1. Stochastic Modelling and Analysis
Ed Brinksma
University of Twente
2nd year Ametist Review
Brussels, May 10th, 2004
AMETIST

2. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

3. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

4. Relevance Stochastic Modelling
stochastic system features
average measures: delay, throughput, etc.
variation, jitter
soft timing constraints
e.g.: 99.9% of the requests gets a response within 1 ms
operational vs. absolute correctness
e.g.: 99.9% of the request gets a correct response
stochastic evaluation
performance analysis: transient & stationary behaviour
reward modelling: risk analysis, cost optimization
abstraction
complex systems may have simple stochastic models

5. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

6. Stochastic Process Algebra
Compositional theories for the integration of functional behaviour with stochastic delays
uses & extends concepts from classical process algebra
can be used to obtain evaluation models (CTMC, CTSMC, GSMP) directly from extended, structured functional specifications
AMETIST contributions
integration and overview:
Hermanns, Herzog, Katoen 2002 (Markovian case)
Bravetti, D’Argenio 2002 (General case)
Brinksma 2003 (Markovian & General case)
compositional abstraction to timed automata
D’Argenio 2002

7. Modelling Languages AMETIST contributions:
Stochastic extensions to UML Statecharts
Jansen, Hermanns, Katoen 2003
well-received by UML community
MoDeST/Motor modelling environment
Bohnenkamp, Hermanns, Katoen, Klaren 2003
extensive stochastic modelling features & evaluation via stochastic activity networks

8. An Extended UML-Statechart
stochastic features
It models a car damage assessment process.

9. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

10. Probabilistic Model Checking
requirements
system
Not biased towards
most probable scenarios
formalizing
modelling
error location
prop. spec.
sys. model
model checking
violated &
counter example
simulation
satisfied
out of memory

11. Probabilistic Model Checking
AMETIST contributions:
Model-checking discrete time reward models
Andova, Hermanns, Katoen 2003 (PCTL, numerical)
Daws 2004 (PCTL, symbolic)
Model-checking continuous timed systems
Baier, Haverkort, Hermanns, Katoen 2003 (CSL, CTMC)
Baier, Haverkort, Hermanns, Katoen 2004 (min/max prob, CTMDP)
Haverkort, Cloth, Hermanns, Katoen, Baier 2002 (CSRL,CTMRM)

12. Abstraction Techniques
AMETIST contributions:
Weak equivalences and pre-orders
Baier, Katoen, Hermanns, Haverkort (weak simulation, CTMC).
Baier, Hermanns, Katoen (pol. decidability weak simulation, CTMC)
Baier, Hermanns, Katoen, Wolf (branching-time spectrum DTMC & CTMC)
Andova, Willemse (branching bisimulation, alternating model).
Reduction techniques
Jeannet, D’Argenio, Larsen 2002 (MDP, Rapture)
D’Argenio and Niebert 2004 (MDP, PO reduction)

13. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

14. Stochastic Scheduling
AMETIST contributions:
Abdeddaïm, Asarin, Maler (backward reachability, acyclic CTMDP)
Sand, Engell 2004a (stochastic integer programming)
Sand, Engell 2004b (risk guided scheduling)

15. Outline Relevance of stochastic modelling Stochastic modelling
Stochastic process algebra
Modelling languages
Stochastic analysis
Model checking probabilistic systems
Abstraction techniques
Stochastic Scheduling
Tools & case studies
Outlook & future developments

16. Tools AMETIST has contributed to the development of: ETMCC CADP
a tool for CTMC model checking
CADP
extension of this well-known tool environment for functional analysis with performance and dependability analysis modules
Rapture
verification tool for quantified reachability properties over MDPs.
MoDeST/MOTOR
broad-spectrum modelling language /discrete event simulator

17. Case Studies Stochastic modelling/analysis has been relevant for:
Bohnenkamp, Hermanns, Klaren, Mader, Usenko Synthesis and stochastic assessment of schedules for lacquer production (Axxom case study).
Bohnenkamp, Van der Stok, Hermanns, Vaandrager Cost-optimisation of the IPv4 zeroconf protocol. See also: Andova, Hermanns, Katoen 2003; Daws 2004
Daws, Kwiatkowska, Norman Automatic verification of the IEEE 1394 root contention protocol.

18. Outlook & Future Development
Theory
Extend results CTMDPs e.g. time-bounded reachability for non-uniform CTMDPs
Further research & evaluation symbolic techniques contain the effect of numerical errors
Modelling Languages/Tools
Extend general modelling/analysis tool environments MoDeST/MOTOR
Case studies
Evaluate generic vs specific approaches for stochastic aspects of timed systems e.g. specific stochastic scheduling techniques vs model checking CTMCs or CTMDPs