Difference between revisions of "Examples"

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== <span style="font-size:120%">Fault-Tolerant Multiprocessor System</span> ==
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Below are a list of example models built in M&ouml;bius. These examples come from the Mobius team and user community. '''Please consider sharing''' the models you have built in the past. If you do decide to share your model, please look at the [[Examples#Share_Your_Model|Share Your Model]] section for instructions on creating a new page and linking it here.
  
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This section presents an example of a system that can be modeled using Möbius. It starts with a description of the system, and then guides you through one way to build a model of the system and solve it using both simulation and numerical solution. The example is intended to take you step-by-step through the process of creating and solving a model in Möbius, and to exhibit many of the capabilities and features of the tool.
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== Examples ==
  
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* [[SCADA Case Study from QEST 2011]] - A case study that uses the ADVISE formalism to study the security of a SCADA and corporate network.
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*[[ADVISE Bank Robbery Tutorial Model]]- An example using advise with full steps and project included.
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*[[Conveyor Belt]]- Incomplete
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*[[Database2]]- Incomplete
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*[[Ian2]]- Incomplete
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*[[Faulty Proc2]]- Incomplete
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*[[Multi-Proc]]- Incomplete
  
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=== <span style="font-size:110%">System Description</span> ===
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== Share Your Model ==
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Here is [[Example Model Template|the template]] that people should use. If you are not familiar with mediawiki here are steps involved in adding your own model.
  
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The system under consideration is a highly redundant fault-tolerant multiprocessor system adapted from <ref name=L:Fault:92>D. Lee, J. Abraham, D. Rennels, and G. Gilley. A numerical technique for the evaluation of large, closed fault-tolerant systems. In ''Dependable Computing for Critical Applications'', pages 95–114. Springer-Verlag, Wien, 1992.</ref> and shown in <xr id="fig:ex_multiproc" />. At the highest level, the system consists of multiple computers. Each computer is composed of 3 memory modules, of which 1 is a spare module; 3 CPU units, of which 1 is a spare unit; 2 I/O ports, of which 1 is a spare port; and 2 non-redundant error-handling chips.
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# Log in to https://www.mobius.illinois.edu/wiki/.
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# On the top right search for the name of the page you want to create.
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# If there are no matching results it should prompt you to create a page with the name that you searched for.
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<figure id="fig:ex_multiproc">
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# Under the page, create a submission by simply following the template of the [[Example Model Template|the template]]. Also, one has been created as an example for your reference and can be found [[Example Model Template|here]].
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[[Image:multiproc.png|center]]
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# To view the source code of the page just click on the edit tab on the top right of the page. Copying the source code should have the format ready for you.
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<br/>
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# Under description you can simply copy your paper's Abstract section to give viewers a brief idea about your paper. Please be sure to link your paper and website. If you are confused about the syntax to create a link please refer to [https://www.mediawiki.org/wiki/Help:Links#External_links Links]. Also please upload your project by clicking on the [[Special:Upload]] link at the bottom of your page.  
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<center><xr id="fig:ex_multiproc" nolink />: Fault-tolerant multiprocessor system.</center></figure>
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# If you have any questions feel free to contact Ken Keefe at [mailto:kjkeefe@illinois.edu kjkeefe@illinois.edu].
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Internally, each memory module consists of 41 RAM chips (2 of which are spare chips) and 2 interface chips. Each CPU unit and each I/O port consists of 6 non-redundant chips. The system is considered operational if at least 1 computer is operational. A computer is classified as operational if, of its components, at least 2 memory modules, at least 2 CPU units, at least 1 I/O port, and the 2 error-handling chips are functioning. A memory module is operational if at least 39 of its 41 RAM chips, and its 2 interface chips, are working.
 
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Where there is redundancy (available spares) at any level of system hierarchy, there is a coverage factor associated with the component failure at that level. For example, following the parameter values used by Lee et al.<ref name=L:Fault:92 />, if one CPU unit fails, with probability 0.995 the failed unit will be replaced by the spare unit, if available, and the corresponding computer will continue to operate. On the other hand, there is also a 0.005 probability that the fault recovery mechanism will fail and the corresponding computer will cease to operate. <xr id="tab:ex_coverage" /> shows the redundant components and their associated fault coverage probability. Finally, the failure rate of every chip in the system, as in <ref name=L:Fault:92 />, is assumed to be 100 failures per billion hours<sup>1</sup>.
 
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:: <span style="font-size:88%"><sup>1</sup> 0.0008766 failures per year.</span>
 
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<figtable id="tab:ex_coverage">
 
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{| border="1" cellspacing="0" cellpadding="5" align="center"
 
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  |+ <xr id="tab:ex_coverage" nolink />: Coverage probabilities.
 
