Resource Allocation in Network Virtualization

Jie Wu

Computer and Information Sciences

Temple University

Road Map

1. Motivation and Applications

2. Tracing Back: Embedding

3. Basic Models

4. Extensions

1. Hose model

2. Virtual backbone

5. Looking Forward: Other Fields

6. Conclusions

1. Motivation

Network virtualization (Peterson, Shenker, and

Turner’04)

A number of virtual networks (VNs) co-exist over the

same physical network (PN) (substrate network)

VN: a group of nodes that are connected, with

bandwidth reserved in the underlying network

Implementation: RSVP and MPLS A

CD E

F

B

Applications Coexistence

Flexibility

Manageability

Scalability

Isolation

Heterogeneity

ISP = SP + InP

SP: Service Provider

InP: Infrastructure Provider

SDN Programmable switches and

routers than (using virtualization) can process packets for multiple isolated networks

Virtualization Data center networks (DCNs)

2. Tracing Back: Embedding

Embedding (E) of tasks (G) in processors (G’)

Dilation of an edge of G is the length of the path in G’

onto which an edge of G is mapped. Dilation of E is the

maximum edge dilation of G.

Expansion of G is the ratio of the number of nodes in G to

the number of nodes in G’.

Congestion of E is the maximum number of paths

containing an edge in G’, where every path represents an

edge in G.

Load of an E is the maximum number of tasks of G

assigned to any processor of G’.

Embedding Examples

Virtualization Examples

(a) optimal link stress (b) optimal node stress

3. Basic Models

Embed VNs in PN

Subject to CPU (node)

and bandwidth (link)

constraints

General VN embedding NP-hard (multiway

separator problem)

Special VN embedding (fixed nodes) Multicommodity flow

problem

An example of VN embedding

A

C D E

F

B

d e

b a

c

10 10

5

5 5

70

60

90

40

80

40

10

10

2040

20

40 40

40

15 25

25

d e

c

b

a

2010

10

Minimum Cost Multicommodity Flow Multicommodity flow

Capacity constraints, flow

conservation, demand satisfaction

Minimum cost

Sum of a(u, v) f(u, v) on edge (u, v)

Integer flow: hard

Fractional flows: solvable

(Yu et al 06)

Path split

Path migration

Illustration of the benefit of path splitting

Illustration of the benefit of path migration

A

C D

B

20

20

20

20

1040

30

20

10a

a b5 5

20

b

20

20

Existing VN

request 1

A

C D

B

20

20

20

20

1040

30

20

10a

bcd

20

20

New VN request 2 c d

10 1020

10 10

10

a b5 5

20Existing

VN request 1

A

C D

B

20

20

20

20

1040

30

20

10a

bcd

10

10

New VN request 2 c d

10 1030

10 10

20

10

10

A

C D

B

20

20

20

20

1040

30

20

10a

bcd

20

20

Scheduling of Network Updates

Dionysus (Jin et al’14)

Loop freedom

Congestion freedom

Special constraint

A link must occur after an update

that removes an existing flow

Dynamic scheduling

Dependency graph

(Resource allocation graphs)

A network update example. Flows are labeled with their sizes

(a) Current State (b) Target State

A

C D

B

20

20

20

20

2020

20

20

20

F3: 10

F2: 10

A

C D

B

20

20

20

20

2020

20

20

20

F2: 10

F3: 10

F1: 10

F1: 10

One sequence: [F1ĺ F3][F2]

Other sequence: [F1] [F2ĺ F3]

Scheduling of Network Updates

Schedulability

Extension

Introducing intermediate

steps

A Deadlock Example

A

C D

B

20

20

20

20

2020

20

20

20

F3: 20

(a) Current State (b) Target State

F2: 20

A

C D

B

20

20

20

20

2020

20

20

20

F2: 20

F3: 20

(a) Current State (d) Target State

A

C D

B

20

20

20

20

2020

20

20

20

F3: 20

(b) Middle State 1 (c) Middle State 2

A

C D

B

20

20

20

20

2020

20

20

20

F2: 20

F3: 20

F2: 20

A

C D

B

20

20

20

20

2020

20

20

20

F3: 20

F2: 20

A

C D

B

20

20

20

20

2020

20

20

20

F2: 20

F3: 20

4. Extensions: Hose Model (Duffield, Goyal, and Greenberg’99)

Hose: aggregate traffic to

and from endpoints in a VN

Routing structures

Pipe

Ingree (Egree) tree

Shared tree

Mesh

E.g. X (in 3), Y (out 2), and Z

(out 2) using a Steiner tree

Extensions: Virtual Backbone

Mapping VNs onto a shared

substrate (Lu and Turner’06)

Backbone-star, a complete

graph, a ring or a star

Connected dominating set

(CDS) (Wu and Li’99)

A subset (V) of nodes such that

all other nodes not in V have

at least one neighbor in V

Resilience (Dai and Wu’05) K-covered CDS: each node

has k CDS nodes in its 1-hop neighborhood (including itself)

K-connected CDS: can tolerate k-1 faults and still connected

Challenges

Different modelsStaticDynamic (long-term statistical guarantees)

QoS Different provisioning models

Different measurements Minimization of weighted

sum of maximum values of node and link stress

Minimization of long term average value of the weighted sum of bandwidth and CPU revenue

QoS-based Slice Provisioning

Safe vs. Unsafe In terms of available

network resource QoS-based slice provisioning

Slice reservation in unsafe areas

Other extensions K-hop CDS: A subset V such

that each node not in V can reach a node in V within k hops

K-spanner: A spanning subgraph S in which every two vertices are at most k times as far apart in S than on G

6. Looking Forward: Other Fields Virtualization in data

center networks

Virtual machines (VMs)

assignment in physical

machines (PMs)

Subject to CPU and

network bandwidth

constraints

Virtualization in DSN Hadoop scheduling: map,

shuffle, and reduce

Split 1

Split 2

Split 3

Split N

Input data

Mapper 1

Mapper 2

Mapper 3

Mapper N

Map Phase

Reducer 1

Reducer 2

Reducer N

Reduce Phase

Shuffle

Virtualization in SDNs

Virtualization of

controller in SDNs

Multiple controllers

Disjointed

Overlapped (token-

based access control)

Controller placement

Hose Model in DCNs

Elasticity (Li, Wu, and Blaisse’12)

The CPU / bandwidth utilization is the ratio of

the used CPU / bandwidth among all PMs / links

The combined utilization is the maximal one of

the CPU and bandwidth utilizations (bottleneck)

Minimizing the combined

utilization To provide flexibilities for new VM requests

(elasticity)

Hose Model in DCNs (cont’d)

Iterative stack up

Layer by layer

recursive placement

CPU bottleneck: load

balancing placement

Link bottleneck: load

unbalancing

placement

Conclusions

Allocation

centralized vs. distributed

Reconfiguration

migration and dynamic scheduling

Survivability and Flexibility

resource overprovisioning and controlled slicing

Other Applications SDNs and DCNs

Future Challenges

Performance guarantee

Deterministic vs. statistic

Resource discovery and allocation

Cooperation and competition between IPs

Heterogeneity and diversity of infrastructure