an optimization problem in adaptive virtual environments ananth i. sundararaj manan sanghi jack r....

An Optimization Problem in Adaptive Virtual Environments

Ananth I. Sundararaj

Manan Sanghi

Jack R. Lange

Peter A. Dinda

Prescience Lab

Department of Computer Science

Northwestern University

http://virtuoso.cs.northwestern.edu

2

Summary

• Virtual execution environments provide opportunities for dynamic adaptation

• Important components are– Resource monitoring and inference– Application independent adaptation mechanisms– Efficient adaptation algorithms

• Previously proposed simple heuristics– Significant scope for improvement

• In this work– Formalize the adaptation problem– Show that it is NP-hard– Propose future research directions

3

Outline• Virtual execution environments – An example• Virtuoso system – Introduction• Virtual networks

– Measurement and inference (VTTIF)– Adaptation mechanisms (VNET)

• Problem formalization• A special case of the adaptation problem• Analysis• Status • Summary

4

Aim

Grid Computing

New Paradigm

Traditional Paradigm

Deliver arbitrary amounts of computational power to perform distributed and parallel computations

Problem1:

Grid Computing using virtual machines

Problem2:

Solution

How to leverage them?

Virtual Machines What are they?

6b

6a

5

4

3b3a

2

1

Resource multiplexing using OS level mechanism

Complexity from resource user’s perspective

Complexity from resource owner’s perspective

Virtual Machine Grid Computing

5

Virtual Machines

Virtual machine monitors (VMMs)

•Raw machine is the abstraction

•VM represented by a single image

•VMware GSX Server

6

The Simplified Virtuoso Model

Orders a raw machine

User

Specific hardware and performance

Basic software installation available

User’s LAN

VM

Virtual networking ties the machine back to user’s home network

Virtuoso continuously monitors and adapts

7


– Measurement and inference– Adaptation mechanisms


8

User’s friendlyLAN

Foreign hostile LAN

Virtual Machine

VNET: A bridge with long wires

Host

Proxy

X

Virtual NetworksVM traffic going out on foreign LAN

IP network

A machine is suddenly plugged into a foreign network. What happens?

• Does it get an IP address?• Is it a routeable address?• Does firewall let its traffic through? To any port?

http://images.google.com/imgres?imgurl=www.np.k12.mn.us/School/ISD721/High/computer.gif&imgrefurl=http://www.np.k12.mn.us/School/ISD721/High/&h=235&w=208&sz=5&tbnid=9PHQKkFo7wQJ:&tbnh=103&tbnw=92&prev=/images%3Fq%3D%2B%2522computer%2522%26start%3D40%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26sa%3DN

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Measurement and Inference

Application (VTTIF)• Topology

• Traffic load

Underlying network layer Physical hosts

Virtual network layerVNET daemons

Application layerVM layer

Host and VM • Size and compute capacities

• Size and compute demands

• Topology

• Bandwidth

• Latency

Underlying network

[Gupta et al. LNCS 05]

[Gupta et al. In submission]

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Adaptation Mechanisms

Resource reservation• Network

• CPU

Resource reservationPhysical hosts

Topology changesVNET daemons

VM MigrationVM layer

Topology changes • Overlay links

• Overlay forwarding rules

VM Migration• Third party migration schemes

X

XX

[Sundararaj et al. LCR 04, HPDC 05]

[Lange et al. HPDC 05]

[Lin et al. GRID 2004]

11




12

bw12

H3

H2

H1H4

VM1 VM2 b1 l1

VM1 VM3 b2 l2

VM2 VM3 b3 l3

VM3 VM1 b4 l4

A set of ordered 4-tuples, “A”

disi bi

Generic Adaptation Problem In Virtual Execution Environments (GAPVEE)

bw24

bw14

bw13

bw34

lat12

lat13

lat34

lat24

lat14compute4

compute1

compute2

compute3

size4size1

size2

size3

VM1

vm_compute1

vm_size1

VM2vm_compute2

vm_size2

VM3

vm_compute3

vm_size3

liA1

A2

A3

A4

Input:1.

2. 3.

13

Generic Adaptation Problem In Virtual Execution Environments

Output:

H3

H2

H1H4

VM1

vm_compute1

vm_size1

VM1

vm_compute3

vm_size3VM1

vm_compute2

vm_size2

map

ped

map

ped

mapped

A mapping from VMs to Hosts

• Size and compute demands of VMs must be met within host constraints

VM demands

compute4 size4

Host constraints

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Output:

H3

H2

H1H4

A mapping from 4-tuples to Paths

• Bandwidth and latency demands of 4-tuples must be met within constraints

compute4 size4

Host constraints

VM1 VM2 b1 l1

VM1 VM3 b2 l2

VM2 VM3 b3 l3

VM3 VM1 b4 l4


disi bi liA1

A2

A3

A4

VM1

VM2 VM3

bw13

lat13

Hence

b1 + b2 <= bw13

l1 , l2 >= lat13

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Output:

H3

H2

H1H4

compute4 size4

Host constraints

VM1 VM2 b1 l1

VM1 VM3 b2 l2

VM2 VM3 b3 l3

VM3 VM1 b4 l4


disi bi liA1

A2

A3

A4

VM1

VM2 VM3

bw13

lat13

H1

H3

bw13

A1 (b1)

A2 (b2)

bw13 – (b1+b2) is the residual capacity of the edge

Bottleneck bandwidth: min residual capacity along a path

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• Goal: – VMs to Hosts mapping

– Path to each 4-tuple

– Meeting all demands within constraints

– Such that• Sum of residual bottleneck bandwidth over

each mapped path is maximized

17

Optimizing Objective functions

• Many possibilities

• Maximizing sum of residual bottleneck bandwidths over each mapped path– Intuition:

• Leave the most room for application to increase performance

• Minimizing the residual bottleneck capacity– Intuition:

• Increase room for other applications to enter system

18




19

bw12

H3

H2

H1H4

H1 H3 b1

H1 H3 b2

H2 H3 b3

H3 H4 b4


disi bi

Special Case of GAPVEE: Routing Problem In Virtual Execution Environments (RPVEE)

bw24

bw14

bw13

bw34

A1

A2

A3

A4

Input:1.

2.

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Special Case of GAPVEE: Routing Problem In Virtual Execution Environments (RPVEE)

Output:

H3

H2

H1H4

A mapping from 3-tuples to Paths

• Bandwidth demands of 3-tuples must be met within constraints

•Sum of residual bottleneck bandwidth is maximized over each path

bw13

H1 H3 b1

H1 H3 b2

H2 H3 b3

H3 H4 b4


disi bi

A1

A2

A3

A4

21

Analysis• Theorem 1: RPVEE is NP-hard

• Edge Disjoint Path Problem (EDPP)– Arbitrary instance of EDPP

– Convert to an instance of RPVEED

– A “Yes” solution for RPVEED implies a “Yes” solution for EDPP

– A “No” solution for RPVEED implies a “No” solution for EDPP

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Edge Disjoint Path Problem (EDPP)

• A well known NP-complete problem• Input

– A graph G = (H,E)– A set of ordered 2-tuples S = {(si,di), where si, di

in H}

• Output– “Yes” if for all (si,di) in S, there exist edge

disjoint paths from si to di in G = (H,E)– “No” otherwise

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Decision version of RPVEE (RPVEED)

• Input– A graph G = (H,E)– A function bw: E -> R– A set of ordered 3-tuples S = {(si,di,bi), where si, di

in H, bi in R, i = 1,…k}

• Output– “Yes” if for all (si,di,bi) in S, there exist paths from

si to di in G = (H,E), such that sum of bottleneck bandwidth = k*ε

– “No” otherwise

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H3

H2

H1H4

1+ε

H3

H2

H1H4

1+ ε

1+ ε 1+ ε

1+ ε

1

11

1

1

1 1

H1 H2

H1 H4

H2 H4

H1 H3

A set of ordered 2-tuples

H1 H2 1

H1 H4 1

H2 H4 1

H1 H3 1

A set of ordered 3-tuples

si di

disi bi

Given an arbitrary instance of EDPP

Converted to a particular instance of RPVEED

A directed graph G = (H,E)

A complete directed graph G = (H,E)

A function bw : E -> R

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Status• Previously developed a variety of heuristics

(Greedy and Simulated annealing)

• Effective in improving performance– Significant scope for improvement

• Formalization and analysis, first steps

• Generic incarnation hard, focus on special cases

• Currently researching the well studied variants of our problem (such as un-splittable flows)

27

Summary

• Virtual execution environments provide opportunities for dynamic adaptation

• Important components are– Resource monitoring and inference– Application independent adaptation mechanisms– Efficient adaptation algorithms

• Previously proposed simple heuristics– Significant scope for improvement

• In this work– Formalize the adaptation problem– Show that it is NP-hard– Propose future research directions

28

• For More Information– Prescience Lab (Northwestern University)

• http://plab.cs.northwestern.edu

– Virtuoso: Resource Management and Prediction for Distributed Computing using Virtual Machines

• http://virtuoso.cs.northwestern.edu

• VNET is publicly available from• http://virtuoso.cs.northwestern.edu

http://plab.cs.northwestern.edu/

http://virtuoso.cs.northwestern.edu/

http://virtuoso.cs.northwestern.edu/

an optimization problem in adaptive virtual environments ananth i. sundararaj manan sanghi jack r....

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