Operating regions for the Algorithms
First fit:
− VMs heavier along all dimensions listed first followed by lighter VMs. This will ensure that
the heavier VMs first take up PMs required and then lighter VMs fill in the 'gaps'.
− This method can be used when it is known that for any individual VM, generally the
requirements along all dimensions are going to be more or less similar.
1D Best Fit:
− VMs heavier along the consolidation dimension first followed by VMs consuming less
along that dimension (other dimensions consuming less).
− This method can be used when we know that usage along a particular dimension is going to
be generally high and it is enough to consider that dimension while consolidating.
Heuristic based best fit:
− VMs heavier in volume (not necessary 'heavy' across all dimensions) listed first, followed
by low volume VMs.
− This method can be used when we know that some (increasing) function of the dimensions
(the volume) is going to be high for most VMs.
Dot Product based Fit:
− The general nature of usage along any dimension should remain more or less similar across
VMs. For eg, if the cpu usage of the 1st VM placed was high, and the cpu usage of the
second VM to be placed is also high, then their dot product will be higher.
− This method can be used when the general nature of resource usage remains similar along
all dimensions.
Base idea: For a heuristic to perform better, it should figure out the min number of PMs
required early in the placement process. Later, it can fit in the lighter VMs in the 'gaps'.
Sample Runs:
1. For First Fit:
Dimensions: 3
VMs: 6
PMs: 6
Matrix:
0.8
0.8
0.7
0.7
0.6
0.6
0.2
0.2
0.3
0.4
0.2
0.3
0.8
0.7
0.6
0.3
0.3
0.2
First Fit uses: 4 PMs
Single Dimensional Best Fit uses: 4 PMs
Heuristic-based Best Fit uses: 4 PMs
Vector Based Fit uses: 4 PMs
Heuristic-based Worst Fit uses: 6 PMs
Observation: First Fit behaves similar to other algorithms (for its hypothesized best
case).
Todo: For general case, it is expected to perform worse.
2. For 1D Best Fit:
Dimensions: 3
VMs: 6
PMs: 6
Matrix:
0.4
0.8
0.4
0.7
0.3
0.6
0.3
0.2
0.2
0.4
0.1
0.3
0.1
0.2
0.3
0.3
0.4
0.4
First Fit uses: 3 PMs
Single Dimensional Best Fit uses: 3 PMs
Heuristic-based Best Fit uses: 4 PMs
Vector Based Fit uses: 4 PMs
Heuristic-based Worst Fit uses: 6 PMs
Observation: 1D Best fit performs better as predicted.
Placement Plan:
FIRST FIT
First Fit uses: 3 PMs
The Allocation Matrix after First Fit is:
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
The PM Variables are:
1
1
1
0
0
0
----------------------------------------------------------Solution is Valid!
SINGLE DIMENSIONAL BEST FIT
Single Dimensional Best Fit uses: 3 PMs
The Allocation Matrix after Single Dimensional Best Fit is:
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
The PM Variables are:
1
1
1
0
0
0
----------------------------------------------------------Solution is Valid!
HEURISTIC-BASED BEST FIT
Heuristic-based Best Fit uses: 4 PMs
The Allocation Matrix after Heuristic-based Best Fit is:
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
The PM Variables are:
1
1
1
1
0
0
----------------------------------------------------------Solution is Valid!
VECTOR BASED FIT
Vector Based Fit uses: 4 PMs
The Allocation Matrix after Vector Based Fit is:
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
The PM Variables are:
1
1
1
1
0
0
----------------------------------------------------------Solution is Valid!
HEURISTIC-BASED WORST FIT
Heuristic-based Worst Fit uses: 6 PMs
The Allocation Matrix after Heuristic-based Worst Fit is:
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
The PM Variables are:
1
1
1
1
1
1
----------------------------------------------------------Solution is Valid!
3. For Heuristic Based Best Fit:
Dimensions: 3
VMs: 6
PMs: 6
Matrix:
0.8
0.3
0.8
0.2
0.2
0.8
0.2
0.7
0.1
0.3
0.1
0.2
0.4
0.3
0.2
0.2
0.6
0.7
First Fit uses: 4 PMs
Single Dimensional Best Fit uses: 4 PMs
Heuristic-based Best Fit uses: 4 PMs
Vector Based Fit uses: 4 PMs
Heuristic-based Worst Fit uses: 6 PMs
The Allocation plans are also same:
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
Observation: The plan doesnt seem to make Heuristic based best fit to perform better.