Optimal Server Allocation in Reconfigurable Clusters with Multiple Job Types 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

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 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 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 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 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 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 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 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 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 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 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 Increasing number of servers M = 2

14 Increasing loadsM = 2

15 Increasing number of servers M = 3

16 Increasing loadsM = 3

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 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: