.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 49 / 99
Distance Spectrum Assignment in Elastic Optical Networks
DSA Conflict Graph and Output
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 50 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Comparison of related coloring problems
Classical Coloring Fractional Traditional DSA(e.g., WA ) Coloring SA (this work)
Vertex Color One color Set of colors Set of colors Set of colorsColor Contiguity N/A No need Required RequiredColor Distance of Disjoint Disjoint Identical positive Various positiveAdjacent Vertices Disjoint Disjoint integer integers
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 51 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Hardness and Inapproximability
MHP: Minimum Hamitolion Path
Theorem 1
MHP ≤P DSA⇒ DSA is NP-hard.
Theorem 2
Unless NP ⊂ ZPP , no polynomial-time DSA heuristic algorithm APX can
guaranteeAPX(I)OPT(I)
within O(n1−ε) for all instances I, where n is the number
of vertices of I and ε > 0.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 52 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Hardness and Inapproximability
MHP: Minimum Hamitolion Path
Theorem 1
MHP ≤P DSA⇒ DSA is NP-hard.
Theorem 2
Unless NP ⊂ ZPP , no polynomial-time DSA heuristic algorithm APX can
guaranteeAPX(I)OPT(I)
within O(n1−ε) for all instances I, where n is the number
of vertices of I and ε > 0.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 52 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Upper and Lower Bounds
|opt(G)| : optimal solution of DSA problem
χ(G): chromatic number of G
∆(G): maximum nodal degree, χ(G) ≤ ∆(G) + 1
ψ ∈ Ψ(G): maximal clique / clique set
MHP(ψ): minimum Hamilton path length in ψ
ψw: sum of node weights in ψ
Theorem 3
Given any DSA conflict graph G, inequality (17) is held for the optimalsolution of the DSA problem.
maxψ∈Ψ(G)
|MHP(ψ)|+ ψw ≤ |opt(G)| ≤χ(G)−1∑
i=1
de′i+
χ(G)∑i=1
v′wi . (17)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 53 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Upper and Lower Bounds
|opt(G)| : optimal solution of DSA problem
χ(G): chromatic number of G
∆(G): maximum nodal degree, χ(G) ≤ ∆(G) + 1
ψ ∈ Ψ(G): maximal clique / clique set
MHP(ψ): minimum Hamilton path length in ψ
ψw: sum of node weights in ψ
Theorem 3
Given any DSA conflict graph G, inequality (17) is held for the optimalsolution of the DSA problem.
maxψ∈Ψ(G)
|MHP(ψ)|+ ψw ≤ |opt(G)| ≤χ(G)−1∑
i=1
de′i+
χ(G)∑i=1
v′wi . (17)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 53 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Upper and Lower Bounds
|opt(G)|: optimal solution of DSA problem
∆(G): maximum nodal degree in G, χ(G) ≤ ∆(G) + 1
Corollary 4
If G(V,E, vwi , dvivj) is a DSA graph, then |opt(G)| ≤
∆(G)∑i=1
dei +
∆(G)+1∑i=1
vwi .
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 54 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Two-phased Algorithm
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 55 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Algorithm Analysis
First Phase Greedy Algorithm (FPGA):
Theorem 5
If G(V,E, vwi , dvivj) is a complete DSA graph with triangle inequality
then the approximation ratio of FPGA is not bigger than12(dlog2 |V|e+ 1).
Theorem 6
If a DSA graph G(V,E, vwi , dvivj) is a bipartite graph whose vertex label
is well, then FPGA can get the optimal solution of G.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 56 / 99
Distance Spectrum Assignment in Elastic Optical Networks
The Numerical Results
Two-phase algorithm is compared with FPGA, ILP and PRA.
(a) 14 (b) 15 (c) 16
(d) 17 (e) 18 (f) 19
Figure 18: Six random graphs with 14-19 vertices.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 57 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Table 4: Numerical results for six random graphs
# vertex 14 15 16 17 18 19PRA 92.0 103. 101. 133. 125. 180.
FPGA 72.4 76.6 83.4 94.2 89.8 126.Two-phase 69.0 74.4 81.6 91.2 88.2 124.ILP-DSA 67.4 72.4 79.6 88.8 83.8 116.
