dynamic server allocation in heterogeneous clusters j. palmer i. mitrani school of computing science...
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Dynamic Server Allocation in Heterogeneous Clusters
Dynamic Server Allocation in Heterogeneous Clusters
J. Palmer I. Mitrani
School of Computing Science
University of Newcastle
NE1 7RU
[email protected] [email protected]
J. Palmer I. Mitrani
School of Computing Science
University of Newcastle
NE1 7RU
2
Outline
Introduction
The model
Computation of the optimal policy
Experimental 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
Users
Job Requests
Pool Manager
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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
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
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Arrival rates and
Average service times b1 and b2
Holding Costs (the cost of waiting) c1 and c2
Switching Costs C1,2 and C2,1
Switching Rates and
b
b
The model - 3
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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
),,,,( 1,22,1121 mmkjjS
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Computation of the optimal policy
Principles of dynamic programming have been used to solve the finite-horizon optimization problem
'
)(),()(min)( '1
'2211
S
SVssqdccjcjSV ndd
n
The computational complexity of determining the optimal switching policy is of the order
)( 32 nNJO
The optimal policy is specified by the action d which minimises the right-hand side
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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
j1
j2
10
9
8
7
6
5
4
3
2
1
0
10 9 876543210
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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. Static Do no switching at all
ii. Heuristic Attempts to balance the total holding costs of the two job
types. E.g. switch from queue 1 to queue 2 if:
iii. Optimal Use pre-computed tables of optimal decisions
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Increasing number of servers
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Increasing loads
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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
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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/