1. 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

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. Virtual Machines What are they?
Virtual Machine Grid Computing
Deliver arbitrary amounts of computational power to perform distributed and parallel computations
Aim 1
Traditional Paradigm
New Paradigm 2 5
Grid Computing using virtual machines
Resource multiplexing using OS level mechanism
Grid Computing 4 3a 3b 6a
Problem1: 6b
Virtual Machines What are they?
Complexity from resource user’s perspective
Solution
Problem2:
How to leverage them?
Complexity from resource owner’s perspective

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
Virtual networking ties the machine back to user’s home network
User’s LAN
Specific hardware and performance VM
Basic software installation available
Orders a raw machine
Virtuoso continuously monitors and adapts
User

7. Outline Virtual execution environments – An example
Virtuoso system – Introduction
Virtual networks
Measurement and inference
Adaptation mechanisms
Problem formalization
A special case of the adaptation problem
Analysis
Status
Summary

8. VNET: A bridge with long wires
Virtual Networks
VM traffic going out on foreign LAN
Foreign hostile
LAN X
User’s friendly
LAN
IP network
Virtual Machine
Host
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?
Proxy
VNET: A bridge with long wires

9. Measurement and Inference
Underlying network
Host and VM
Size and compute capacities
Size and compute demands
Topology
Bandwidth
Latency
Application (VTTIF)
[Gupta et al. In submission]
Topology
Traffic load
[Gupta et al. LNCS 05]
Application layer
VM layer
Virtual network layer
VNET daemons
Underlying network layer
Physical hosts

10. Adaptation Mechanisms
VM Migration
Topology changes
Overlay links
Overlay forwarding rules
Third party migration schemes
[Sundararaj et al. LCR 04, HPDC 05]
Resource reservation
Network
CPU
[Lange et al. HPDC 05]
[Lin et al. GRID 2004] X
VM Migration
VM layer X
Topology changes X
VNET daemons
Resource reservation
Physical hosts

11. 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

12. Generic Adaptation Problem In Virtual Execution Environments (GAPVEE)
Input:
compute2
size2 1. H2
lat12
bw24
bw12
lat24
compute1
compute4
bw14
lat14 H4 H1
size1
size4
bw13
lat34
lat13
bw34 H3
compute3
size3 si di bi li 2. 3. A1
VM1
VM2 b1 l1
VM3 b2 l2 b3 l3 b4 l4
vm_compute1
VM1
vm_size1 A2 A3
vm_compute2
VM2 A4
vm_size2
vm_compute3
VM3
A set of ordered 4-tuples, “A”
vm_size3

13. Generic Adaptation Problem In Virtual Execution Environments
Output:
compute4
size4
Host constraints H2 H4 H1
A mapping from VMs to Hosts
Size and compute demands of VMs must be met within host constraints
mapped H3
mapped
vm_compute1
VM1
mapped
vm_size1
vm_compute2
vm_compute3
VM1
VM1
vm_size2
vm_size3
VM demands

14. Generic Adaptation Problem In Virtual Execution Environments
Output:
compute4
size4
Host constraints H2 H4
VM1 H1
bw13
lat13
A mapping from 4-tuples to Paths
Bandwidth and latency demands of 4-tuples must be met within constraints H3
VM2
VM3 si di bi li A1
VM1
VM2 b1 l1
VM3 b2 l2 b3 l3 b4 l4
Hence
b1 + b2 <= bw13
l1 , l2 >= lat13 A2 A3 A4
A set of ordered 4-tuples, “A”

15. Generic Adaptation Problem In Virtual Execution Environments
Output:
compute4
size4
Host constraints H2 H4
VM1 H1
bw13
lat13 H3 H1
bw13
VM2
VM3 H3 si di bi li
A1 (b1) A1
VM1
VM2 b1 l1
VM3 b2 l2 b3 l3 b4 l4
A2 (b2) A2
bw13 – (b1+b2) is the residual capacity of the edge
Bottleneck bandwidth: min residual capacity along a path A3 A4
A set of ordered 4-tuples, “A”

16. Generic Adaptation Problem In Virtual Execution Environments
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
Increase room for other applications to enter system

18. 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

19. Special Case of GAPVEE: Routing Problem In Virtual Execution Environments (RPVEE)
Input: 1. H2
bw24
bw12
bw14 H4 H1
bw13
bw34 H3 2. si di bi A1 H1 H3 b1 b2 H2 b3 H4 b4 A2 A3 A4
A set of ordered 3-tuples, “A”

20. Special Case of GAPVEE: Routing Problem In Virtual Execution Environments (RPVEE)
Output: H2 H4 H1
bw13 H3
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 si di bi A1 H1 H3 b1 b2 H2 b3 H4 b4 A2 A3 A4
A set of ordered 3-tuples, “A”

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

22. 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

23. 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

24. Given an arbitrary instance of EDPPsi di H2 H1 H2 H4 H3 H4 H1
A set of ordered 2-tuples
A directed graph G = (H,E) H3
Converted to a particular instance of RPVEED si di bi H2 1 H1 H2 1 H4 H3 1
1+ε
1+ ε 1
1+ ε H4 H1 1 1
1+ ε
1+ ε
A set of ordered 3-tuples 1
A complete directed graph G = (H,E)
A function bw : E -> R H3 1

25. 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

26. 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. VNET is publicly available from
For More Information
Prescience Lab (Northwestern University)
Virtuoso: Resource Management and Prediction for Distributed Computing using Virtual Machines
VNET is publicly available from