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Resolve the Virtual Network Embedding Problem: A Column Generation Approach. Qian Hu, Yang Wang, Xiaojun Cao Department of Computer Science Georgia State University Atlanta, GA, 30303. What is Network Virtualization?. - PowerPoint PPT Presentation
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Resolve the Virtual Network Embedding Problem: A Column Generation Approach
Qian Hu, Yang Wang, Xiaojun Cao Department of Computer Science
Georgia State UniversityAtlanta, GA, 30303
2Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
ISP Decoupling: Infrastructure Providers (InPs) and Service Providers (SPs)
InPs: manage the physical infrastructureSPs: operate virtual network, offer E2E user services
What is Network Virtualization?
A programmable infrastructure InPs resources efficient utilization
Hardware, energy, recovery
SPs can deploy services fast No high initial investments on the infrastructuresFlexible deploymentDisruptive technologies deployed by InPs will not affect
supported services
3Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Virtual Network Embedding Problem Given the virtual network (VN) request GV = (NV , LV ), and substrate network GS = (NS , LS ),
Objective: Map the VN with least cost
Constraints: Node Computing:
One virtual node mapped onto one substrate nodeNo two virtual nodes share the same substrate node;
Link/path bandwidth capacityOne virtual link mapped to substrate links or path(s)
Others such as location, protection
4Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Bridging SP and InP: Virtual Network EmbeddingVirtual Network: the logical network of SP
Substrate Network: the physical network of InP
2 20
2026
30
30
520
20
40
20
4
83
85
6
5Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Literature WorkVirtual Network Embedding (VNE): NP-Complete
Optimal solutions from link-based ILP [Chowdhury etc, INFOCOM’09]
Extensive computational timeNot practical
Heuristic approaches Relaxation of link-based ILP [Chowdhury etc, INFOCOM ’09]
Others [e.g., Lischka etc, ACM VISA’09]
Not optimalNot sure how far away from optimal
6Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Major Contributions of Our WorkPropose path-based ILP model for VNE problem
Propose a column generation processIntegrated with a branch-and-bound framework
Resolve the VNE problem optimally in practiceObtain sub-optimal results with guaranteed performance (with branch-and-bound)
7Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Network Embedding: Network Flow ModelVirtual
Network
Substrate Network
a
b c
4
2
5
3
1
4
2
5
3
1
a
b
c
a
b c
4
2
5
3
1
auxiliary edge: connect a virtual node to eligible substrate nodes
Virtual Network Embedding => Multi-commodity Flow problem
8Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Path-based ILP Formulation
AEiI
iIp
Pp
iIp
NI
AEiIi
iI
Ni
AEiII
iI
kk
Pp
p
e
pep
ep
Mxf
x
x
rf
f
K
V
S
k
),(
,),(,
),(:
,
),(:
,
:
,
,1
,1
,
,
Pp
pp fcMin
Primal
Exponential number of paths
Link is not overloaded
Each commodity is satisfied
Node Assignment
Traffic only on the link to the “mapped” node
Amount of Flow on Path p
4
2
5
3
1
a
b
c
Xa,2
Xa,4
9Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Path-based Formulation-Primal and Dual
AEiI
iIp
Pp
iIp
NI
AEiIi
iI
Ni
AEiII
iI
kk
Pp
p
e
pep
ep
Mxf
x
x
rf
f
K
V
S
k
),(
,),(,
),(:
,
),(:
,
:
,
,1
,1
,
,
edunrestrict,,,0,,
),(,
I,
,0
yyy
AEiIiIiI
kiIie
yy
Pp
pp fcMin
Primal
:ye
:λk
:yi
:yI
:ΠI,i
)(
I
I
i
i
e
ee
k
kkMax yyyr
Dual
kPp
pe piI
kiIee cy
,0)(),(
,
exponential # path choices => exponential # of constraints
Fact 1: OPT(P) = OPT(D-P)
10Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Column Generation to try path selection
P
P’PO
P
P’
PO
PO: set of optimal pathsP’: path space we look atP: potential exponential path space
Q1: Is P’ optimal? Q2: Which path to add to P’ ?
Target: OPT(P’) =OPT(P)
11Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Q1: P’ optimal? & Q2: which path to add to P’
Exponential # of Constraints (D-P)
Solution with some Constraints (D-P’)
Feasible for other
constraints in P?Q1
pcype piI
kiIee
,0)(),(
,
Yes
No
Add the constraint’s corresponding path to P’: Q2
Q3: Check Exp. # of constraints?
OPT(D-P’) =OPT(D-P)
OPT(D-P’) = OPT(P’) >= OPT(P) = OPT(D-P)
OPT(P’) = OPT(P)
P
P’PO
OPT(D-P’)
12Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Check all the Constraints: Shortest Path Problem
Ppcy k
pe piI
iIee
,)(),(
,
4
1
a
b
c
2
5
3
Weight for substrate links
We = ye+ce
Weight for auxiliary edge
WI,i=ΠI,i
W1-2
W1-4
W2-4
Wa-4
Wa-2
Wc-1
Wc-3
Wb-4Wb-5
W3-5
W4-5
W3-4
W1-3
Rational: if the shortest path of each commodity satisfies, all the paths satisfy.
Wa-2+W1-2+Wc-1 ≥λk
13Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Overall Framework
Solve the D-P’
Solution feasible for
D-P
Solution for D-P Found
YES
Obtain a subset P’
NOIncrease P’
Theorem 1: The process to identify a set of optimal paths is Polynomial.
14Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Performance EvaluationSimulation Setting
Virtual network node number [2-10]Substrate network node number [10-50]Average connectivity 50%Virtual network link/node capacity [1-20]Substrate network link/node capacity [1-50]
Compared ApproachesLink-based ILP (from prior work Infocom’09)Path-based ILP
ILP P-VNERelaxed Path-based ILP
ILP P-VNE’ k=1ILP P-VNE’ k=2ILP P-VNE’ k=3
15Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Optimality Comparison
Both P-VNE and Link-based ILP achieve optimality Increasing k improves the performance for relaxed P-VNE
P-VNE has considerable less computational time than Link-based ILP
Increasing k also increases timeOver small k may leads to infeasible solution
Resource Consumption (ce=1) QoS (ce=latency of e)
16Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
SummaryWhat is Network Virtualization?Virtual Network Embedding and Network Flow Model
Path-based VNE ModelColumn Generation Approach
17Qian Hu, Yang Wang, Xiaojun Cao Infocom 2013
Questions?
Thank you!
Qian Hu, Yang Wang, Xiaojun Cao
Resolve the Virtual Network Embedding Problem: A Column Generation Approach