1. Optimal Server Allocation in Reconfigurable Clusters with Multiple Job Types 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  System State  Computation of the optimal policy  Experimental Results  Look-up tables  Policy Comparison  The Heuristic Policy  Simulation 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  Demands (jobs) of M types are submitted to a pool of N servers  A configuration consists of dedicating k i of the servers to job type i, such that queue 1 queue M N Servers k1k1 kMkM type 1 type M   bb bb type 2  queue 2 bb k2k2...

5. 5 Switch a server  Servers can be switched from type i to type j  What is a good policy for deciding dynamically when to reconfigure the system? The model queue 1 queue M N Servers k1k1 kMkM type 1 type M   bb bb type 2  queue 2 bb k2k2...

6. 6 The model  Arrival rates    ,...,   Average service times  b 1, b 2,..., b M  Holding Costs (the cost of waiting)  c 1, c 2,..., c M  Switching Costs   Switching Rates   i bibi

7. 7 System State  The system state iswhere  The system has been modelled by a continuous Markov process, the transition rates of which depend on the decisions taken in various states  A dynamic configuration policy must decide, for any given state S, whether to i. Do nothing ii. Initiate a switch from queue i to queue j

8. 8 Computation of the optimal policy  Principles of dynamic programming have been used to solve the 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 – Look-up Tables N = 2, M = 2  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 Key Do nothing Switch 1 2 Switch 1 3 Switch 2 3 j2j2 j3j3 Experimental Results – Look-up Tables N = 3, M = 3, j 1 =0

11. 11 Policy Comparison  An exact characterisation of the optimal policy is unlikely  Instead, we formulate a heuristic which performs reasonably well and is easy to implement  Three policies compared in simulations: i.StaticAssign servers in proportion to the holding cost and offered load for each type ii.HeuristicAttempts to balance the total holding costs of the job types iii.OptimalUse pre-computed tables of optimal decisions

12. 12 The Heuristic Policy  Calculate the following for each of the M(M-1)/2 possible switches from queue a to queue b.  Find the maximum of all quantities calculated.  If strictly positive, this will be the most advantageous switch to take, so take the action corresponding to this switch. Otherwise, do nothing.

13. 13 Increasing number of servers M = 2

14. 14 Increasing loadsM = 2

15. 15 Increasing number of servers M = 3

16. 16 Increasing loadsM = 3

17. 17 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

18. 18 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/