1. CS/ECE 541 - Computer Systems Analysis
Möbius Introduction
Ken Keefe - 9/18/2013

2. Talk Outline Motivation The Möbius Framework The Möbius Tool
Möbius Models
Fault Trees
Rep/Join
Performance Variables
Set Study
Flat State Space/Symbolic State Space Generators
Analytical Solvers
Example Demo - Car System
Getting Möbius
Homework Assignment #2 Discussion
Conclusion

3. Challenges of Modeling Complex Systems
Dealing with many levels of abstraction in system models
E.g., when modeling complex cyber-physical systems, one must represent models at many levels
Need structured models, able to represent system subcomponents in a composable way
Need way to decompose models, and solve parts separately
Modeling many different types of system components
May need multiple model representations
Solving many types of models, with differing assumptions and characteristics
May need multiple model solution methods
Challenging to support solution of extremely large and stiff models in both simulation and analytic/numerical solution:
State space largeness (largeness)
Large time scale differences in event rates (stiffness)

4. Möbius Framework C++ Libraries
Abstract base classes for building and executing models (blue)
Formalisms define formalism specific base classes that inherit from the abstract base classes and are included in the Mobius framework (orange)
C++ representation of models in a formalism are classes that inherit from the formalism base classes (green)
Möbius AFI
Model-Level AFI
State Variables and Actions
State-Level AFI
BaseAtomicModel
BaseAction
BaseSANModel
SANActivity
ProcSANModel
CPUFailureActivity

5. Möbius Tool Java front-end for Graphically defining models
Generating C++ code representations
Building executable models
Executing the models
Reporting, storing, and visualizing results
Atomic
Editors
Composer Editors
Reward
Editor
Study
Editor
Atomic
Object
Code
Reward
Object
Code
Study
Object
Code
Comp.
Object
Code
Linker
Formalism
Libraries
Solver
Libraries
Executable Model

6. Möbius Models Overview
Study
Reward
Composed
Atomics
Composed
Transformer
Simulator
Analytical
Solver

7. Fault Trees Fault trees consist of the following primitives:
Node - State variable representing failure state of the system. > 0 is a failure
Event - Action that fires only once and represents failure of a system component
And - Failure is passed if all children fail
Or - Failure is passed if at least one child fails
Xor - Failure is passed if exactly one child fails
KofN - Failure is passed if at least K children fail
PriorityAnd - Failure is passed if the children fail in the order specified by the gate
Fault trees typically have a single node at the top that represents system failure, several events that are leaves in the tree and represent component failures, and a set of logic gates that build the tree structure and defines what component failures must exist before the system fails.

8. Rep/Join
Rep/Join is a state sharing composed formalism. The three primitives are:
Models
These can be either atomic models or other composed models
Cycles are not allowed
Join nodes
Join nodes define a set of shared variables that are joined across the child models and nodes
Shared variables must all have the same type and initial value
Rep nodes
Rep nodes define a set of identical replicas and a set of shared variables across those replicas

9. Performance Variables
A performance variable model contains a set of performance variables that are used to define measures of the system model. Each performance variable defines:
A reward function (either)
A rate reward function which is fired and aggregated based on the timing information
A set of impulse reward functions which are each tied to an event in the system. When the event fires, the impulse reward function fires.
Timing information (instant of time, interval of time, time averaged interval, etc.)
Simulation information:
Whether to calculate mean, variance, interval, or distribution
The required confidence interval for the performance variable to converge to before simulation may halt.

10. Set Study Studies are used to vary initial model parameters.
Global variables are defined in an atomic, composed, or reward model.
Global variables can be used in any C++ expression box, e.g. the rate of an event in a fault tree can be some function of one or more global variables
Studies then define a set of experiments with values for each global variable defined earlier
The set study allows the sets of experiments to be defined one by one manually.
The range study allows sets of experiments to be defined by expressing a range of values for each global variable.
Every executable model must have a study defined. If there are no global variables, the study is simply empty.

11. State Space Generators
State Space Generators must be executed before an analytical solver is executed. The simulator does not require an SSG.
The Flat SSG builds a set of possible states and table of transitions between those states.
The Symbolic SSG builds MDDs for the possible states, MxDs for the transitions, and MTMDDs for the performance variable values in each state.
Analytical solvers can use either representation of the CTMCs to evaluate the model.
The Flat SSG can build a state space several orders of magnitude larger than the Symbolic SSG and uses significantly more disk space to store the data structures it generates. However, analytical solvers will run dramatically faster because the data structures are easier to read in an work with.
The Symbolic SSG uses much less disk space and leverages several state lumping techniques to decompose the state space and can produce a state space size several orders of magnitude smaller than the Flat SSG. However, solvers can run significantly slower on the output of the symbolic SSG.

12. Solvers
Simulator can execute any well formed model, but provides inaccurate results and typically takes longer.
Analytical solvers can only solve certain classes of models (CTMCs) and require a state space to be generated first, but provide precise results.

13. Example Demo - Car Car has two systems Wheels
4 independent tires that each fail with a rate of 2.0 E -7
Engine
Engine can overheat (rate of 6.3 E -6) or blow a head gasket (rate of 5.5 E -5)
Car fails if either system fails
Wheels fail if one tire fails
Engine fails if it overheats and blows a head gasket
Rates above are per hour.
Determine the 90 day reliability of the car (2160 hours)

14. Getting Möbius
Available on Windows XP-8, OSX , and Ubuntu Linux
Visit

15. Homework #2 Build a model of a reliable web server using:
A fault tree model of one part of the web server
Define a performance variable for the reliability of this component
Calculate the mean by hand and compare it to the result you get from Möbius
Define the remaining components of the web server
Define a Rep/Join model to compose the components together
Execute the system model and collect results
Use Möbius’ built in documentation feature to document your work
Due on Friday, September 27th. Give yourself plenty of time to download, install, and work out the kinks.
My office is CSL 225
My is
When you me for help, be sure to send a minimal archive of your model!

16. Conclusion