PERFORMANCE AND ENERGY-EFFICIENCY ASPECTS OF CLUSTERS OF SINGLE BOARD COMPUTERS

International Journal of Distributed and Parallel Systems (IJDPS) Vol.7, No.2/3/4, July 2016
DOI:10.5121/ijdps.2016.7402 13
PERFORMANCE AND ENERGY-EFFICIENCY
ASPECTS OF CLUSTERS OF SINGLE BOARD
COMPUTERS
Christian Baun
Faculty of Computer Science and Engineering, Frankfurt University of Applied Sciences,
Nibelungenplatz 1, 60318 Frankfurt am Main, Germany
ABSTRACT
When a high performance cluster is demanded and the cost for purchase and operation of servers,
workstations or personal computers as nodes is a challenge, single board computers may be an option to
build inexpensive cluster systems. This paper describes the construction of such clusters and analyzes their
performance and energy-efficiency with the High Performance Linpack (HPL) benchmark.
KEYWORDS
Single Board Computers, Performance evaluation, High Performance Linpack
1. INTRODUCTION
For research projects, dealing with parallel applications, options for implementing clusters of
inexpensive nodes are useful. Compared with commodity hardware servers, such clusters require
lesser purchase costs and operating costs.
This paper is organized as follows. In Section 2, options for providing cluster resources to
research projects with limited financial resources are discussed. Section 3 contains a discussion of
related work. Section 4 presents a list of components of the clusters, which were constructed for
this work. In Section 5, the performance and speedup of the entire cluster of single board
computers is analyzed, by using the High Performance Linpack (HPL). Section 6 contains a
calculation of the energy costs and an analysis of the energy-efficiency of the clusters. Finally,
Section 7 presents conclusions and directions for future work.
2. SINGLE BOARD COMPUTERS - AN OPTION FOR IMPLEMENTING
CLUSTERS
Depending of the available funding resources, the purchase cost for physical servers, workstations
or personal computers can be challenging for scientific projects. Decommissioned hardware can
be bought for little money, but it requires much space and the maintenance is labour intensive.
Another important characteristic are costs, which arise from running physical computer resources.
These include electricity cost.
Building clusters of single board computers with ARM architectures like the Raspberry Pi,
BeagleBone Black, PandaBoard, BananaPi or ODROID is a further option for implementing
clusters. Table 1 contains the single board computers, which were used to build the clusters that
are studied and compared in this paper

14
Table 1. The Single Board Computers, which were used to build the Clusters
Raspberry Pi B BananaPi Raspberry Pi 2 B
CPU family ARM 11 ARM Cortex A7 ARM Cortex A7
CPU cores 1 2 4
Clock rate 800 MHz1
900 MHz 900 MHz
Main memory 512 MB 1024 MB 1024 MB
Ethernet interface 100 Mbit 1000 Mbit 100 Mbit
Storage interfaces SD SD, SATA microSD
1
Increasing the clock rate from 700 to 800 MHz does not require overvolting the CPU and results
in a noticeable increase of the processing power. For this reason, the Raspberry Pi nodes of the
cluster were overclocked to 800 MHz
3. RELATED WORK
In the literature, several works propose implementing high performance clusters of single board
computers.
Cox et al. [1] assembled in 2012 at the University of Southampton for a total cost of around
£3400 a cluster, called Iridis-pi, of 64 Raspberry Pi nodes with 256 MB main memory per node.
This system performed 1.14 Gflops (Flops is an acronym for floating-point operations per
second). The nodes were powered by using 64 individual 5 V power supplies. The power
consumption of the cluster was not presented.
Balakrishnan [2] constructed in 2012 at the University of Edinburgh a cluster by using six
PandaBoard single board computers and two Raspberry Pi nodes, which performed 6.484 Gflops
using the six PandaBoard nodes. The work provides the power consumption of the cluster, which
is around 170 W in idle state and around 200 W during peak load.
Kiepert [3] assembled in 2013 at the Boise State University a cluster of 32 Raspberry Pi nodes
with 512 MB main memory per node, which performed 10.13 Gflops [4]. To power the nodes, he
used two standard PC power supplies and attached them by using one of the 5 V pins of the I/O
header, each Raspberry Pi provides. The maximum total power usage of the cluster is 167 W.
Abrahamsson et al. [5] presented in 2013 a cluster, called MegaRPi, which was assembled at the
Free University of Bozen-Bolzano. The cluster consists of 300 Raspberry Pi nodes with 512 MB
main memory per node. To power the cluster, standard PC power supplies were used. The work
identified several challenges and a number of opportunities. Additionally, the work compared the
power consumption of a single node with other computers when executing a HTTP server
benchmark. Unfortunately, no further power measurements or Gflops results were presented.
Sukaridhoto et al. [6] presented in 2013 a cluster of 16 Pandaboard nodes which was assembled at
the Electronics Engineering Polytechnics Institute Surabaya. The cluster used a single 200 W,
5 V, 40 A power supply to power the nodes. Only the performance of a single node was
measured, which is 0.6 Gflops. The power consumption of the entire cluster was not presented.
Ou et al. [7] compared in 2012 the performance, energy-efficiency and cost-efficiency of a single
PandaBoard computer with an Intel X86 workstation for the three applications web server
throughput, in-memory database and video transcoding. The work examines how many nodes a
cluster of single board computers are required to compete with the workstation.
Tso et al. [8] presented in 2013 the Raspberry Pi Cloud, which was assembled at the University of
Glasgow. This cluster is a scale model of a data center, composed of 56 Raspberry Pi Model B
nodes, that emulates the layers of a cloud stack. The work compares the acquisition cost,
electricity costs (196 W) and cooling requirements of the cluster of single board computers with a

