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

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

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

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

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

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

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

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

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

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

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)

Abstraction Techniques 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)

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

Stochastic Scheduling AMETIST contributions: Abdeddaïm, Asarin, Maler 2003 (backward reachability, acyclic CTMDP) Sand, Engell 2004a (stochastic integer programming) Sand, Engell 2004b (risk guided scheduling)

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

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

Case Studies 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.

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