14 15 16 17 18 190 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
Rel
ativ
ega
p
Two-phaseFPGAPRA
Figure 19: Relative gaps by Two-phase, FPGA and PRA.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 58 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Table 5: Numerical results for random complete graphs
# vertices 14 15 16 17 18 19PRA 168.8 193.8 237.6 238.6 283.0 290.3
FPGA 144.6 164.2 197.2 199.4 229.6 238.3Two-phase 143.2 163.2 196.2 196.6 226.8 233.6ILP-DSA 142.2 160.4 194.0 194.2 223.2 224.0
14 15 16 17 18 190 %
10 %
20 %
30 %
Rel
ativ
ega
p
Two-phaseFPGAPRA
Figure 20: Relative gaps by Two-phase, FPGA and PRA.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 59 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Figure 21: Six random graphs with 14 vertices cum edge number from 15 to 90
15 30 45 60 75 90
40
60
80
100
120
140
35
4858
82
102
136
35
4859
85
106
140
The number of edges
The
max
imum
FS’i
ndex
0 %
1 %
2 %
3 %
4 %
App
roxi
mat
ion
ratio
Two-phaseILP-DSAratio
Figure 22: Numerical results for Edge number scenario.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 60 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Table 6: Simulation results for NSFNET and US Backbone
NSFNET US Backbone
# request ILP-DSA Two-phased PRA # request ILP-DSA Two-phased PRA
10 29 29 29 10 33 33 33
20 72 72 76 30 186 189 197
30 153 153 177 50 351 363 462
40 200 201 252 100 — 1339 1898
50 420 423 500 150 — 2843 4666
60 — 469 602 200 — 3784 7743
70 — 598 805 250 — 6347 13020
80 — 890 1155 300 — 8140 17303
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 61 / 99
Distance Spectrum Assignment in Elastic Optical Networks
Summary
DSA in EONsNP-Hard and inapproximability
Lower and upper bounds
Near optimal two-Phase algorithm
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 62 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 63 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Optical DCNs Survivability (Thesis of Min JU)Link Failure
Construction, damagedconnectors ... ...
Node FailureNode equipment failure(transponder, switching) ... ...
Large Area DisasterDatacenter system damage,earthquake, flood ... ...
→ →
Most common!! Threat on Datacenter networks!!
Cables were cut by ship, 2017,Somalia. $10 million/day
Weather and climate disasters,2017, USA. $306 billion
A ”power surge” in one BritishAirways’ datacenter, 2017
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 64 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Optical DCNs Survivability (Thesis of Min JU)Link Failure
Construction, damagedconnectors ... ...
Node FailureNode equipment failure(transponder, switching) ... ...
Large Area DisasterDatacenter system damage,earthquake, flood ... ...
→ →
Most common!! Threat on Datacenter networks!!
Cables were cut by ship, 2017,Somalia. $10 million/day
Weather and climate disasters,2017, USA. $306 billion
A ”power surge” in one BritishAirways’ datacenter, 2017
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 64 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Optical DCNs Survivability (Thesis of Min JU)Link Failure
Construction, damagedconnectors ... ...
Node FailureNode equipment failure(transponder, switching) ... ...
Large Area DisasterDatacenter system damage,earthquake, flood ... ...
→ →
Most common!! Threat on Datacenter networks!!
Cables were cut by ship, 2017,Somalia. $10 million/day
Weather and climate disasters,2017, USA. $306 billion
A ”power surge” in one BritishAirways’ datacenter, 2017
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 64 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Optical DCNs Survivability (Thesis of Min JU)Link Failure
Construction, damagedconnectors ... ...
Node FailureNode equipment failure(transponder, switching) ... ...
Large Area DisasterDatacenter system damage,earthquake, flood ... ...
→ →
Most common!! Threat on Datacenter networks!!
Cables were cut by ship, 2017,Somalia. $10 million/day
Weather and climate disasters,2017, USA. $306 billion
A ”power surge” in one BritishAirways’ datacenter, 2017
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 64 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Large Area Disaster Failure in Datacenter Networks
Disasters: Volcan, Tsunamis, Hurricane, Flood, etc
Disaster zones: Set of OXC nodes and fibers
DC content survivability
Disaster-disjoint primary path and backup path
5
4
61
3
2
Disaster zone
Primary path 1-2
Backup path 1-3-5
Request at node 1 with content
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 65 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Path Protection against Disaster Failure
5
4
61
3
2
Disaster zonePrimary path 1-2
Backup path 1-3-5 Content
Primary path 1-4
Backup path 1-3-5
5
4
61
3
2
DEBPP SEBPP
r1 r2
1
1
21 21
1
1
11
Data center with content replia
The same content can be replicated at multiple DC nodes.
Anycast routing, i.e., from one to one of many
One to one of many: the service can be provisioned from any of the DC withcontent replica.
DEBPP (Dedicated end-to-content backup path protection)
SEBPP (Shared end-to-content backup path protection)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 66 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Path Protection against Disaster Failure
5
4
61
3
2
Disaster zonePrimary path 1-2
Backup path 1-3-5 Content
Primary path 1-4
Backup path 1-3-5
5
4
61
3
2
DEBPP SEBPP
r1 r2
1
1
21 21
1
1
11
Data center with content replia
The same content can be replicated at multiple DC nodes.
Anycast routing, i.e., from one to one of many
One to one of many: the service can be provisioned from any of the DC withcontent replica.
