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 J. Palmer I. Mitrani School of Computing Science University of Newcastle NE1 7RU

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

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

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

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

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

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

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

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:

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

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 :

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

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

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

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: