1. Dynamic Server Allocation in Heterogeneous Clusters 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. 2 Outline Introduction The model Computation of the optimal policy Experimental Results Conclusions

3. 3 Introduction In a Grid environment, heterogeneous clusters of servers provide a variety of services to widely distributed user communities Users submit jobs without necessarily knowing or caring where they will be executed

4. 4 The model - 1 Demands (jobs) of two types are submitted to a pool of N servers A configuration consists of dedicating k of the servers to type 1 and N-k to type 2 queue 1 queue 2 N Servers k N - k type 1 type 2 b b

5. 5 queue 1 queue 2 N Servers k N - k type 1 type 2 Switch a server b b Servers can be switched from type 1 to type 2 and vice versa What is a good policy for deciding dynamically when to reconfigure the system? The model - 2

6. 6 Arrival rates and Average service times b 1 and b 2 Holding Costs (the cost of waiting) c 1 and c 2 Switching Costs C 1,2 and C 2,1 Switching Rates and b b The model - 3

7. 7 System State The system state is The system has been modelled by a continuous Markov process A dynamic configuration policy must decide, for any given state S, whether to i. Do nothing ii. Initiate a switch from queue 1 to queue 2 iii. Initiate a switch from queue 2 to queue 1

8. 8 Computation of the optimal policy Principles of dynamic programming have been used to solve the finite- horizon optimization problem The computational complexity of determining the optimal switching policy is of the order The optimal policy is specified by the action d which minimises the right-hand side

9. 9 Experimental Results Optimal decisions have been stored in look-up tables which may then be referred to during simulations Key Do nothing Switch 1 2 Switch 2 1 j1j1 j2j2

10. 10 Heuristic Policies An exact characterisation of the optimal policy is unlikely Instead, formulate a heuristic which performs reasonably well and is easy to implement Three policies compared in simulations i.StaticDo no switching at all ii.HeuristicAttempts to balance the total holding costs of the two job types. E.g. switch from queue 1 to queue 2 if: iii.OptimalUse pre-computed tables of optimal decisions

11. 11 Increasing number of servers

12. 12 Increasing loads

13. 13 Conclusions A problem of interest in the area of distributed computing and dynamic Grid provision has been examined The optimal reconfiguration policy can be computed and tabulated For practical purposes, an easily implementable heuristic policy is available A natural generalization of this problem would be to consider more than two job types and clusters

14. 14 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/