Optimal Tree Structures for Large-Scale Grids

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

[email protected] [email protected]

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


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


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

. . .


Job arrivals

Server Server

Master Node Master Node

Server

. . .

additional transfer delays

additional decision-making process


Master Node

. . .


Job arrivals

Server Server

Master Node Master Node

Server

. . .Master Node

Job arrivals

Master Node Master NodeMaster Node


. . .

Server ServerServer

. . .

Server ServerServer

. . .

dynamic network reconfiguration


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


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



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



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:



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


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


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


Results Optimal number of clusters as load increases Parameters: 1.0,001.0,100,100 121 TccN


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


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/

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Optimal Tree Structures for Large-Scale Grids