Optimal Tree Structures for Large-Scale Grids
-
Upload
hyatt-knight -
Category
Documents
-
view
29 -
download
0
description
Transcript of Optimal Tree Structures for Large-Scale Grids
![Page 1: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/1.jpg)
Grid Performability, Modelling and Measurement AHM’04
Optimal Tree Structures for Large-Scale Grids
Optimal Tree Structures for Large-Scale Grids
J. Palmer I. Mitrani
School of Computing Science
University of Newcastle
NE1 7RU
[email protected] [email protected]
J. Palmer I. Mitrani
School of Computing Science
University of Newcastle
NE1 7RU
![Page 2: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/2.jpg)
2Grid Performability, Modelling and Measurement AHM’04
Outline
Introduction
The model
Computation of the optimal tree structure
A simple heuristic
Results
Conclusions and future work
![Page 3: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/3.jpg)
3Grid Performability, Modelling and Measurement AHM’04
Introduction In the provision of a Grid
service, a provider may have heterogeneous clusters of resources offering a variety of services
Within such a provision, it will be desirable that the clusters are hosted in a cost effective manner
Master Node
. . .
Server Server Server
Job arrivals
Server Server
Potential bottle-neck
![Page 4: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/4.jpg)
4Grid Performability, Modelling and Measurement AHM’04
The problem of load-balancing considers how best to distribute incoming jobs across a fixed tree structure
Instead, our approach considers the dynamic reconfiguration of the underlying tree structure as load changes
Master Node
. . .
Server Server Server
Job arrivals
Server Server
Master Node Master Node
Server
. . .
additional transfer delays
additional decision-making process
![Page 5: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/5.jpg)
5Grid Performability, Modelling and Measurement AHM’04
Master Node
. . .
Server Server Server
Job arrivals
Server Server
Master Node Master Node
Server
. . .Master Node
Job arrivals
Master Node Master NodeMaster Node
Server Server Server
. . .
Server ServerServer
. . .
Server ServerServer
. . .
dynamic network reconfiguration
![Page 6: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/6.jpg)
6Grid Performability, Modelling and Measurement AHM’04
What value of k minimizes the overall average response time of the system?
The model
. . .
. . .
transfer delay T1
level 1 master node
level 2
. . .
k master nodes
ck
. . .
c k)
k sub-clusters ofN/k service nodes
![Page 7: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/7.jpg)
7Grid Performability, Modelling and Measurement AHM’04
Different job distribution policies have been considered:
Job distribution policies
transfer delay Ti
level i
level i+1
ici ki
. . .
1. Each dependent has a separate queue; the master places new jobs into
i. those queues in random order
ii. the queue which is currently shortest
iii. those queues in cyclic order
2. Dependents at the final service cluster level have a joint queue
![Page 8: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/8.jpg)
8Grid Performability, Modelling and Measurement AHM’04
Computation of the optimal tree structure
The average response time at each level i master node is given by:
)1(
1
iiiW
11
0
1
12
2
)()!1(!)()!1(
)(
)!1(
1
n
j
njn
j
nj
final nnjnn
nn
jW
ii
ii
c
,
dependents ofnumber where
At the final service level, approximated by an M/M/n queue:
where ,clustereach in servers ofnumber n
![Page 9: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/9.jpg)
9Grid Performability, Modelling and Measurement AHM’04
Computation of the optimal tree structure
The objective is to minimise the latter with respect to k
finalWWW 1
finalWWTWW 211
For a flat structure ( c1>N for stability):
For a two level tree structure:
![Page 10: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/10.jpg)
10Grid Performability, Modelling and Measurement AHM’04
Computation of the optimal tree structure
At each master node we require So, for a given parameter set, k has upper and lower
bounds so that no master node becomes saturated:
1
2
ck
c
N
Average response times for each value of k within this range
have been evaluated and compared to find the minimum Hence, the optimal value of k has been determined numerically This gives the optimal network configuration with a single layer
of master nodes
1i
![Page 11: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/11.jpg)
11Grid Performability, Modelling and Measurement AHM’04
A simple heuristic
Consider the total offered load at the level 1 master node and one of the level 2 master nodes:
This total load can be minimized with respect to k to find an initial value for k given N, c1 and c2:
Nkc
N
c
kkf
221
)(
3
2
12
c
Nck
![Page 12: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/12.jpg)
12Grid Performability, Modelling and Measurement AHM’04
Results Average response time as k varies Parameters: Load is 80%, flat structure not feasible
1.0,8,001.0,100,100 121 TccN
optimal k = 4
heuristic predicts k = 6
![Page 13: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/13.jpg)
13Grid Performability, Modelling and Measurement AHM’04
Results Optimal number of clusters as load increases Parameters: 1.0,001.0,100,100 121 TccN
![Page 14: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/14.jpg)
14Grid Performability, Modelling and Measurement AHM’04
Conclusions and Future Work
Encouraging results suggest dynamic network configuration will reduce long-term average response times
A simple heuristic is available for initial network configuration
Future work includes:
1. extension to include further tiers of master nodes
2. different modelling assumptions for how a master node makes a routing decision
- shortest queue
- cyclic order
![Page 15: Optimal Tree Structures for Large-Scale Grids](https://reader035.fdocuments.us/reader035/viewer/2022062517/5681341c550346895d9b0987/html5/thumbnails/15.jpg)
15Grid Performability, Modelling and Measurement AHM’04
Acknowledgment This work was carried out as part of the
collaborative project GridSHED, funded by
North-East Regional e-Science Centre
and
BT
This project also aims to develop Grid middleware to demonstrate the legitimacy of our models, providing a basis for the development of commercially viable Grid hosting environments
Project web page:
http://www.neresc.ac.uk/projects/GridSHED/