DEBPP (Dedicated end-to-content backup path protection)
SEBPP (Shared end-to-content backup path protection)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 66 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Disaster-aware Path Protection Schemes in the Literature
ILP Heuristics
SLR WDM
[C. Develder et al, Trans. Netw., 2014] [C. Develder et al, Trans. Netw., 2014][M. F. Habib et al, J. Lightw. Technol., 2012] [M. F. Habib et al, J. Lightw. Technol., 2012]
[S. S. Savas et al, Photon. Netw. Commun., 2014] [S. S. Savas et al, Photon. Netw. Commun., 2014][S. S. Savas et al, Photon. Netw. Commun., 2016] [S. S. Savas et al, Photon. Netw. Commun., 2016]
EON
[R. Xu et al, Optoel. Global Conf., 2016][C. Ma et al, Photon. Netw. Commun., 2015] [C. Ma et al, Photon. Netw. Commun., 2015]
[X. Li et al, Opt. Express, 2016] [X. Li et al, Opt. Express, 2016][B. Chen et al, Photon. Netw. Commun., 2017]
ILP formulation: not scalable
Heuristics: not tractable
Impacts of No. DC and replica: not yet studied
Comparison of protection techniques: missing
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 67 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Objective and Constraints
Inputs:
Set of disaster zones (DZs)
Set of requests and their requiredcontent
Number of DCs and content replica (k)
EON topology and set of FSs
Output:
DC location
Placement of content replica
Disaster-disjoint primary and backuppaths
FS allocation
Objective: Minimize total spectrum usage for disaster protection
Single disaster zone protection
DEBPP vs. SEBPP
Impacts of No. Dc and replica
Scalable and tractable approach
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 68 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Objective and Constraints
Inputs:
Set of disaster zones (DZs)
Set of requests and their requiredcontent
Number of DCs and content replica (k)
EON topology and set of FSs
Output:
DC location
Placement of content replica
Disaster-disjoint primary and backuppaths
FS allocation
Objective: Minimize total spectrum usage for disaster protection
Single disaster zone protection
DEBPP vs. SEBPP
Impacts of No. Dc and replica
Scalable and tractable approach
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 68 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Objective and Constraints
Inputs:
Set of disaster zones (DZs)
Set of requests and their requiredcontent
Number of DCs and content replica (k)
EON topology and set of FSs
Output:
DC location
Placement of content replica
Disaster-disjoint primary and backuppaths
FS allocation
Objective: Minimize total spectrum usage for disaster protection
Single disaster zone protection
DEBPP vs. SEBPP
Impacts of No. Dc and replica
Scalable and tractable approach
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 68 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 1: Joint ILP Formulation
Ojective: Link-FSs Max-FSs
Minimize θ1 · (∑a∈A
∑r∈R
pWra · φr +
∑a∈A
Ta) + θ2 ·∆
Constraints:(1) Datacenter and content assignment
(2) Disaster-disjoint path generation
(3) Spectrum allocation
Computational complexity
DEBPP
No. of dominant variablesO(|R|2, |R||A|, |R||Z|, |C||D|)No. of dominant constraintsO(|R|2|A|, |R||Z||A|)
SEBPP
No. of dominant variablesO(|R|2, |R||A|, |R||Z|, |C||D|)No. of dominant constraintsO(|R|2|A|, |R|2|Z|, |R||Z||A|)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 69 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 1: Joint ILP Formulation
Ojective: Link-FSs Max-FSs
Minimize θ1 · (∑a∈A
∑r∈R
pWra · φr +
∑a∈A
Ta) + θ2 ·∆
Constraints:(1) Datacenter and content assignment
(2) Disaster-disjoint path generation
(3) Spectrum allocation
Computational complexity
DEBPP
No. of dominant variablesO(|R|2, |R||A|, |R||Z|, |C||D|)No. of dominant constraintsO(|R|2|A|, |R||Z||A|)
SEBPP
No. of dominant variablesO(|R|2, |R||A|, |R||Z|, |C||D|)No. of dominant constraintsO(|R|2|A|, |R|2|Z|, |R||Z||A|)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 69 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
Step 2: Initial solution
Dijkstra’s
shortest path
algorithm
Initial columns
Step 3: Master problem
Solving linear relaxation of
master problem
Get low bound and
dual variables
Step 4: Pricing problem
Solving pricing problem
with ESWBP algorithm
Reduced cost < 0 ?Yes No
Step 5: Final solution
Solving master
problem
Integer solution
Add
new
columns
Integerizing all the
relaxed variables
Step 1: DC assignment
and content placement
Content placement with
content protection ILP model
in [Habib et al., 2012]
DC nodes and content replicas
Column generation
procedure
Advantages of CG
Scalable iterative optimization
Lower bound z∗
ρ-optimum, ρ ≤ (z− z∗)/z∗
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
2
68
1
4
75
3
DC
DC
DC
Contents
Step 1: DC assignment and content placement
K DC nodes: Average minimum distance
Place content replica in DCs closer to its popular region
Habib et al. Design of disaster-resilient optical DC networks. J. Lightw. Technol., 2012.F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
