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

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k

),(

,),(,

),(:

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),(:

,

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,

,

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)

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SummaryWhat is Network Virtualization?Virtual Network Embedding and Network Flow Model

Path-based VNE ModelColumn Generation Approach

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Questions?

Thank you!

Qian Hu, Yang Wang, Xiaojun Cao

Resolve the Virtual Network Embedding Problem: A Column Generation Approach