Dynamic Server Allocation in Heterogeneous Clusters J. Palmer I. Mitrani School of Computing Science...

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

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

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

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

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

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

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

),,,,( 1,22,1121 mmkjjS

8

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

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

j1

j2

           10

           9

           8

           7

           6

           5

           4

           3

           2

           1

           0

10 9 876543210 

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. 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

11

Increasing number of servers

12

Increasing loads

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

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/