1. Grid Performability, Modelling and Measurement AHM’04 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 J. Palmer I. Mitrani School of Computing Science University of Newcastle NE1 7RU jennie.palmer@ncl.ac.uk isi.mitrani@ncl.ac.uk

2. Grid Performability, Modelling and Measurement AHM’04 2 Outline  Introduction  The model  Computation of the optimal tree structure  A simple heuristic  Results  Conclusions and future work

3. Grid Performability, Modelling and Measurement AHM’04 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. Grid Performability, Modelling and Measurement AHM’04 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. Grid Performability, Modelling and Measurement AHM’04 5 dynamic network reconfiguration

6. Grid Performability, Modelling and Measurement AHM’04 6  What value of k minimizes the overall average response time of the system? The model

7. Grid Performability, Modelling and Measurement AHM’04 7 Different job distribution policies have been considered: Job distribution policies 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

8. Grid Performability, Modelling and Measurement AHM’04 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. Grid Performability, Modelling and Measurement AHM’04 9 Computation of the optimal tree structure  The objective is to minimise the latter with respect to k  For a flat structure ( c 1 > N for stability):  For a two level tree structure:

10. Grid Performability, Modelling and Measurement AHM’04 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. Grid Performability, Modelling and Measurement AHM’04 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, c 1 and c 2 :

12. Grid Performability, Modelling and Measurement AHM’04 12 Results  Average response time as k varies  Parameters:  Load is 80%, flat structure not feasible optimal k = 4 heuristic predicts k = 6

13. Grid Performability, Modelling and Measurement AHM’04 13 Results  Optimal number of clusters as load increases  Parameters:

14. Grid Performability, Modelling and Measurement AHM’04 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: 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

15. Grid Performability, Modelling and Measurement AHM’04 15 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/