Building A Linux Cluster Using Raspberry PI #2!
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A cluster of 8 Raspberry Pi computers was created to demonstrate parallel processing. Various algorithms like sorting and searching were tested on the cluster and compared to single CPU performance. The cluster showed limitations due to communication overhead between processors. Simpler operating systems and limiting tasks assigned to each Raspberry Pi helped improve performance. For example, an 8 node parallel system saw approximately double processing speed without network time protocol, remote desktop, and system logging. Message passing interface (MPI) was used to share tasks among the Raspberry Pis. Tests showed that problems with divisible, independent subtasks had better speedup than those relying on interdependent results.
![7 Refrences
B. Peguero. (2014). MpichCluster in Ubuntu [Online].
Available https://help.ubuntu.com/community/MpichCluster
J. Burkardt. (2011). MPI C Examples [Online].
Available http://people.sc.fsu.edu/ jburkardt/c src/mpi/mpi.html
MPICH. (2015). MPICH Guide [Online].
Available http://www.mpich.org/documentation/guides/
J. Fitzpatrick. (2013). The HTG Guide to Getting Started with Raspberry Pi
[Online]. Available http://www.howtogeek.com/138281/the-htg-guide-to-
getting-started-with-raspberry-pi/all/
7](https://image.slidesharecdn.com/rpicluster-190413160756/85/Building-A-Linux-Cluster-Using-Raspberry-PI-2-7-320.jpg)
Building A Linux Cluster Using Raspberry PI #2!
- 1. Raspberry Pi Computer Cluster Noel J. Petit Ken Johnson Paulina Vo Don Vo Christian Grant April 10, 2015 Computer Science Augsburg College 2211 Riverside Avenue Minneapolis,MN 55454 [email protected] [email protected] 1
- 2. 1 Abstract A cluster of Raspberry Pi computers has been created to test and demon- strate the effectiveness of small computers in parallel processing. The comput- ers use MPICH, a message passing protocol to share a large task and then co- ordinate their results at the end of the processing among a group of 8 or more Raspberry Pi computers. We compare the single CPU (such as the common Intel Core i5) vs cluster performance of various parallel algorithms such as sorting and searching. We found limitations in the ability to speed up a pro- cess because of the communication and operating system overhead among pro- cessors. We tested various operating systems and configurations for their abil- ity to speed up a process shared by many CPU’s. Results were improved by using simpler operating systems and limiting the tasks assigned to the Rasp- berry Pi. For example, by removing services such as Network Time Protocol, Remote Desktop, and system logging, we were able to approximately double the processing speed of an 8 node parallel system. In addition, we tested file sharing with NFS and SecureNFS as well as file sharing with file systems out- side the cluster (for example, Google storage). We will review the technical findings as well as what we learned by building a cluster of small computers to simulate a high performance processor. 2 Introduction Created a cluster of inexpensive Raspberry Pi computers to demonstrate the power of parallel computing. Each node of the cluster is a Raspberry Pi mini- computer in a family of computers introduced in 2012 as a full-featured mini- computer for $35. At that cost, it is possible to acquire many computers and network them via Ethernet or WiFi. In our case we used an Ethernet switch to join 6 to 8 model B Raspberry Pi’s and demonstrate various parallel pro- cessing features. 3 Raspberry Pi This minicomputer has passed through three versions – B, B+, and 2. Here is a rough comparison of the models available. Model Number B B+ 2 Processor Broadcom BCM 2835 BCM 2835 BCM 2836 CPU Speed 700 MHz Single 700 MHz Single 900 MHz Quad Core ARM 1176 Core ARM 1176 Core ARM Cortex A7 Memory 512 MB SD RAM 512 MB SD RAM 1 GB SD RAM All have USB 2.0. ports, audio and video outputs as well as Ethernet and power connectors. Each draws about 700 ma at 5 volts for a power draw of about 4 watts. 2
- 3. A number of operating systems are available. The install manager for the Raspberry Pi is NOOBS. The operating systems included with NOOBS are: • Arch Linux ARM • OpenELEC • Pidora (Fedora Remix) • Puppy Linux • Raspbmc and XBMC open source digital media center • RISC OS - The operating system of the first ARM-based computer • Raspbian In our case we wanted to have as many features and languages as possible so we used the Raspbian available from the Raspberry Pi foundation. That may not be the fastest of operating systems but it is very close to the Ubuntu that students use in our public lab and provided the widest of features. The B and B+ processors were measured at about 40 Megaflops with the quad core 2 processor at 98 Megaflops (1). On the CPUlevel the performance is similar to a 300MHzPentium IIof 1997-1999. Connecting machines is done with a simple 100 Mbps Ethernet switch. Each processor in our cluster is assigned a fixed IP. 4 MPICH The MPICH consortium of contributors who develop and support a library or message passing protocols for communication among computers. MPICH includes compilers for FORTRAN, C, C++. In our case we chose C as our language and used many of the example parallel programs to demonstrate the cluster. MPICH includes a specialized compiler and run time for C which manages the distribution and collection of tasks and data among connected processors. To allow processors to share compiled programs and their data, all computers share files via Network File Sharing (NFS) on either one of the Raspberry Pi’s or a separate Ubuntu server running NFS server. For simple programs, MPICH starts all of the programs on as many proces- sors as specified and runs all to completion. Each processor is aware of how many other processors are in the cluster as well as its index in the array of processors. Thus, every processor knows who it is as well as how to address all of the other neighbor processors. Some of the programs distribute the task among processors by breaking the shared data into blocks. Some distribute the tasks by sending data to each processor and waiting for the “master” pro- cessor to receive data from all the slaves. 5 Parallel vs Single Processor Tasks 3
- 4. As a start, let’s consider running a simple mathematical task on a single pro- cessor and then distributing this task among several processors. There will always be start-up time spent distributing the task to multiple processors so we expect short tasks to take longer when distributed among processors. 5.1 Calculating Prime Numbers Prime MPI calculates prime numbers and distributes the work amongst the various numbers of processors. Prime MPIs code is derived from [email protected]. The work is divided up amongst two Raspberry Pi 2s. Each Raspberry Pi 2 has quad core capabilities. The way the work division is represented in this paper is shown as ... (Raspberry Pi #1) / (Raspberry Pi #2) The work distribution of the two Raspberry Pis was tested on prime number lists of size 3.2 · 104 , 6.4 · 104 , 1.25 · 105 , 2.56 · 105 , and 5.12 · 105 . The predicted data for this segment will show a logarithmic plot for the graph. It is also pre- dicted that the graph will display close to the same results between processes between corresponding division. For example, 1/0 will display the same data as 1/1. The process should run faster, however the time must also account for the communication between Pis. It is also predicted that at 5/4 and 5/5, the runtimes will increase since the code will divide up the processes to be run on more processes that exist. The data collected is shown below. Number of Processes per Pi Number of Primes 1/0 1/1 2/1 2/2 3/2 3/3 4/3 4/4 5/4 5/5 32,000 3.66 3.66 1.84 1.84 0.92 0.92 0.65 0.92 0.95 1.25 64,000 13.6 13.6 6.84 6.84 3.4 3.4 2.37 3.46 3.1 128,000 51.3 51.3 25.7 25.7 13.0 13.0 8.62 13.0 10.6 256,000 192.8 192.8 96.6 96.6 48.5 48.5 32.5 48.6 40.1 512,000 729.9 729.9 367.3 367.3 183.6 183.6 122.4 188.6 150.1 Using Microsoft Excel, the data was entered and compiled to form the graph below. The horizontal axis represents the number of processors the work is distributed amongst. The vertical axis represents the runtime for each test. 4
- 5. As shown from the data collected, the predictions made were true. There was some variation once the program was run on eight (4/4) and nine (5/4) pro- cessors. The variation between the two is fairly small except for size 512,000 (difference of 66.2). There is a max of eight processors, so when the code was tested on nine processors the runtime decreased which was also predicted. 5.2 Ring MPI Ring MPI sends messages of size 100, 1000, 10000, 100000, and 1000000 from processor 0 to 1 to 2 to ... to P-1 then back to 0. P represents the number of processors used. We expect the program to take longer with more processors since the message needs to be relayed to more processors before returning to processor 0. Number of Processes per Pi Values Sent 1/0 1/1 2/1 2/2 3/2 3/3 4/3 4/4 5/4 5/5 100 N/A 0.001 0.001 0.003 0.004 0.006 0.007 0.010 0.010 0.011 1000 N/A 0.003 0.003 0.006 0.008 0.009 0.009 0.015 0.015 0.015 10000 N/A 0.018 0.017 0.039 0.034 0.051 0.051 0.070 0.074 0.086 100000 N/A 0.139 0.141 0.277 0.280 0.417 0.419 0.560 0.573 0.705 1000000 N/A 1.365 1.385 2.730 2.740 4.095 4.117 5.464 5.496 6.834 As expected, the amount of time it took to relay a message took longer with more processors. There is no result for 1/0 processors because there is no other processor to communicate with processor 0. 5.3 Search MPI Search MPI is a function which utilizes parallel programming to find a value J which satisfies the condition F(J) equals some value C. It works by searching integers between two endpoint values, A and B, and evaluating each integer on a function F. Based on the number of processors the function has access to it will divide up the “search” work accordingly. We should expect to see the time it takes for the program to run to decrease as the number of processors increases. 5
- 6. Number of Processes per Pi Range 1/0 1/1 2/1 2/2 3/2 3/3 4/3 4/4 5/4 5/5 1 3.0 1.5 1.0 75.0 0.64 0.51 0.46 0.38 0.39 0.41 1 · 108 29.7 14.8 9.9 7.4 6.0 5.0 4.2 3.7 4.0 4.0 1 · 109 297.0 148.0 99.0 74.0 60.0 50.0 42.0 37.0 43.0 37.0 Looking at the table above we can see the time it takes for the function to execute decay as more processors are employed. The second row displays a time of 14.8 when two are active and a time of 4 when 10 are active. This data output is what we expected and agrees with our assumption about the relationship between processors and time to execute. 6 Conclusion After a series of tests, it can be concluded that there are benefits as well as limitations when implementing parallel processing on Raspberry Pis. Some of these limitations are simply due to the communication overhead that is in- herent to many parallel processing structures. For certain problems, there is a significant gain in performance however the best cases for these are divisible problems that are not interdependent on results of other nodes. Cases that depend on computation results from other nodes in a parallelized cluster ex- perience less of a gain in performance time. This method of parallel process- ing is ideally suited for Monte Carlo simulations. 6
- 7. 7 Refrences B. Peguero. (2014). MpichCluster in Ubuntu [Online]. Available https://help.ubuntu.com/community/MpichCluster J. Burkardt. (2011). MPI C Examples [Online]. Available http://people.sc.fsu.edu/ jburkardt/c src/mpi/mpi.html MPICH. (2015). MPICH Guide [Online]. Available http://www.mpich.org/documentation/guides/ J. Fitzpatrick. (2013). The HTG Guide to Getting Started with Raspberry Pi [Online]. Available http://www.howtogeek.com/138281/the-htg-guide-to- getting-started-with-raspberry-pi/all/ 7