2
68
1
4
75
3
DC
DC
DC
Contents
R1 at node 8: 3 spectrum slots
Primary path: 8-1-2 with spectrum
Backup path: 8-7-6-5 with spectrum
1 2 3
1 2 3
Step 2: Initial solution
Primary path and backup path via Dijkstra’s shortest path
Spectrum usage allocation with coloring heuristic
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
2
68
1
4
75
3
DC
DC
DC
Contents R1 at node 8: 3 spectrum slots
Output:
Configuration 1:
Primary path: 8-1-2 with spectrum
Backup path: 8-7-6-5 with spectrum
1 2 3
1 2 3
Input:
Configuration 1:
Primary path: 8-1-2 with spectrum
Backup path: 8-7-6-5 with spectrum
1 2 3
1 2 3
… …
Step 3: Master problemA configuration ωr for request r:
1 Primary path and backup path2 Spectrum usage for primary and
backup paths
Input: ∀r ∈ R, ωr
Output: Final primary and backup pathsand associated spectrum
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
2
68
1
4
75
3
DC
DC
DC
Contents R1 at node 8: 3 spectrum slots
Output:
Configuration 1:
Primary path: 8-1-2 with spectrum
Backup path: 8-7-5 with spectrum
1 2 3
1 2 3
Primary path: 8-1-2 with spectrum
Backup path: 8-7-5 with spectrum
2 3 4
1 2 3
New configuration 2:
New configuration 3:
… …
Primary path: 8-1-2 with spectrum
Backup path: 8-7-6-5 with spectrum
1 2 3
1 2 3
Step 4: Pricing problem (k shortest paths)
Input: R, G(V,A), Disaster zones
Output: Configuration ωr, ∀r ∈ R
1 Primary path and backup path of ∀r ∈ R
2 Spectrum usage on primary path of ∀r ∈ R
3 Spectrum usage on backup path of ∀r ∈ R
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Methodology 2: Column Generation (CG)
Step 2: Initial solution
Dijkstra’s
shortest path
algorithm
Initial columns
Step 3: Master problem
Solving linear relaxation of
master problem
Get low bound and
dual variables
Step 4: Pricing problem
Solving pricing problem
with ESWBP algorithm
Reduced cost < 0 ?Yes No
Step 5: Final solution
Solving master
problem
Integer solution
Add
new
columns
Integerizing all the
relaxed variables
Step 1: DC assignment
and content placement
Content placement with
content protection ILP model
in [Habib et al., 2012]
DC nodes and content replicas
Column generation
procedure
Step 5: Final solution
Convert all variables to integer
Solve the master problem again
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 70 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Numerical results: Simulation settings
NSFNET network14 nodes, 44 links3.1 nodal degree, 14 DZs
6
87
54
3
1
14
13
1112
9
10
2
US Backbone network28 nodes, 90 links3.2 nodal degree, 15 DZs
26
28
27
1094 61
1423
2115 7
24
1215
25
8
13 18
1619
21
22
20
317
DZ
Hardware: 3.5 GHz CPU, 8 GBytes RAM
Software: CPLEX 12.06
Traffic
FSs: randomly [1, 10]No. requests: [10, 100]
Parameters:
300 Available FSs10 Available contentcontent replicas K
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 71 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Spectrum usage of DEBPP and SEBPP vs. # requests
No. RequestsJoint ILP models CG approach
GapzILP
1h FStotal FSlink tILP zLP zCG1h FSlink FSmax tCG tCG
LPR tCGILP
10DEBPP 290 260 30 8s 312 312 270 42 1s 1s 0s 7.59%SEBPP 253 233 20 448s 275 275 243 32 5s 5s 0s 8.70%
20DEBPP 448 412 36 3600s 488 493 431 62 6s 6s 0s 10.04%SEBPP 379 345 34 3600s 424.733 432 388 44 7s 7s 0s 13.98%
30DEBPP 663 613 50 3600s 691.998 700 630 70 7s 7s 0s 5.58%SEBPP 614 570 44 3600s 608 630 572 58 23s 23s 0s 2.61%
40DEBPP 867 792 75 3600s 898.389 912 826 86 54s 8s 46s 5.19%SEBPP 832 765 67 3600s 761.612 792 719 73 49s 44s 5s -
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 72 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
SEBPP spectrum usage vs. # DCs and # content replica K
US BackboneNo. of DCs Location of DCs
4 Nodes 1, 12, 21, 286 Nodes 1, 7, 14, 19, 21, 288 Nodes 1, 7, 9, 12, 14, 19, 21, 28
10 Nodes 1, 3, 7, 9, 12, 14, 19, 21, 24, 28
20 40 60 80
1,000
2,000
3,000
No. of Requests
Tota
lFSs
Usa
ge
DC4DC6DC8
(a) FSs vs. # DCs
20 40 60 80
1,000
2,000
3,000
No. of Requests
Tota
lFSs
Usa
ge
K=2K=3K=4K=5
(b) FSs vs. # K (6 DCs)
20 40 60 80
1,000
2,000
3,000
No. of Requests
Tota
lFSs
Usa
ge
K=2K=4K=6K=8
(c) FSs vs. # K (8 DCs)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 73 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Summary of Disaster Protection
Comparison of Protection Techniques
Spare capacity efficiency: SEBPP > DEBPP > p-Cycle
Recovery speed: DEBPP > p-Cycle > SEBPP
DEBPP vs. SEBPP, less spectrum usage, higher computation complexities.
Impacts on Spectrum usage
Reasonable # DCs,→ spectrum savings.
Reasonable # content replica k→ spectrum savings.
Optimization
ρ-optimum CG approach
Scalable for large disaster failure in DCNs
Path generation
Spectrum allocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 74 / 99
Disaster-Resilient Service Provisioning in Optical Datacenters Networks
Summary of Disaster Protection
Comparison of Protection Techniques
Spare capacity efficiency: SEBPP > DEBPP > p-Cycle
Recovery speed: DEBPP > p-Cycle > SEBPP
DEBPP vs. SEBPP, less spectrum usage, higher computation complexities.