15
testbed of 56 commodity hardware servers. This work does not provide any performance
measurements.
Pfalzgraf and Driscoll [9] assembled in 2014 at the Bradley University a cluster of 25 Raspberry
Pi nodes and used a single 600 W PC power supply to power the cluster nodes. This work does
not provide any power measurements or Gflops results.
These works show the potential of clusters of single board computers, but none of them compares
the performance and energy-efficiency of different single board computer clusters with each
other.
4. COMPONENTS OF THE CLUSTERS OF SINGLE BOARD COMPUTERS
Three clusters (see Table 2) have been constructed for this work. The acquisition cost for each
cluster was less than 500 €. The prices of all components were checked in March 2015 in
Germany and they may vary on the free market.
Table 2. Components of the Clusters
Quantity Component Cluster A Cluster B Cluster C
8 Raspberry Pi Model B 240 €
8 Banana Pi 280 €
8 Raspberry Pi 2 Model B 320 €
8 SD card (16 GB) 40 € 40 €
8 microSD card (16 GB) 50 €
1 16-Port switch (100 Mbit/s) 40 € 40 €
1 16-Port switch (1 Gbit/s) 70 €
8 Network cable CAT 5e 10 € 10 € 10 €
1 10-Port USB power supply 40 € 40 € 40 €
8 USB cable USB-A/Micro-USB 10 € 10 € 10 €
1 Power strip 10 € 10 € 10 €
some Screws, cable ties, spacers, etc. 10 € 10 € 10 €
Price for the entire cluster 400 € 470 € 490 €
The most expensive components are the nodes used. The price for one Raspberry Pi Model B was
around 30 €. The price for one Banana Pi was around 35 € and the price for one Raspberry Pi 2
Model B was around 40 €. A 100 Mbit Ethernet switch is sufficient for the clusters A and C.
Because the Banana Pi nodes provide a faster network interface, cluster B was equipped with a
Gigabit Ethernet switch. The Raspberry Pi 2 nodes of cluster C require microSD flash memory
cards, which are slightly more expensive compared with SD cards. All other components of the
clusters are equal with each other.
5. ANALYZING THE CLUSTERS' PERFORMANCE WITH THE HPL
The High Performance Linpack (HPL) benchmark is a method to investigate the performance of
cluster systems. As described by Dunlop et al. [10] and Luszczek et al. [11], the benchmark
solves a linear system of equations of order n.
× = ; ∈ ℝ ×
; , ∈ ℝ (1)

16
That is divided into blocks of size × , by using double-precision (8 Bytes) floating-point
arithmetic (Gaussian elimination with partial pivoting) on computer systems with distributed
memory. × is equal to the number of processor cores used. The developers of the HPL
recommend in [12] that (the number of process rows) and (the number of process columns)
should be approximately equal, with slightly larger than .
Parameter specifies the problem size. To find the largest problem size that fits into the main
memory of a specific system, the main memory capacity for storing double precision (8 Bytes)
numbers is calculated. Utilizing the entire main memory for the benchmark is impossible because
the operating system and running processes still consume memory. Thus, it is promising to set
to a value 80-90% of the available main memory [13].
Figure 1. Gflops performance of all three clusters, when using all eight nodes, by using the HPL
benchmark. The concrete values for problem size N provides Table 3

