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
Outline
Introduction
The model
Computation of the optimal policy
Experimental 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
Pool Manager
Job Requests
Users
3
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
N Servers
l1
b1
type 1
k
queue 1
l2
b2
type 2
queue 2
N-k
4
The model - 2
 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?
N Servers
l1
Switch a
server
b1
type 1
k
queue 1
type 2
l2
b2
queue 2
N-k
5
The model - 3
 Arrival rates
l1 and l2
l1
 Average service times
b1 and b2
l2
b1
b2
 Holding Costs (the cost of waiting)
c1 and c2
 Switching Costs
C1,2 and C2,1
h
z
 Switching Rates
z and h
6
System State
 The system state is
S  ( j1 , j2 , k1 , m1, 2 , m2,1 )
 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
7
Computation of the optimal policy
 The optimal policy
is specified by the
action d which
minimises the
right-hand side
 Principles of dynamic
programming have been
used to solve the finitehorizon optimization
problem


Vn ( S )  j1c1  j2 c2  min c(d )    qd ( s, s ' )Vn 1 ( S ' )
d 

S'


 The computational complexity of determining the
optimal switching policy is of the order
2
3
O ( J N n)
8
Experimental Results
 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
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
10
Increasing number of servers
11
Increasing loads
12
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
13
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/
14