Impacts on Spectrum usage
Reasonable # DCs,→ spectrum savings.
Reasonable # content replica k→ spectrum savings.
Optimization
ρ-optimum CG approach
Scalable for large disaster failure in DCNs
Path generation
Spectrum allocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 74 / 99
Conclusions and Perspectives
1 Curriculum Vitae
2 Introduction
3 Delivery of Multiple Video Channels in Telco-CDNs
4 Maximizing Lifetime for Data Collection in Wireless Sensor Networks
5 Distance Spectrum Assignment in Elastic Optical Networks
6 Disaster-Resilient Service Provisioning in Optical Datacenters Networks
7 Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 75 / 99
Conclusions and Perspectives
Conclusions
1: Video Delivery in Telco-CDNs
Overlay construction (Thesis of J. Liu)
Bandwidth allocation
2: Data Collection in WSNsGathering tree
Data aggregation
Energy allocation (lifetime)
3: DSA in EONsSpectrum allocation (Thesis of H. Wu)
Distance constraint
4: Protection in Optical DCNs
Replica placement (Thesis of M. Ju)
Path protection against diasters
Frequency slot allocationwwOptimization of routing and resource allocation
Tools: ILP, CG, heuristic, approximation algorithm
Optimization techniques do help!
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 76 / 99
Conclusions and Perspectives
Conclusions
1: Video Delivery in Telco-CDNs
Overlay construction (Thesis of J. Liu)
Bandwidth allocation
2: Data Collection in WSNsGathering tree
Data aggregation
Energy allocation (lifetime)
3: DSA in EONsSpectrum allocation (Thesis of H. Wu)
Distance constraint
4: Protection in Optical DCNs
Replica placement (Thesis of M. Ju)
Path protection against diasters
Frequency slot allocationwwOptimization of routing and resource allocation
Tools: ILP, CG, heuristic, approximation algorithm
Optimization techniques do help!
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 76 / 99
Conclusions and Perspectives
Conclusions
1: Video Delivery in Telco-CDNs
Overlay construction (Thesis of J. Liu)
Bandwidth allocation
2: Data Collection in WSNsGathering tree
Data aggregation
Energy allocation (lifetime)
3: DSA in EONsSpectrum allocation (Thesis of H. Wu)
Distance constraint
4: Protection in Optical DCNs
Replica placement (Thesis of M. Ju)
Path protection against diasters
Frequency slot allocationwwOptimization of routing and resource allocation
Tools: ILP, CG, heuristic, approximation algorithm
Optimization techniques do help!
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 76 / 99
Conclusions and Perspectives
Conclusions
1: Video Delivery in Telco-CDNs
Overlay construction (Thesis of J. Liu)
Bandwidth allocation
2: Data Collection in WSNsGathering tree
Data aggregation
Energy allocation (lifetime)
3: DSA in EONsSpectrum allocation (Thesis of H. Wu)
Distance constraint
4: Protection in Optical DCNs
Replica placement (Thesis of M. Ju)
Path protection against diasters
Frequency slot allocation
wwOptimization of routing and resource allocation
Tools: ILP, CG, heuristic, approximation algorithm
Optimization techniques do help!
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 76 / 99
Conclusions and Perspectives
Conclusions
1: Video Delivery in Telco-CDNs
Overlay construction (Thesis of J. Liu)
Bandwidth allocation
2: Data Collection in WSNsGathering tree
Data aggregation
Energy allocation (lifetime)
3: DSA in EONsSpectrum allocation (Thesis of H. Wu)
Distance constraint
4: Protection in Optical DCNs
Replica placement (Thesis of M. Ju)
Path protection against diasters
Frequency slot allocationwwOptimization of routing and resource allocation
Tools: ILP, CG, heuristic, approximation algorithm
Optimization techniques do help!
