[PPT] - Mathematical Optimization Methods for Research Context NFV and PowerPoint Presentation

SLIDE 1

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Optimization Methods for NFV and Cloud Resource Allocation Problems

HDR Defense

by:

Makhlouf Hadji 3 March, 2017

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 1 / 69

SLIDE 2

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Research Activities, Projects and Collaborations

2005 2006 2007 2008 2009 2010 2011 2012 2013 to.. 2017

DEA Operations Research Paris Dauphine University PhD thesis Paris-6 University Research Engineer Télécom SudParis Researcher SystemX Head of "Networks&Infra" Research Team Collaborations : with more than 30 researchers More than 50 papers Mentoring

f 6 PhD

students 3 Patents filed Involved in 8 R&D projects (Orange, Nokia,...) Combinatorial Optimization, Graph theory, Linear algebra Game theory, Cloud, Openstack, NFV, SDN, C-RAN, 5G Teaching : Combinatorial Optimization, Mathematical Programming,... Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 2 / 69

SLIDE 3

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Outline

1

Research Context

2

Virtual Machines Placement and Repacking Optimization

3

Critical Resource Allocation in Cloud Federations

4

Virtualized Network Functions Chaining and Placement Problems

5

Open Research Challenges

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 3 / 69

SLIDE 4

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Resource Allocation in Cloud Data Centers

Context : How/Where to deploy/reallocate optimally a set of VMs in a cloud data center ?

Placement Cloud Manager

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 4 / 69

SLIDE 5

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Critical Resource Allocation in Cloud Federations

Context : Where to place interconnected VMs in a federation taking into account the importance of certain services ?

Placement Cloud Federation Prov j Prov i

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 5 / 69

SLIDE 6

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Network Resource Allocation

Context : What is the optimal placement of VNFs chains in the NFV context ?

f1 f2 f3

Flow 1 Flow 2 VNF-FG (SFC) Physical substrate Optimal Mapping

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 6 / 69

SLIDE 7

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Outline

1

Research Context

2

Virtual Machines Placement and Repacking Optimization Our contribution Conclusion and Further Research

3

Critical Resource Allocation in Cloud Federations

4

Virtualized Network Functions Chaining and Placement Problems

5

Open Research Challenges

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 7 / 69

SLIDE 8

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Motivation

To achieve increasing revenues, cloud providers require very efficient resource utilization and the strict respect of quality of service, Without virtual resources (VMs) consolidation, initial smart placement alone can not efficiently reduce costs since all expenses matter : hosting, energy consumption, maintenance, configuration and management costs

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 8 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Motivation

Definitions SLA Violation : is represented by the percentage

f over used servers

Focus of our Work Online placement and re-packing algorithms to reduce overall cost and improve resource utilization and, at the same time, minimize SLA violations

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 9 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Problem Statement

Description

The Figure depicts the placement problem of N VMs on K available ser-

vers. Cloud services are

characterized by elastic requirements from users, that induce variable workloads on the system that requires consolidation to use more efficiently resources.

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 10 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Problem Complexity

Complexity

If we consider each VM as an item and each available server as a bin, then our VMs placement problem is very similar to the well known NP-Hard problem of the Bin-Packing. Thus, our problem is also NP-Hard. We investigate scalable and cost-efficient algorithms to cope with large problem instances in negligible times.

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 11 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Modeling

Server k VM i Server k Server k Server k’ VM i

ik e H

W

ik ik e

R H W  

Bipartite Graph Construction If a VM i is currently hosted by a server k, then we consider hosting costs wik = Hik. Reconfiguration costs (Rik) are added if the VM i should be migrated from a server k′ to a server k (wik = Hik + Rik)

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 12 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Modeling

1

VM

2

VM

N

VM

1

S

2

S

K

S

11

H

12 12 R

H 

K K

R H

1 1 

V S Bipartite Graph Construction There is an edge e = (i, k) between each VMi and each available server k The weight of each edge e = (i, k) is provided according to the current placement of VMi

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 13 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

b-Matching Approach

Proposition Let G = (V ∪ S, E) be a complete weighted bipartite graph, where V represents a set of Virtual Machines, and S a set of physical servers hosting the VMs. Finding an optimal VMs repacking solution is equivalent to the polynomial time solution of the uncapacitated minimum weight b-Matching problem, such as : b(v) = 1, ∀v ∈ V b(v) = min

|V|; ⌈

CPUv

e∈δ(v) CPUI(e) ⌉
, ∀v ∈ S

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 14 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

b-Matching Approach

Linear Program : Objec- tive function

min Z =

e∈E,e=(i,k) (He + Re1e) xe

where

1e = 1(i,k) =

1,

if VM i is NOT on Sk ; 0, else Linear Program : Constraints

e∈δ(v) xe = 1, v ∈ V
e∈δ(v) xe ≤ b(v), v ∈ S
e∈E(G(A)) xe + x(F) ≤

⌊

v∈A b(v)+|F|

2

⌋, A ∈

V ∪ S, F ∈ δ(A) xe ∈ R, ∀e ∈ E

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 15 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Graphic Matroid

Matroid Definition A matroid M = (E; F ) is a structure in which E is a finite set of elements and F is a family of sub- sets of E such that :

∅ ∈ F

If A ∈ F and B ∈ A, then B ∈ F If A, B ∈ F , and

|B| > |A| then ∃e ∈ B \ A, such that

A ∪ {e} ∈ F . Proposition Let G

= (V ∪ S; E)

be a simple bipartite graph. By relaxing servers limited capacity constraints, M

= (E; F )

is a matroid, with F

= {I ⊆ E, I

is a forest of trees

VM 1 S1 VM 2 VM n S2 Sk

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 16 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Graphic Matroid

Greedy Approach Put F = ∅ ; we1 ≤ we2 ≤ . . . ≤ wem ; for i = 1 to m do if F ∪ {ei} ∈ F then if cpu(I(ei)) ≤ CPU(T(ei)) then F := F ∪ {ei} CPU(T(ei))− = cpu(I(ei)) end if end if end for

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 17 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Numerical Results : Execution time

|V| |S| b- Matching (s) Bin- Packing (s) Greedy (s) Best-Fit (s) 100 25 0.02 0.04 50 0.02 0.04 0.04 75 0.04 0.06 0.1 0.02 500 100 0.05 0.4 0.56 0.06 250 0.1 1.3 1.09 0.2 350 0.4 2 1.88 0.3 1000 200 0.4 4 2.45 0.44 400 0.5 4.2 3.77 0.6 700 0.8 9.8 5.96 1 3000 500 1.6 205 149.3 5.4 700 2.2

≥ 4H

355.6 7.6 900 3.2

≥ 4H

534.2 9.6

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 18 / 69

SLIDE 19

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Numerical Results : Cost Evolution

Algorithms Costs

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 19 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

SLA Violation Comparison

SLA Violations

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 20 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Conclusion

Remarks The b-matching algorithm improves as the numbers of servers and VMs increase by gradually reducing from an acceptable number of SLA violations to zero (no) violations for large instances Ongoing extensions to our work include security constraints that will be introduced as affinity and anti-affinity relationships between VMs Collaborations

C. Ghribi, M. Zekri, N. Djenane : PhD Students

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 21 / 69

SLIDE 22

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Outline

1

Research Context

2

Virtual Machines Placement and Repacking Optimization

3

Critical Resource Allocation in Cloud Federations Our Contribution Conclusion and Future Work

4

Virtualized Network Functions Chaining and Placement Problems

5

Open Research Challenges

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 22 / 69

SLIDE 23

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Motivation and Problem Status

Motivation We address a cloud federation dealing with hosting critical tenant services Typical intelligent placement solutions take partially into account the level of criticality of nodes (services) and links (relationships) in a composite service We focus on how to rapidly detect critical nodes and links in a service request

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 23 / 69

SLIDE 24

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Problem Status

Problem Description

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 24 / 69

SLIDE 25

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Problem Status

Costs Description According to different requirements, a provider j is looking for solutions that optimize the total costs :

Γj = γji + Hostj + Hosti

with i j (1) We define the following thresholds :

α = 1

N

v∈VGH

dGH(v) (2)

β =

1 N − 1

e∈EGH

Be (3)

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 25 / 69

SLIDE 26

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Problem Complexity

Virtual Network Embed- ding Problem Similarity

Placement Cloud Federation

7 5 4 5 15 11 4 2 3

Complexity Analysis

The goal is to place virtual nodes in the federation physical

nodes. This consists
f selecting a subset
f cloud providers

that can host the virtual nodes and their connectivity. This is very similar to the well known NP-Hard problem of Virtual Network Embedding.

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 26 / 69

SLIDE 27

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Gomory-Hu Tree Transformation

GH Transformation

1 5 2 4 3 1 5 2 4 3 7 19 26 6 25 62 GH Tree Transformation

Flow Example The maximum flow between nodes 1 and 5 is

min {31, 62, 43}

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 27 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Our Proposal

Proposal We focus on improving and optimizing two operations : Gomory-Hu request transformation :

◮ This will reveal dominant nodes and links ◮ This will translates the initial NP-Hard problem to

a placement of trees of smaller sizes

Placement optimization

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 28 / 69

SLIDE 29

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Proposed Approaches

Critical Node Detection (CND) Algorithm CND Details Critical nodes (nodes with degrees exceeding α) are

ptimally placed

in provider j. All nodes that are less critical are outsourced to other providers i j.