17
can be calculated with equation 2. It depends on the number of nodes in the system, the
reduction coefficient which specifies how much percent of the entire main memory of the
cluster shall be utilized by the benchmark and the main memory capacity of a single node.
Table 1 shows how much main memory the single nodes have. A part of the main memory must
be assigned as video memory to the GPU, which lacks own dedicated memory. Because the
GPUs are not used at all in the clusters, the minimal GPU memory was set, which is for all nodes
16 MB. This results in 496 MB main memory left on each node of cluster A and 1008 MB on
each node of the clusters B and C. After the Raspbian operating system and all daemons are
started, approximately 400-430 MB main memory remains available on each node of cluster A.
Each node of the clusters B and C has around 890-920 MB free main memory.
= (
× 1024 × 1024 × 1024 ×
8
) ∗ (2)
If for example shall be big enough to fill around 80% of the memory capacity of four nodes
( = 4) of cluster system C, the calculation is as follows:
= (
1008 GB × 1024 × 1024 × 1024 × 4
8
) ∗ 0.8 ≈ 18,610
A further important parameter is the block size . As optimization, should be
aligned [13]. For this example, if we consider = 64, we calculate !"#,$"%
$&
! × 64 =
290,78125 ≈ 290 and next 290 × 64 = 18,560 = . For this work, the HPL benchmark was
executed with different parameters in the three clusters. Figure 1 shows the Gflops when
executing the benchmark with different values for the parameter when using all eight nodes
and utilizing different proportions of the systems' total main memory. These tests were carried out
to find for each cluster the most recommendable value for .
As BLAS (Basic Linear Algebra Subprograms) implementation was ATLAS (Automatically
Tuned Linear Algebra Software) revision 3.8.4 used on all three clusters.
The results in Figure 1 show that increasing the problem size N results in a better Gflops
performance. The performance drop for = 16 and = 32 in cluster A, when utilizing 95%
of the main memory, is caused by the heavy use of swap memory. The peak performance of
cluster A (1.367 Gflops) is achieved with = 32. The peak performance of cluster B
(4.034 Gflops) and cluster C (7.101 Gflops) is achieved with = 64.
5.1. ANALYSIS OF THE SPEEDUP
The Tables 3, 4 and 5 show the values of the parameters , , and , as well as the runtimes,
required to solve the linear system and the resulting Gflops.
The benchmark was executed in the clusters with just a single node, two nodes, four nodes and
eight nodes to investigate the speedup. The speedup +,, that can be achieved when running a
program on processors is defined as
+, =
-,
-"
(3)

18
where -" is the Gflops on a single-processor system and -, is the Gflops on a multiprocessor
system. The theoretical maximum speedup is equal to the number of single-processor nodes.
Therefore it is value 2 for two nodes, value 4 for four nodes, etc.
The best benchmark results were obtained when is set to a value 80-90% of the available main
memory. These results contain Table 3, 4 and 5 and they show that increasing the number of
nodes also increases the speedup significantly.
Table 3. Analysis of the performance and speedup of Cluster A (Raspberry Pi B) by using the HPL
benchmark
Memory
utilized
N Nodes
used
NB P Q Time [s] Gflops Speedup
≈ 80%
6496 1 32 1 1 722.29 0.212 1.00
9216 2 32 1 2 1503.04 0.347 ≈ 1.63
13024 4 32 1 4 2328.03 0.632 ≈ 2.98
18432 8 32 2 4 3055.37 1.367 ≈ 6.44
≈ 85%
6912 1 32 1 1 1037.84 0.212 1.00
9792 2 32 1 2 1705.12 0.367 ≈ 1.73
13856 4 32 1 4 2782.23 0.637 ≈ 3.00
19584 8 32 2 4 3688.51 1.358 ≈ 6.40
≈ 90%
7328 1 32 1 1 1246.73 0.210 1.00
10368 2 32 1 2 1993.88 0.372 ≈ 1.77
14656 4 32 1 4 3274.85 0.641 ≈ 3.05
20768 8 32 2 4 4370.31 1.367 ≈ 6.50
Table 4. Analysis of the performance and speedup of Cluster B (Banana Pi) by using the HPL benchmark
Memory
utilized
N Nodes
used
≈ 80%
9280 1 64 1 2 928.09 0.574 1.00
13120 2 64 1 4 1456.33 1.034 ≈ 1.80
18560 4 64 2 4 2120.46 2.010 ≈ 3.50
26304 8 64 2 8 3094.01 3.922 ≈ 6.83
≈ 85%
9856 1 64 1 2 1116.91 0.571 1.00
13952 2 64 1 4 1714.48 1.056 ≈ 1.84
19712 4 64 2 4 2510.06 2.035 ≈ 3.56
27904 8 64 2 8 3635.13 3.985 ≈ 6.97
≈ 90%
10432 1 64 1 2 1313.42 0.576 1.00
14784 2 64 1 4 2018.12 1.068 ≈ 1.85
20928 4 64 2 4 2988.12 2.045 ≈ 3.55
29568 8 64 2 8 4272.77 4.034 ≈ 7.00