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 76 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
Perspectives
Similar optimization techniques will also be helpful to solve:⇓
Physical-layer security in EONs
Threats: attacks, interferences
Routing, spectrum assignment andprotection
QoE for 360 video streaming
QoE
360 video delivery
Intelligent transportation systems
Road security via VANETs
Car redistribution for carsharing
Hazardous transportation
Network function virtualizationNetwork embedding
Service function chain provision
+ new directionBi-level optimization for ITS and green networking.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 77 / 99
Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 78 / 99
Conclusions and Perspectives
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 79 / 99
Overview of Research Activities
Overview of Research Activities
Routing optimization and resource allocation
Optical networks, RF/VLC HetNets
Wireless ad-hoc networks (VANET, WSN et MANET)
Content delivery networks
Intelligent transportation systems
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 80 / 99
Overview of Research Activities
Optical Networks and Datacenter Networks
ProblemsRouting and spectrum assignment (RSA)
Survivability and security
Multicast, network functionvirtualization,
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 81 / 99
Overview of Research Activities
Optical Networks and Datacenter Networks
ProblemsRouting and spectrum assignment (RSA)
Survivability and security
Multicast, network functionvirtualization,
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 81 / 99
Overview of Research Activities
Optical Networks and Datacenter Networks
ProblemsRouting and spectrum assignment (RSA)
Survivability and security
Multicast, network functionvirtualization,
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 81 / 99
Overview of Research Activities
Wireless Ad-Hoc Networks
ProblemsVANETs: Routing for thedissemination of safety messages
WSNs: Data gathering andaggregation
ProblemsMANETs: Malicious nodedetection
RF/VLC HetNets: Resourceallocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 82 / 99
Overview of Research Activities
Wireless Ad-Hoc Networks
ProblemsVANETs: Routing for thedissemination of safety messages
WSNs: Data gathering andaggregation
ProblemsMANETs: Malicious nodedetection
RF/VLC HetNets: Resourceallocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 82 / 99
Overview of Research Activities
Content Delivery Networks
ProblemsVideo streaming using rateless coding
Overlay optimization
Bandwidth allocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 83 / 99
Overview of Research Activities
Content Delivery Networks
ProblemsVideo streaming using rateless coding
Overlay optimization
Bandwidth allocation
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 83 / 99
Overview of Research Activities
Intelligent Transportation Systems (ITS)
ProblemsCar relocation optimization forcar-sharing systems
Personalized visit tours
Hazardous transport design
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 84 / 99
Overview of Research Activities
Intelligent Transportation Systems (ITS)
ProblemsCar relocation optimization forcar-sharing systems
Personalized visit tours
Hazardous transport design
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 84 / 99
Overview of Research Activities
Intelligent Transportation Systems (ITS)
ProblemsCar relocation optimization forcar-sharing systems
Personalized visit tours
Hazardous transport design
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 84 / 99
Overview of Research Activities
Intelligent Transportation Systems (ITS)
ProblemsCar relocation optimization forcar-sharing systems
Personalized visit tours
Hazardous transport design
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 84 / 99
Additional Slides for Data Collection Trees in WSNs
MILP for FAM
max L (FAM-MIP) (18)
s.t. constraints (19)-(27).
∑v∈V
∑a∈δ+(v)
Xa = n, (19)
∑a∈δ−(s)
Fa = n, (20)
∑a∈δ+(v)
Fa −∑
a∈δ−(v)
Fa = 1, ∀v (21)
Xa ≤ Fa, ∀a (22)
Xa ≥1
nFa, ∀a (23)∑
a∈δ−(v) Xa − i + 12
dv≤ Bi
v, ∀v, ∀i ∈ Jdv − 1K (24)
∑a∈δ−(v) Xa − i + 1
2
dv≥ Bi
v − 1, ∀v, ∀i ∈ Jdv − 1K (25)
Ev − (et + i · er)Lv
M1v
≥ Biv − 1, ∀v, ∀i ∈ Jdv − 1K (26)
L ≤ Lv, ∀v (27)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 85 / 99
Additional Slides for Data Collection Trees in WSNs
MILP for NAM
max L (NAM-MIP) (28)
s.t. constraints (29)-(37).
∑v∈V
∑a∈δ+(v)
Xa = n, (29)
∑a∈δ−(s)
Fa = n, (30)
∑a∈δ+(v)
Fa −∑
a∈δ−(v)
Fa = 1, ∀v (31)
Xa ≤ Fa, ∀a (32)
Xa ≥1
nFa, ∀a (33)∑
a∈δ−(v) Fa − i + 12
n≤ Bi
v, ∀v, ∀i ∈ Jn− 1K (34)∑a∈δ−(v) Fa − i + 1
2
n≥ Bi
v − 1, ∀v, ∀i ∈ Jn− 1K (35)
Ev −(
et + i(et + er))
Lv
M2v
≥ Biv − 1, ∀v, ∀i ∈ Jn− 1K (36)
L ≤ Lv, ∀v (37)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 86 / 99
Additional Slides for Data Collection Trees in WSNs
MILP for HAM (part 1)
Flow Constraintsmax L (HAM-MIP) (38)
s.t. constraints (39)-(52).
∑v∈V
∑a∈δ+(v)
Xa = n, (39)
∑a∈δ−(v)
Fa ≤ (k − 1) + (n− k)Hkv , ∀v (40)
∑a∈δ−(v)
Fa ≥ k · Hkv , ∀v (41)
∑a∈δ+(v)
Fa −∑
a∈δ−(v)
Fa ≥ 1− (n− k)Hkv , ∀v (42)
∑a∈δ+(v)
Fa ≥ (k − 1)Hkv + 1, ∀v (43)
Xa ≥1
kFa, ∀a (44)
Xa ≤ Fa, ∀a (45)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 87 / 99
Additional Slides for Data Collection Trees in WSNs
MILP for HAM (part 2)
Energy Constraints (Linearization)max L (HAM-MIP) (46)
s.t. constraints (39)-(52).
