A TOOL FOR DEPENDABILITY EVALUATION
BASED ON MARKOV CHAINS
AND STOCHASTIC PETRI NETS
SURF-2 is a dependability evaluation tool for hardware and software systems, based on strict construction, validation and numerical resolution of Markov models.
System behaviour is modelized by either a Markov Chain or a Generalized Stochastic Petri Net (GSPN).
SURF-2 makes the comparison of dependability of various system architectures easy.
Reward structures can be added to the behavioural model and permit to get combined measures of dependability, performance or cost.
Quantitative evaluation of system dependability can be divided in 2 steps:
SURF-2allows 2 types of modelization:
Theoretical Background. Table of contents.
It is fully automatic.
Dependability measures are obtained from the processing of the Markov Chain.
The transformation of the GSPN into a Markov chain in continuous time is based on the markings which sensibilize timed transitions:
Theoretical Background.Table of contents.
The tools provided by SURF-2 allow the creation and update of following objects:
A GSPN or a Markov Chain modelizes the behaviour of a system as perceived by the user under the following form:
These two state classes allow the definition of most of the dependability measures, "CATASTROPHIC" class being used for safety measures. For a same model, it is possible to define several partitions in order to analyze various failure cases.
Model parameters can be numerical or symbolic expressions. A symbolic parameter is a local variable which is viewable only in the model wherein it has been defined. The combined use of symbolic parameters and the definition of several partitions for a same model permits to build generic models which can be stored in the SURF-2 database in order to be reused in other models.
An assigned model corresponds to the assignment of a value to each model parameter. This value can be a numerical value or a global value; in the latter, it can be common to different models. This global value concept is similar to the extern variable notion used in programming languages. Model genericity and the possibility to define several assigned models for a given model offer flexibility of modelization and allows to study the sensibility of a measure to different parameters.
The modelization of several architectural solutions for comparative evaluation, needs the simultaneous evaluation of a dependability measure common to different solutions or to various sytem configurations. This is the role of Model Folder.
A Model Folder includes:
The assignment of a value (or of a set of numerical values in case of study of sensibility) to each global value is made at this step.
Figure below shows two examples of very simple use of global values to make
comparative studies of architectures.
Other main objects of the databased managed by the supervisor of the application are Intermediate Results and Computation Results of a measure. Intermediate Results come from the processing of a Petri Net whose numerical and dimension variables have been assigned. That is:
Computing results, for a given measure, are shown under numeric or graphic form and can be printed out in Postscript.
As shown below, SURF-2 provides a set of tools permitting the creation and update of objects:
When SURF-2 is launched the window below appears:
When the cursor moves on MODEL command, the following menu is shown:
Then, the user can create a new Markov Chain (CREATE) or update an existing one (OPEN).
The Petri Net Editor and Markov Chain Editor are very similar. When an editor is started, following windows can be open:
Select and Copy functions allow to exchange components between windows. Working windows allow for instance:
When a Model Editor is started, one of the following window appears:
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Its aim is the creation, update and validation of the Petri Net, of the Partitions and of the Invariants of the model.
The Edit window looks like this:
.
PART command opens the Edit Partition window.
INV command opens the Edit Invariants window.
VALIDATION & SAVE command allows to save and validate the open model.
Validation checks the consistency of:
Its aim is the creation, update and validation of the Markov chain and corresponding Partitions.
Edit Window looks like this:
.
PART command opens the Edit Partition window.
VALIDATION & SAVE command allows to save and validate the open model.
Validation checks the consistency of:
Its aim is the creation or update of all the values of the parameters of the corresponding model:
This tool provides to the user a powerful and flexible way to display results. User can select a subset of viewable results under the form of a set of curves.