Optimal Tree Structures for Large-Scale Grids

1. Optimal Tree Structures for Large-Scale Grids J. Palmer I. Mitrani School of Computing Science University of Newcastle NE1 7RU jennie.palmer@ncl.ac.uk isi.mitrani@ncl.ac.uk

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

3. 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

4. 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

5. dynamic network reconfiguration

6. The model • What value of k minimizes the overall average response time of the system?

7. 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

8. 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

9. Computation of the optimal tree structure • For a flat structure ( c1>lN for stability): • For a two level tree structure: • The objective is to minimise the latter with respect to k

10. 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

11. 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:

12. Results • Average response time as k varies • Parameters: • Load is 80%, flat structure not feasible heuristic predicts k = 6 optimal k = 4

13. Results • Optimal number of clusters as load increases • Parameters:

14. 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

15. Acknowledgment • This work was carried out as part of the collaborative project GridSHED, funded by North-East Regional e-ScienceCentre 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/