Ev − (i · et + j · er)Lv
M3v
≥ Biv + Bj
v − 2, ∀v, ∀i ∈ JkK,
∀j ∈ Jn− 1K (47)∑a∈δ+(v) Fa − i + 1
2
k + 1≤ Bi
v, ∀v, ∀i ∈ JkK (48)
∑a∈δ+(v) Fa − i + 1
2
k + 1≥ Bi
v − 1, ∀v, ∀i ∈ JkK (49)
∑a∈δ−(v) Fa − j + 1
2
n≤ Bj
v, ∀v, ∀j ∈ Jn− 1K (50)∑a∈δ−(v) Fa − j + 1
2
n≥ Bj
v − 1, ∀v, ∀j ∈ Jn− 1K (51)
L ≤ Lv, ∀v (52)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 88 / 99
Additional Slides for Disaster Failure Protection (DFP)
Why not p-Cycle Protection?
2
68
1
4
75
3
P-Cycle 1-2-3-6-7-8
Working path 7-5
Protection path 7-6-3-2
p-Cycle vs. DEBPP vs. SEBPP
Drawbacks: Waste spare capacity
Backup Datacenter on p-cycle
Inefficient spare capacity sharing
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 89 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Joint ILP Formulation—DEBPP & SEBPP
Ojective: Link-FSs Max-FSs
Minimize θ1 · (∑a∈A
∑r∈R
pWra · φr +
∑a∈A
Ta) + θ2 ·∆
Constraints1.DC assignment and contentplacement constraints
∑d∈D
ΛWrd = 1, ∀r (53)
∑d∈D
ΛBrd = 1, ∀r (54)
∑d∈D
Rcd ≤ K, ∀c (55)
ΛWrd + Λ
Brd ≤ Rcr
d , ∀r, ∀d (56)
2.Flow-conservation constraints
∑a∈Ψ
+v
pWra −
∑a∈Ψ−v
pWra =
1, v = sr
− ΛWrv , v ∈ D, ∀r, ∀v.
0, otherwise
(57)
∑a∈Ψ
+v
pBra −
∑a∈Ψ−v
pBra =
1, v = sr
− ΛBrv, v ∈ D, ∀r, ∀v.
0, otherwise
(58)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 90 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Joint ILP Formulation—DEBPP+SEBPP
Ojective: Link-FSs Max-FSs
Minimize θ1 · (∑a∈A
∑r∈R
pWra · φr +
∑a∈A
Ta) + θ2 ·∆
Constraints
3.Disaster-zone-disjoint pathconstraints
αWrz ≤
∑a∈z
pWra, ∀r, ∀z (59)
αWrz ≥ pW
ra, ∀r, ∀z, ∀a ∈ z (60)
αBrz ≤
∑a∈z
pBra, ∀r, ∀z (61)
αBrz ≥ pB
ra, ∀r, ∀z, ∀a ∈ z (62)
αWrz + α
Brz ≤ 1, ∀r, ∀z (63)
4.Spectrum allocation constraintspW
ra + pWr′a − 1 ≤ γW
rr′ , ∀r, r′, r > r′, ∀a (64)
γWrr′ = γ
Wr′r, ∀r, r′, r > r′ (65)
pBra + pB
r′a − 1 ≤ γBrr′ , ∀r, r′, r > r′, ∀a (66)
γBrr′ = γ
Br′r, ∀r, r′, r > r′ (67)
pWra + pB
r′a − 1 ≤ γWBrr′ , ∀r, r′, r 6= r′, ∀a (68)
βWrr′ + β
Wr′r = 1, ∀r, r′, r > r′ (69)
βBrr′ + β
Br′r = 1, ∀r, r′, r > r′ (70)
gWr + φr ≤ ∆, ∀r (71)
gBr + φr ≤ ∆, ∀r (72)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 91 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Column Generation (CG)Step 1: DC assignment
Minimize∑d∈V′
∑r∈R
Hs,d · Rc,r
∑d∈V′
Rc,r = K, ∀c (73)
∑d∈z
Rc,r ≤ 1, ∀c, ∀z (74)
a aFarhan Habib, et al, J.Lightw. Technol., 2012.
Step 2: Initial solution
Computing Initial primary path and backup path
1 for each r2 Traditional Dijkstra’s shortest path to compute primary path3 Calculate threat disaster zones4 remove all the links in the threat disaster zones5 Traditional Dijkstra’s shortest path to compute backup path
Allocation spectrum usage
1 Construct the conflict graph among the primary path and backup paths2 Coloring heuristic
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 92 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Column Generation (CG)
Step 3: Master problem
Spectrum channel H: a set of contiguous spectrum.For example, H for a request with 2 FSs:1, 1, 0, 0, 0, ..., 0, 0,0, 1, 1, 0, 0, ..., 0, 0,0, 0, 1, 1, 0, ..., 0, 0,· · · · · · ,0, 0, 0, 0, 0, ..., 1, 1.A configuration ωr for request r:
1 primary path and backup path2 spectrum channels for primary and backup paths
Variables:
1 qωr ∈ 0, 1: Equals 1 if ω-th configuration for request r is used including theworking path, backup path and assigned channels, and 0 otherwise.
2 eaf ∈ 0, 1: Equals 1 if link a with FS f is used by the working or backup pathsof all the requests, and 0 otherwise.
3 of ∈ 0, 1: Equals 1 if FS f is used, and 0 otherwise.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 93 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Column Generation (CG)
Step 3: Master problemOjective: Link-FSs Max-FSs
Minimize θ1 ·∑a∈A
∑f∈S
eaf + θ2 ·∑f∈S
of
Constraints:
1.DEBPP
∑ω∈Ωr
qωr = 1, ∀r (75)
∑r∈R
∑ω∈Ωr
(pWωrah + pB
ωrah′ ) · qωr ≤ eaf , ∀a, ∀f ∈ Bh, Bh′
(76)
of ≥ eaf , ∀a, ∀f (77)
of ≥ of+1, ∀f (78)
2.SEBPP
∑ω∈Ωr
qωr = 1, ∀r
(79)∑r∈R
∑ω∈Ωr
pWωrah · qωr ≤ eaf , ∀a, ∀f ∈ Bh (80)
∑r∈R
∑ω∈Ωr
pWωrah · (1− αW
ωrz) + pBωrah′ · α
Wωrz · qωr ≤ eaf ,
∀a, ∀f ∈ Bh, Bh′ , ∀z (81)
of ≥ eaf , ∀a, ∀f(82)
of ≥ of+1, ∀f(83)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 94 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Column Generation (CG)Step 4: Pricing problem
Dual variables:
1 µr : dual variable for DEBPP and SEBPP2 ζaf ≥ 0 : dual variable for DEBPP3 ρaf ≥ 0 : dual variable for SEBPP4 ηafz ≥ 0 : dual variable for SEBPP
Reduced cost for DEBPP:
cDEBPPωr
= 0− µr −∑a∈A
∑f∈Bh∪Bh′
(pWωrah + pB
ωrah′ ) · ζaf = −µr +∑a∈A
pWωrah · CostWωrah +
∑a∈A
pBωrah′ · CostBωrah′
CostWωrah =∑
f∈Bh
ζaf CostBωrah′ =∑
f∈Bh′
ζaf (84)
Reduced cost for SEBPP:
cSEBPPωr
= 0−(µr −
∑a∈A
∑f∈Bh
pWωrah · ρaf −
∑a∈A
∑f∈Bh∪Bh′
∑z∈Z
pWωrah · (1− αW
ωrz)− pBωrah′ · α
Wωrz
· ηafz
)
= −µr +∑a∈A
pWωrah · CostWωrah +
∑a∈A
pBωrah′ · CostBωrah′ (85)
CostWωrah =∑
f∈Bh
ρaf +∑
f∈Bh∪Bh′
∑z∈Z
(1− αWωrz) · ηafz CostBωrah′ =
∑f∈Bh∪Bh′
∑z∈Z
αWωrz · ηafz (86)
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 95 / 99
Additional Slides for Disaster Failure Protection (DFP)
Disaster Failure: Column Generation (CG)
Step 4: Pricing problemConfiguration ωr in DEBPP
1 For each d ∈ D2 For each d′ ∈ D, d′ 6= d3 For each h ∈ Hr4 For each h′ ∈ Hr5 Calculate shortest path with
CostWωrah
6 Calculate threat disaster zones7 remove all the links in the threat
disaster zones8 Calculate shortest path with
CostBωrah′
Configuration ωr in SEBPP
1 For each d ∈ D2 For each d′ ∈ D, d′ 6= d3 For each h ∈ Hr4 For each h′ ∈ Hr5 Calculate K=2 shortest path with
hop count6 Calculate threat disaster zones7 remove all the links in the threat
disaster zones8 Calculate shortest path with
CostBωrah′
Step 5: Final solution
Convert all variables to integer
Solve the master problem again
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 96 / 99
Additional Slides for DSA Problem
Ordered Distance Spectrum Assignment (ODSA)
Giving a G(V,E, vwi , dvivj) with a vertex order Oi,
the beginning FS indices for each vertex are sorted in the increaseing order inthe final solution i.e.,
Oi = (vi1 , vi2 , ..., vin) : vbij ≥ vb
ik , ∀j > k (87)
where, vbij and vb
ik is the beginning FS’ index of the contiguous FS’ setassigned to vij and vik respectively.
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 97 / 99
Additional Slides for DSA Problem
Input : A DSA graph G(V,E, vwi , dvivj), and a vertex order Oi = (vi1 , vi2 , ..., vin)
Output: An assignment strategy for the beginning index Seq = vbij : 1 ≤ j ≤ n and the maximum
FS’ indexvb
i1 ← 1;va
i1 ← vwi1 ;
Seq← vbi1 ;
j← 2;while j ≤ n do
s1 ← max∀k<j,vik vij∈E
vaik + dvik vij
+ 1;
s2 ← vbij−1
;vb
ij ← maxs1, s2;va
ij ← vbij + vw
ij − 1;Seq← Seq ∪ vb
ij;j← j + 1;
endreturn Seq and max
1≤j≤n(va
ij)
Algorithm 1: Procedure O-L
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 98 / 99
Additional Slides for DSA Problem
The time complexity of Procedure O-L is O(|E|)
Theorem 7
The Procedure O-L results in an optimal spectrum assignment strategy for theODSA.
Corollary 8A DSA problem can be optimally solved by the Procedure O-L under certainvertex order.
Now, DSA has been transform to a Permutation-based Optimization Problem(POP).
F. Zhou (ISEP/UAPV) HDR Defence Sept. 26, 2018 99 / 99