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
Outline
 Introduction
 The model
System State
 Computation of the optimal policy
 Experimental Results
Look-up tables
Policy Comparison
The Heuristic Policy
Simulation results
 Conclusions
2
Introduction
 In a Grid environment,
 Users submit jobs without
heterogeneous clusters of
necessarily knowing or
servers provide a variety of
caring where they will be
services to widely distributed
executed
user communities
Cluster 2
Cluster 3
...
Cluster 1
Cluster M
Pool Manager
Job Requests
Users
3
The model
 Demands (jobs) of M types are submitted to a
pool of N servers
 A configuration consists of dedicating ki of the
servers to job type i, such that
M
k
i 1
type 1
i
N
l1
N Servers
b1
k1
queue 1
type 2
l2
k2
queue 2
bM
queue M
...
...
type M
lM
b2
kM
4
The model
 Servers can be switched from type i to type j
 What is a good policy for deciding dynamically when
to reconfigure the system?
N Servers
type 1
l1
b1
k1
Switch a
server
queue 1
type 2
l2
k2
queue 2
bM
queue M
...
...
type M
lM
b2
kM
5
The model
 Arrival rates
 l1 , l 2 , . . . , lM
 Average service times
 b1 , b2 , . . . , b M
li
bi
 Holding Costs (the cost of waiting)
 c1 , c2 , . . . , c M
 Switching Costs
 c
 i, j
i, j
 Switching Rates
 
i, j
6
System State
 The system state is
S  ( j, k , m)
where
j  ( j1 , j2 ,..., jM ) k  (k1 , k2 ,..., kM ) m  (mi , j )iM, j 1
 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
7
Computation of the optimal policy
 Principles of dynamic
programming have been
used to solve the
optimization problem
M
V (S )  
i 1
 The optimal policy
is specified by the
action d which
minimises the
right-hand side


ji ci  min c(d )    qd ( s, s ' )V ( S ' )
d 

S'


 The computational complexity of determining the
optimal switching policy is of the order
O( J M N M 1 M ( M 1) / 2 )
8
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
j2
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
j1
4
5
6
Key
7
Do nothing
Switch 1
2
8
Switch 2
1
9
10
9
Experimental Results – Look-up Tables
N = 3, M = 3, j1=0
j3
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
Key
j2
Do nothing
Switch 1
2
4
5
6
7
Switch 1
3
Switch 2
3
8
9
10
10
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. Static
Assign servers in proportion to the
holding cost and offered load for each
type
ii. Heuristic
Attempts to balance the total
holding costs of the job types
Use pre-computed tables of optimal
decisions
iii. Optimal
11
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.


1


lb  b min( kb , jb ) 
cb  jb 
 a ,b






1


la  a min( k a  1, ja )
Kca  ja 
 a ,b




12
Increasing number of servers
M=2
13
Increasing loads
M=2
14
Increasing number of servers
M=3
450
static
optimal
heuristic
Average cost
400
350
300
250
200
150
100
50
0
3
4
5
Number of servers
6
15
Increasing loads
M=3
700
Average cost
600
static
optimal
heuristic
500
400
300
200
100
0
2.6
2.8
3
3.2
Total load
3.4
3.6
16
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
17
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/
18