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|-
 
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! align=center| Redundant Component
 
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! align=center| Fault Coverage Probability
 
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|-
 
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| align=center| RAM Chip
 
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| align=center| 0.998
 
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|-
 
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| align=center| Memory Module
 
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| align=center| 0.95
 
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|- align=center
 
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| CPU Unit
 
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| 0.995
 
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|- align=center
 
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| I/O Port
 
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| 0.99
 
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|- align=center
 
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| Computer
 
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| 0.95
 
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|} </figtable>
 
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Möbius
 
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== <span style="font-size:120%">Möbius</span> ==
 
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=== <span style="font-size:110%">Motivation</span> ===
 
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==== <span style="font-size:106%">''Solution''</span> ====
 
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<span style="font-size:102%">'''Graph'''</span>
 
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<span style="font-size:108%"><span style="font-variant:small-caps">Edit</span></span>
 
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<span style="font-size:115%">Möbius</span>
 
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<span style="font-size:125%"><font face=Courier>Documentation</font></span>
 
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“” –
 
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<equation id="eqn:binom" shownumber>
 
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<center><math>f(k)=\binom{n}{k}p^k(1-p)^{n-k}\quad k=0,1,\dots,n</math></center>
 
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</equation>
 
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Sort of like <xr id="eqn:binom" />, but not really.
 
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== References ==
 
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<references />
 

Latest revision as of 19:41, 24 June 2015

Below are a list of example models built in Möbius. These examples come from the Mobius team and user community. Please consider sharing the models you have built in the past. If you do decide to share your model, please look at the Share Your Model section for instructions on creating a new page and linking it here.

Examples

Share Your Model

Here is the template that people should use. If you are not familiar with mediawiki here are steps involved in adding your own model.

  1. Log in to https://www.mobius.illinois.edu/wiki/.
  2. On the top right search for the name of the page you want to create.
  3. If there are no matching results it should prompt you to create a page with the name that you searched for.
  4. Under the page, create a submission by simply following the template of the the template. Also, one has been created as an example for your reference and can be found here.
  5. To view the source code of the page just click on the edit tab on the top right of the page. Copying the source code should have the format ready for you.
  6. Under description you can simply copy your paper's Abstract section to give viewers a brief idea about your paper. Please be sure to link your paper and website. If you are confused about the syntax to create a link please refer to Links. Also please upload your project by clicking on the Special:Upload link at the bottom of your page.
  7. If you have any questions feel free to contact Ken Keefe at kjkeefe@illinois.edu.

Fault-Tolerant Multiprocessor System[edit]

This section presents an example of a system that can be modeled using Möbius. It starts with a description of the system, and then guides you through one way to build a model of the system and solve it using both simulation and numerical solution. The example is intended to take you step-by-step through the process of creating and solving a model in Möbius, and to exhibit many of the capabilities and features of the tool.


System Description[edit]

The system under consideration is a highly redundant fault-tolerant multiprocessor system adapted from [1] and shown in <xr id="fig:ex_multiproc" />. At the highest level, the system consists of multiple computers. Each computer is composed of 3 memory modules, of which 1 is a spare module; 3 CPU units, of which 1 is a spare unit; 2 I/O ports, of which 1 is a spare port; and 2 non-redundant error-handling chips.


<figure id="fig:ex_multiproc">

Multiproc.png


<xr id="fig:ex_multiproc" nolink />: Fault-tolerant multiprocessor system.
</figure>


Internally, each memory module consists of 41 RAM chips (2 of which are spare chips) and 2 interface chips. Each CPU unit and each I/O port consists of 6 non-redundant chips. The system is considered operational if at least 1 computer is operational. A computer is classified as operational if, of its components, at least 2 memory modules, at least 2 CPU units, at least 1 I/O port, and the 2 error-handling chips are functioning. A memory module is operational if at least 39 of its 41 RAM chips, and its 2 interface chips, are working.

Where there is redundancy (available spares) at any level of system hierarchy, there is a coverage factor associated with the component failure at that level. For example, following the parameter values used by Lee et al.[1], if one CPU unit fails, with probability 0.995 the failed unit will be replaced by the spare unit, if available, and the corresponding computer will continue to operate. On the other hand, there is also a 0.005 probability that the fault recovery mechanism will fail and the corresponding computer will cease to operate. <xr id="tab:ex_coverage" /> shows the redundant components and their associated fault coverage probability. Finally, the failure rate of every chip in the system, as in [1], is assumed to be 100 failures per billion hours1.

1 0.0008766 failures per year.


<figtable id="tab:ex_coverage">

<xr id="tab:ex_coverage" nolink />: Coverage probabilities.
Redundant Component Fault Coverage Probability
RAM Chip 0.998
Memory Module 0.95
CPU Unit 0.995
I/O Port 0.99
Computer 0.95
</figtable>


Möbius

Möbius[edit]

Motivation[edit]

Solution[edit]

Graph

Edit Möbius Documentation

“” –

<equation id="eqn:binom" shownumber>

f(k)=\binom{n}{k}p^k(1-p)^{n-k}\quad k=0,1,\dots,n

</equation>

Sort of like <xr id="eqn:binom" />, but not really.


References[edit]

  1. ↑ 1.0 1.1 1.2 D. Lee, J. Abraham, D. Rennels, and G. Gilley. A numerical technique for the evaluation of large, closed fault-tolerant systems. In Dependable Computing for Critical Applications, pages 95–114. Springer-Verlag, Wien, 1992.
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