19
Table 5. Analysis of the performance and speedup of Cluster C (Raspberry Pi 2 B) by using the HPL
benchmark
Memory
utilized
N Nodes
used
≈ 80%
9280 1 64 1 4 493.13 1.081 1.00
13120 2 64 2 4 753.07 2.000 ≈ 1.85
18560 4 64 2 8 1126.66 3.784 ≈ 3.50
26304 8 64 4 8 1775.34 6.835 ≈ 6.32
≈ 85%
9856 1 64 1 4 589.52 1.083 1.00
13952 2 64 2 4 892.98 2.028 ≈ 1.87
19712 4 64 2 8 1324.80 3.855 ≈ 3.55
27904 8 64 4 8 2076.80 6.975 ≈ 6.44
≈ 90%
10432 1 64 1 4 684.53 1.106 1.00
14784 2 64 2 4 1056.70 2.039 ≈ 1.84
20928 4 64 2 8 1594.88 3.832 ≈ 3.46
29568 8 64 4 8 2427.23 7.101 ≈ 6.42
5.2. ANALYSIS OF THE EFFICIENCY
Especially for the Top500 list of the most powerful computer systems, two performance
indicators are considered important. These are:
• the theoretical peak performance /012 of the system. It is determined by counting the
number of floating-point additions and multiplications (in double precision), that can be
completed during a period of time, usually the cycle time of the machine. The /012 of a
system can be calculated with equation 4. The ARM 11 and ARM Cortex A7 processors,
used by the nodes, can process one floating-point addition in one cycle and require two
cycles for a floating-point multiplication. Table 4 contains the /012 of the three
clusters.
/012 3G4lops9 = clock speed 3GHz9 × cores × operations per cycle (4)
• The maximal performance F1 in Gflops that was achieved with the HPL (see Figure 1
and Table 3, 4 and 5).
The efficiency of a specific system in percent is calculated via F1 / /012 × 100 in case of
our clusters the efficiency depends of the executed operations. For cluster A it is between ≈ 21%
and ≈ 42%, for cluster B it is between ≈ 28% and ≈ 56% and for cluster C it is between ≈ 24%
and ≈ 49% (see Table 6). The exact reason for this low efficiency was not evaluated. But the
HPC Challenge benchmark test suite stresses not only the CPUs, but the memory system and the
network interconnect too [11]. Therefore, the interconnect and memory performance of the single
board computers may have a negative impact here [14].
Table 6. The /012 and F1 of the Clusters
Cluster A Cluster B Cluster C
Nodes 8 × Raspberry Pi B 8 × Banana Pi 8 × Raspberry Pi 2 B
Clock rate 800 MHz 900 MHz 900 MHz
CPU cores 8 16 32
/012 3.2-6.4 Gflops 7.2-14.4 Gflops 14.4-28.8 Gflops
F1 1.367 Gflops 4.034 Gflops 7.101 Gflops
Efficiency ≈ 21% − 42% ≈ 28% − 56% ≈ 24% − 49%

20
6. ANALYSIS OF THE ENERGY-EFFICIENCY
Three options for power supply and its impact to the overall power consumption were evaluated.
In one scenario, each cluster node has its own USB power supply (Samsung ETA-U90EWE, 5 V,
2 A). In a second scenario, two 5-port USB power supplies (Anker Model 71AN7105 40 W, 5 V,
8 A) delivered the required electric energy for the nodes. A third scenario, a single 10-port USB
power supply (Anker Model A2133311 60 W, 5 V, 12 A) was used for the nodes. Table 7 shows
the power consumption of the clusters in idle operation mode and in two different stress mode
scenarios. In the first scenario, just the CPUs of the nodes were put into stress mode by using the
command-line tool stress. In the second scenario, the HPL benchmark was used.
The results in Table 7 show that the more power supplies are used, the more energy is consumed.
The reason for this observation is that each power supply wastes a part of the electric energy as
heat. Therefore, each additional power supply results in additional waste of electric energy.
Table 7. Power Consumption of the Clusters
Cluster Power Supply Idle Mode Stress Mode
(stress)
Stress Mode
(HPL)
A
1 × 10-port USB power supply ≈ 23 W ≈ 25 W ≈ 25 W
2 × 5-port USB power supplies ≈ 24 W ≈ 26 W ≈ 26 W
B
C
The energy costs per year IJ for a 24/7 usage for a specific power consumption in kW during
operation K can be calculated with equation 5. In the equation, energy costs of 0.30 € per kWh
are assumed.
IJ = E × 24
hours
day
× 365.25
days
year
× 0.30
€
kWh
(5)
In a scenario where cluster C and one 10-port USB power supply runs all the time, the energy
cost per year for 24/7 usage is between 39.45 € (if it runs in idle mode with 15 W all the time)
and 65.75 € (if it runs in HPL stress mode with 25 W all the time) per year.
Knowing the clusters' electric energy consumption (see Table 7) and its performance when
executing the HPL benchmark (see Section 5) is the precondition to analyze the clusters' energy-
efficiency.
The Green500 list, which is a complement to the Top500 list, uses the flops per Watt metric [15]
to rank the energy efficiency of supercomputers [16]. The metric is defined as
4lops per Watt =
F1 34lops9
( F1 ) 3Watt9
(6)
( F1 ) is the average system power consumption while executing the HPL with a problem
size that delivers F1 . When executing the HPL benchmark, the power consumption of a
cluster depends of the number of nodes used for the benchmark.