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 29 / 69

SLIDE 30

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Proposed Approaches

Critical Edge Detection (CED) Algorithm CED Details

According to the

btained GH-Tree,

we first select and place critical edges (edges with bandwidth requirements exceeding the threshold β) Select the best cloud providers (in terms

f costs) to host the

remaining nodes

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 30 / 69

SLIDE 31

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

CND Algorithm Performances Feder Size Graph Size GAP (%) Reject Rate (%) Time (msec) B&B Time (msec) 3 4 28.22 1 1 6 32.20 2 1 6 8 41.46 11 3 78 6 4 43.68 1 3 6 51.17 2 173 8 57.42 4 12 sec 10 4 41.62 1 13 6 57.37 2 2518 8 61.12 4

>8mn

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 31 / 69

SLIDE 32

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

CED Algorithm Performance Feder Size Graph Size GAP (%) Reject Rate (%) Time (msec) B&B Time (msec) 3 4 4.03 1 1 1 6 4.37 2 1 6 8 6.48 2 3 78 6 4 1.99 1 3 6 1.53 2 173 8 3.60 4 12 sec 10 4 0.58 1 13 6 1.12 2 2518 8 0.70 4

>8mn

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 32 / 69

SLIDE 33

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

Scalability Analysis

T – 100 providers and requests with 50 nodes

Metric CND CED Time (sec) 6.3 6.41 Reject rate (%) Cost 8014.8 1966.8

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 33 / 69

SLIDE 34

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Conclusion

Remarks

We presented two approaches to solve the cloud federation resource placement and allocation problem in the presence of hard placement constraints for security or protection reasons The proposed algorithms use the Gomory-Hu tree transformation of user requests to identify critical nodes and links The CED algorithm performs well and finds near

ptimal solutions

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 34 / 69

SLIDE 35

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Conclusion

Future Work Ongoing work explores the combination of the methods and joint node and link constraints to enhance the quality of the solution Collaboration

S. Rebai, B. Aupetit, M. Mechtri : PhD Students

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 35 / 69

SLIDE 36

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Outline

1

Research Context

2

Virtual Machines Placement and Repacking Optimization

3

Critical Resource Allocation in Cloud Federations

4

Virtualized Network Functions Chaining and Placement Problems Main Contributions Conclusion

5

Open Research Challenges

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 36 / 69

SLIDE 37

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Motivation

Motivation Provide optimization algorithms for the ETSI-NFV VNF-FG use case, where service providers acquire networking services in the form of a graph Cloud service providers expect placement of their VNFs that ensures routing of their application flows Propose efficient algorithms for VNF chains placement that find good solutions and scale with problem size

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 37 / 69

SLIDE 38

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining : Problem Status

VNF-FG View

VNF f1 VNF f4 VNF f2 VNF f3 VNF f5

VNF-FG Mapping

Chain 2 Physical Network Function Physical Network Function

Physical Infrastructure

VNF-FG Request

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 38 / 69

SLIDE 39

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining : Problem Status

Problem Description

VNF chains Mapping

14 CPU 17 CPU 4 CPU 8 CPU 19 CPU Firewall DPI Transcoder Flow 1=5 Mbps Flow 2=7 Mbps

7 Mbps 7 Mbps 5 Mbps 5 Mbps 4 Mbps

10 7 4 9 8 13 9 8 CPU 6 CPU 9 CPU

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 39 / 69

SLIDE 40

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining : Problem Complexity

Complexity The VNF-FG placement and chaining problem is very similar to the NP-Hard problem of the Virtual Network Embedding a : This can be

btained by simply relaxing the sequencing

requirements/constraints in the VNF-FG. Our problem is NP-Hard, in general.

a. Edoardo Amaldi et al. On the computational complexity of the virtual network embedding problem,

Electronic Notes in Discrete Maths, 52 : 213-220, June 2016. Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 40 / 69

SLIDE 41

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining

Our Proposal An exact solution based on the Perfect 2-Factor theory to solve rapidly the case of VNF chains composed of 3 VNFs An algorithm based on a multi-stage graph representation to find near-optimal solutions for the VNF-FG placement and chaining problem

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 41 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Formulation

