Optimal Tree Structures for Large-Scale Grids

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Optimal Tree Structures for Large-Scale Grids

• J. Palmer I. Mitrani
• School of Computing Science
• University of Newcastle
• NE1 7RU
• jennie.palmer_at_ncl.ac.uk isi.mitrani_at_ncl.ac.uk

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Outline

• Introduction
• The model
• Computation of the optimal tree structure
• A simple heuristic
• Results
• Conclusions and future work

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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

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• 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

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dynamic network reconfiguration
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The model

• What value of k minimizes the overall average
  response time of the system?

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Job distribution policies

• Different job distribution policies have been
  considered

• Each dependent has a separate queue the master
  places new jobs into
• those queues in random order
• the queue which is currently shortest
• those queues in cyclic order
• Dependents at the final service cluster level
  have a joint queue

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Computation of the optimal tree structure

• The average response time at each level i master
  node is given by

where

• At the final service level, approximated by an
  M/M/n queue

where
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Computation of the optimal tree structure

• For a flat structure ( c1gtlN for stability)

• For a two level tree structure

• The objective is to minimise the latter with
  respect to k

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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

• 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

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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

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Results

• Average response time as k varies
• Parameters
• Load is 80, flat structure not feasible

heuristic predicts k 6
optimal k 4
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Results

• Optimal number of clusters as load increases
• Parameters

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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
• extension to include further tiers of master
  nodes
• different modelling assumptions for how a master
  node makes a routing decision
• shortest queue
• cyclic order

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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/