21
With F1 = 1.367 G4lops, when using all eight nodes, and consuming 25 W, cluster A
provides approximately 54.68 Mflops per Watt. With F1 = 4.034 G4lops, when using all
eight nodes, and consuming 38 W, cluster B provides approximately 106.15 Mflops per Watt.
With F1 = 7.101 G4lops, when using all eight nodes, and consuming 25 W, cluster C
provides approximately 284.04 Mflops per Watt. These results demonstrate that more recent
generations of single board computers operate more energy-efficient.
7.CONCLUSIONS AND FUTURE WORK
The performance of single board computer clusters cannot compete with higher-value systems. In
the Top500 list from June 1993, the maximum observed performance F1 of cluster system A
(1.367 G4lops) would be sufficient for 216th
place, F1 = 4.034 G4lops of cluster B would be
sufficient for 45th
place and F1 = 7.101 G4lops of cluster B would be sufficient for 29th
place.
The most recent Top500 list in which our best performing cluster could achieve a place is the list
of November 1996 where cluster C would be sufficient for 277th
place.
Compared with recent cluster sites this performance is very low. In the most recent Top500 list
from November 2015, the last entry (500th
place) provides F1 = 206,400 G4lops, which is
more than factor 150,000 better compared with cluster A, more than factor 51,000 better
compared with cluster B and more than factor 29,000 better compared with cluster C.
Also the energy-efficiency cannot compete with higher-value systems. Cluster A provides
approximately 54.68 Mflops per Watt, which would be sufficient for 166th
place in the Green500
list from November 2007. Cluster B (106.15 Mflops per Watt) would be sufficient for 50th
place
and Cluster C (284.04 Mflops per Watt) would be sufficient for 6th
place in the same list.
In the most recent list from November 2015, the best entry 1st
place) provides 7,031.58 Mflops
per Watt, which is more than factor 128 better compared with cluster A, more than factor 66
better compared with cluster B and more than factor 24 better compared with cluster C.
Regardless of the performance or energy-efficiency, clusters of single board computers like the
evaluated ones are useful for several academic purposes and research projects because of the
lesser purchase costs and operating costs compared with commodity hardware server resources.
Since March 2016, the Raspberry Pi 3 is available for purchase. This single board computer
provides more computational power compared with the cluster nodes that were used in this
project. Building a cluster of these computers is one of the next steps. Such a cluster should also
have more than just eight nodes to further analyze the potential suitability for larger-scale parallel
applications.
ACKNOWLEDGEMENTS
This work was funded by the Hessian Ministry of Higher Education, Research, and the Arts
('Hessisches Ministerium für Wissenschaft und Kunst') in the framework of research for practice
('Forschung für die Praxis').
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cost, compact demonstration cluster”, Cluster Computing, Vol. 17, No. 2, pp 349-358.

22
[2] Balakrishnan, N. (2012) “Building and benchmarking a low power ARM cluster”. Master’s thesis,
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the Green500 List”, The Green500 List: Environmentally Responsible Super-computing.
Authors
Dr. Christian Baun is working as Professor at the Faculty of Computer Science and
Engineering of the Frankfurt University of Applied Sciences in Frankfurt am Main,
Germany. His research interest includes operating systems, distributed systems and
computer networks.

PERFORMANCE AND ENERGY-EFFICIENCY ASPECTS OF CLUSTERS OF SINGLE BOARD COMPUTERS

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