Case of 3 VNFs : 2- Factor Approach

f1 f2 f4

Fictitious arc 7 Mbps 7 Mbps 7 Mbps 2-Factor Approach : Mathe- matical Formulation

min Z =

e∈Es,e=(i,j)(Ce − Rc)1+xe

S.T. :

                              

e∈δ(v) xe = 2,

∀v ∈ Vs

e∈Es(G(A)) xe + x(F) ≤

2|A|+|F|

2

,

∀A ∈ Vs,

F ⊆ δ(A),

v∈A 2 + |F| is odd

xe ∈ R+,

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 42 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Formulation

Multi-stage Algorithm We construct a multi-stage graph G = (V, A, K), as fol- lows : The number of levels of the graph G is equal to the number of VNF types A node/server can appear in as many levels as VNFs types it can handle There is an arc (ik, jk+1) with a weight given by the maximum flow that can be routed from ik to jk+1.

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 43 / 69

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Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Mathematical Formulation

Multi-stage Algorithm

17 CPU 14 CPU 13 CPU 17 CPU S T

+ + + +

19 CPU 9 CPU 5 CPU 13 CPU

Inf Inf

14 CPU 8 CPU 10 Mbps 10 Mbps

f1 f2 f3

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 44 / 69

SLIDE 45

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

Results : Execution Time

Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 45 / 69

SLIDE 46

Contributions to Cloud and NFV Areas Makhlouf Hadji Research Context VMs Placement & Repacking

Our contribution Conclusion and Further Research

Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

Results : Acceptance Ratio

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

Comparison Using Interoute-Network a

a. a network with 100 nodes and 148 edges

MS-max MS-min Sahhaf et al. a Acp Ratio 99.9 95 93 Cost 200 192 180 Time (msec)

≃ 100 ≃ 100 ≃ 100

a. Network service chaining with optimized network function embedding supporting service

decompositions, Computer Networks, pp 492-505, 2015. Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 47 / 69

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Performance Evaluation

Comparison with the State of the Art Avg-Time (s) MS 2-Factor Luizelli et al. a 50 nodes 0.005s 0.13s 60 200 nodes

≈ 0.05s

0.45s 1000

a. Piecing together the nfv provisioning puzzle : Efficient placement and chaining of VNFs.

IFIP/IEEE IM, pp 98-106, 2015. Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 48 / 69

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Conclusion

Future Work Ongoing work explores the convex hull of the VNF chaining and placement problem for VNF-FG with at least 4 VNFs. We will investigate new valid inequalities to accelerate convergence time to the optimum. Collaboration

N. Mharsi : PhD Student
S. Khebbache : Post-Doctorant

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Outline

1

Research Context

2

Virtual Machines Placement and Repacking Optimization

3

Critical Resource Allocation in Cloud Federations

4

Virtualized Network Functions Chaining and Placement Problems

5

Open Research Challenges

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining with Reliability Constraints

VNF-FG Chaining and Placement Under Reliabi- lity Constraints

f1 f2 f3

Flow 1 Flow 2 VNF-FG (SFC)

Optimal Mapping

0.9999 0.99999 0.999999 Link Failure

Research Challenges Placement and

rchestration of

VNF chains to avoid failures on physical nodes and links Investigate new and cost-efficient placement algorithms taking into account SLA constraints

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

vCDN Placement and Migration

vCDN System : ETSI Use-Case

1 2 5 3 4

Youtube server Youtube vCDN Controller

End-Users

Research Challenges Content caches distributed over network operator’s nodes, should be easily updated and migrated to improve QoS Where to migrate vCDN to improve the overall caching performance ?

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

BBU Functions Split in C-RAN

C-RAN Architecture View

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Critical Resource Allocation

Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

BBU Functions Split in C-RAN

BBU Functions Split Research Challenges

What is the optimal BBU functions split leading to :

◮ Reduce

fronthaul network resource consumption

◮ Reduce the

latency, . . . How to optimally deploy/place a BBU function split on the physical substrate ?

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Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

The End

Thanks Thanks for your attention !

Makhlouf Hadji

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Main Contributions Conclusion

Research Challenges

The End

Other Results

Backup !

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Graphic Matroid

Sketch of Proof

To prove the third condition, we note by A = ∪k

i=1Ai

where the Ai represent the connected components (trees) of A. Then, for all i = 1, . . . , k, we suppose Gi = (Ti, Ai), where Gi is a tree with |Ti| vertices and

|Ai| edges. This leads us to deduce the number of

vertices of A given by nA = k

i=1 | Ti |=| A | +k.

Similarly, we define B ∈ F , and suppose B = ∪t

j=1Bj.

