Stochastic Modelling
and Analysis
Ed Brinksma
University of Twente
2nd year Ametist Review
Brussels, May 10th, 2004
AMETIST
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
2
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
3
Relevance Stochastic Modelling AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
4
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
5
Stochastic Process Algebra
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
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Modelling Languages
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
7
An Extended UML-Statechart
AMETIST
It models a car damage assessment process.
Ed Brinksma
Stochastic Modelling and Analysis
8
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
9
Probabilistic Model Checking
requirements
AMETIST
system
Not biased towards
most probable scenarios
formalizing
modelling
prop. spec.
sys. model
error location
model checking
satisfied
Ed Brinksma
out of memory
violated &
counter example
Stochastic Modelling and Analysis
simulation
10
Probabilistic Model Checking
AMETIST
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)
Ed Brinksma
Stochastic Modelling and Analysis
11
Abstraction Techniques
AMETIST
AMETIST contributions:
Weak equivalences and pre-orders
Baier, Katoen, Hermanns, Haverkort 2002
(weak simulation, CTMC).
Baier, Hermanns, Katoen 2004
(pol. decidability weak simulation, CTMC)
Baier, Hermanns, Katoen, Wolf 2003
(branching-time spectrum DTMC & CTMC)
Andova, Willemse 2004
(branching bisimulation, alternating model).
Reduction techniques
Jeannet, D’Argenio, Larsen 2002 (MDP, Rapture)
D’Argenio and Niebert 2004 (MDP, PO reduction)
Ed Brinksma
Stochastic Modelling and Analysis
12
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
13
Stochastic Scheduling
AMETIST
AMETIST contributions:
Abdeddaïm, Asarin, Maler 2003
(backward reachability, acyclic CTMDP)
Sand, Engell 2004a
(stochastic integer programming)
Sand, Engell 2004b
(risk guided scheduling)
Ed Brinksma
Stochastic Modelling and Analysis
14
Outline
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
15
Tools
AMETIST
AMETIST has contributed to the development of:
ETMCC
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
Ed Brinksma
Stochastic Modelling and Analysis
16
Case Studies
AMETIST
Stochastic modelling/analysis has been relevant for:
Bohnenkamp, Hermanns, Klaren, Mader, Usenko 2004.
Synthesis and stochastic assessment of schedules for lacquer
production (Axxom case study).
Bohnenkamp, Van der Stok, Hermanns, Vaandrager 2003.
Cost-optimisation of the IPv4 zeroconf protocol. See also: Andova,
Hermanns, Katoen 2003; Daws 2004
Daws, Kwiatkowska, Norman 2004.
Automatic verification of the IEEE 1394 root contention protocol.
Ed Brinksma
Stochastic Modelling and Analysis
17
Outlook & Future Development
AMETIST
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
Ed Brinksma
Stochastic Modelling and Analysis
18
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Behavioural Hybrid Process Calculus