The number of nodes of B is then given by : nB = t

j=1 | T

′

i |=| B | +t. By using | B |>| A |, two cases

are discussed

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Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Graphic Matroid

Sketch of Proof : Case One If t > k : then | B | +t >| A | +k and nB > nA. In

ther words, B reaches more vertices than A, and

there exists a vertex x covered by B and not by A. Suppose that e ∈ B is an edge which contains x as

ne of its two extremities, we finally deduce that

A ∪ {e} ∈ F .

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Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Graphic Matroid

Sketch of Proof : Case Two If nB < nA : We suppose that the edges of B connect each couple of nodes in A in the same connected component Ai. Using the absurd reasoning, we suppose that there is no edge e ∈ B \ A, such that A ∪ {e} ∈ F . This means that : the edge e ∈ B, links two vertices in the same component Ai and forms a cycle. In this case, the number of edges of B will satisfy

| B |≤| V1 | + | V2 | + . . . + | Vk |, then | B |≤| A |

which contradicts our hypothesis | B |>| A |.

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VMs Repacking

Simulation Parameters A processor with 1.8 GHz and 6 Gb of RAM We generated the complete weighted bipartite graph by assigning to each edge a 0-1 random hosting cost W.L.O.G. we supposed a reconfiguration cost of 0.15 One thousand independent graphs are generated to obtain 1000 independent runs for each simulated point in all the reported results

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Cloud Federation : Comparison to the State of the Art

Some References

N. Samaan et al (2014) a : Proposed an economic model to share resources of different

selfish providers. This solution is presented as a repeated game for VM outsourcing. This model takes into account only the pricing of VMs.

K. Konstanteli et al (2014) b : They focus on optimal cloud federation resource placement

across providers. They take into account computing, networking and storage costs at each

provider. But, there did not consider resource criticality.
S. Rebai et al (2015) c : They presented an exact mathematical formulation of the
ptimization that includes networking and traffic exchanged between the providers. This

model can solve only small and medium federation sizes.

a. A novel economic sharing model in a federation of selfish cloud providers, IEEE TPDS,
vol. 25, pp 12-21, Jan 2014.
b. Elastic admission control for federated cloud services, IEEE TCC, vol. 2, no. 3, pp 348-361,

july 2014.

c. Improving profit through cloud federation, IEEE CCNC, January 2015.

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

Cloud Federation

Simulation Parameters A processor with 1.80 GHz and 3 GBytes of available RAM A random bandwidth in [5; 30] Mbps The required CPU by each VM is drawn randomly between 1 CPU core and 10 CPU cores. Available CPU on each cloud provider is generated randomly in the 60 CPU cores to 600 CPU cores interval We supposed network connectivity cost generated randomly in $0 to $10 per Mbps VMs connectivity in the requested graph is set at 75% One hundred independent requested graphs are generated

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining : State of the Art

State of the Art

R. Mijumbi et al. a : Three greedy solutions and a

tabu-search based heuristic to realize mapping and scheduling of VNFs simultaneously. Only VNFs as nodes are considered. There is no sequencing and chaining between the VNFs.

H. Moens et al. b and A. Bernardetta et al. c considered

exact methods by describing a small portion of the problem convex hull. These approaches do not scale for large problem instances.

a. Design and evaluation of algorithms for mapping and scheduling of virtual network functions.

NetSoft 2015, pp 1-9

b. Vnf-p : A model for efficient placement of virtualized network functions. CNSM Conference, 2014,

pp 418-423

c. Virtual Network Functions Placement and Routing Optimization. IEEE Cloudnet, 2015, pp 171-177

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF Chains Mapping : Mathematical Formulation

2-Factor Approach : Elements of Proof

VNF f1 VNF f2 VNF f3 S1 S2 S3 7 7 7 7

7

13 f1 f2 f3 Fictitious Arc VNF-FG example A cycle in the physical infrastructure Unused edge Makhlouf Hadji Contributions to Cloud and NFV Areas 3 March, 2017 64 / 69

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF-FG Placement and Chaining

Simulation Parameters Physical infrastructure with a number of nodes varying in [10, 150] VNF-FG requests arrive following a Poisson process with an average arrival rate λ = 1 each 25 time units, and have an exponential service rate

µ = 1 departure each 1000 time units.

VNF-FG comprises number of VNFs in the [2; 10] interval

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF Chains Mapping

Convergence Time

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VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF Chains Mapping

Acceptance Ratio : BT Networks a

a. Network with 24 nodes and 37 edges

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Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF Chains Mapping

Acceptance Ratio : Interoute Networks

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Our Contribution Conclusion and Future Work

VNF-FG Placement

Main Contributions Conclusion

Research Challenges

VNF Chains Mapping

Average Cost : BT Networks

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