From Concurrency Models to Numbers - Performance and Dependability

Discrete-state Markov processes are very common models used for performance and dependability evaluation of, for example, distributed information and communication systems. Over the last fifteen years, compositional model construction and model checking algorithms have been studied for these processes, and variations thereof, especially processes incorporating nondeterministic choices. In this paper we give a survey of model checking and compositional model construction for such processes in discrete and continuous time.

[1]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[2]  Robert K. Brayton,et al.  Model-checking continuous-time Markov chains , 2000, TOCL.

[3]  Marcin Jurdzinski,et al.  Concavely-Priced Probabilistic Timed Automata , 2009, CONCUR.

[4]  Nicolás Wolovick,et al.  Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[5]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[6]  J. W. Nieuwenhuis,et al.  Boekbespreking van D.P. Bertsekas (ed.), Dynamic programming and optimal control - volume 2 , 1999 .

[7]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[8]  Abbas Edalat,et al.  A logical characterization of bisimulation for labeled Markov processes , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[9]  Christel Baier,et al.  Performability assessment by model checking of Markov reward models , 2010, Formal Methods Syst. Des..

[10]  Martin R. Neuhäußer,et al.  Model checking nondeterministic and randomly timed systems , 2010 .

[11]  Hans A. Hansson.  Time and probability in formal design of distributed systems , 1991, DoCS.

[12]  Christel Baier,et al.  Comparative branching-time semantics for Markov chains , 2005, Inf. Comput..

[13]  Radu Mateescu,et al.  CADP 2011: a toolbox for the construction and analysis of distributed processes , 2012, International Journal on Software Tools for Technology Transfer.

[14]  B. L. Miller.  Finite State Continuous Time Markov Decision Processes with a Finite Planning Horizon , 1968 .

[15]  Christel Baier,et al.  Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes , 2005, Theor. Comput. Sci..

[16]  William J. Stewart,et al.  Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling , 2009 .

[17]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[18]  Radu Mateescu,et al.  CADP 2006: A Toolbox for the Construction and Analysis of Distributed Processes , 2007, CAV.

[19]  Peter Buchholz,et al.  Numerical analysis of continuous time Markov decision processes over finite horizons , 2011, Comput. Oper. Res..

[20]  B. L. Miller.  Finite state continuous time Markov decision processes with an infinite planning horizon , 1968 .

[21]  Joost-Pieter Katoen,et al.  Three-Valued Abstraction for Continuous-Time Markov Chains , 2007, CAV.

[22]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[23]  D. Griffel.  Linear programming 2: Theory and extensions , by G. B. Dantzig and M. N. Thapa. Pp. 408. £50.00. 2003 ISBN 0 387 00834 9 (Springer). , 2004, The Mathematical Gazette.

[24]  Lijun Zhang,et al.  On Probabilistic Automata in Continuous Time , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[25]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[26]  Martin Leucker,et al.  Don't Know in Probabilistic Systems , 2006, SPIN.

[27]  Joost-Pieter Katoen,et al.  Discrete-Time Rewards Model-Checked , 2003, FORMATS.

[28]  Adnan Aziz,et al.  It Usually Works: The Temporal Logic of Stochastic Systems , 1995, CAV.

[29]  Stephan Merz,et al.  Model Checking , 2000 .

[30]  Joost-Pieter Katoen,et al.  Faster and Symbolic CTMC Model Checking , 2001, PAPM-PROBMIV.

[31]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[32]  Christel Baier,et al.  Model Checking Markov Chains with Actions and State Labels , 2007, IEEE Transactions on Software Engineering.

[33]  Christel Baier,et al.  Model-Checking Algorithms for Continuous-Time Markov Chains , 2002, IEEE Trans. Software Eng..

[34]  Jan Kretínský,et al.  Continuous-Time Stochastic Games with Time-Bounded Reachability , 2009, FSTTCS.

[35]  Prakash Panangaden,et al.  Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes , 2003, J. Log. Algebraic Methods Program..

[36]  Lijun Zhang,et al.  Model Checking Interactive Markov Chains , 2010, TACAS.

[37]  Lijun Zhang,et al.  Time-Bounded Reachability Probabilities in Continuous-Time Markov Decision Processes , 2010, 2010 Seventh International Conference on the Quantitative Evaluation of Systems.

[38]  A. Jensen,et al.  Markoff chains as an aid in the study of Markoff processes , 1953 .

[39]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[40]  Peter W. Glynn,et al.  Computing Poisson probabilities , 1988, CACM.

[41]  Mahesh Viswanathan,et al.  Model-Checking Markov Chains in the Presence of Uncertainties , 2006, TACAS.

[42]  Christel Baier,et al.  Principles of model checking , 2008 .

[43]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[44]  Lijun Zhang,et al.  Concurrency and Composition in a Stochastic World , 2010, CONCUR.

[45]  Bernhard Steffen,et al.  Reactive, generative, and stratified models of probabilistic processes , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[46]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[47]  Christel Baier,et al.  Performance evaluation and model checking join forces , 2010, Commun. ACM.

[48]  Holger Hermanns,et al.  Symbolic partition refinement with automatic balancing of time and space , 2010, Perform. Evaluation.

[49]  William H. Sanders,et al.  Optimal state-space lumping in Markov chains , 2003, Inf. Process. Lett..

[50]  Giuliana Franceschinis,et al.  Simple O(m logn) Time Markov Chain Lumping , 2010, TACAS.

[51]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[52]  Holger Hermanns,et al.  Towards Performance Prediction of Compositional Models in Industrial GALS Designs , 2009, CAV.

[53]  Mariëlle Stoelinga,et al.  A Compositional Semantics for Dynamic Fault Trees in Terms of Interactive Markov Chains , 2007, ATVA.

[54]  Joost-Pieter Katoen,et al.  Compositional Abstraction for Stochastic Systems , 2009, FORMATS.

[55]  Holger Hermanns,et al.  Interactive Markov Chains , 2002, Lecture Notes in Computer Science.

[56]  Tommaso Bolognesi,et al.  Tableau methods to describe strong bisimilarity on LOTOS processes involving pure interleaving and enabling , 1994, FORTE.

[57]  Lijun Zhang,et al.  Probabilistic Logical Characterization , 2011, Inf. Comput..

[58]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[59]  Sven Schewe,et al.  Finite optimal control for time-bounded reachability in CTMDPs and continuous-time Markov games , 2010, Acta Informatica.

[60]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[61]  Andrew Hinton,et al.  PRISM: A Tool for Automatic Verification of Probabilistic Systems , 2006, TACAS.

[62]  E. Altman,et al.  Asymptotic Optimization of a Nonlinear Hybrid System Governed by a Markov Decision Process , 1997 .

[63]  Christel Baier,et al.  Deciding Bisimilarity and Similarity for Probabilistic Processes , 2000, J. Comput. Syst. Sci..

[64]  R. Segala,et al.  Automatic Verification of Real-Time Systems with Discrete Probability Distributions , 1999, ARTS.

[65]  Roberto Segala,et al.  Decision Algorithms for Probabilistic Bisimulation , 2002, CONCUR.

[66]  Mariëlle Stoelinga,et al.  Dynamic Fault Tree Analysis Using Input/Output Interactive Markov Chains , 2007, 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'07).

[67]  Joost-Pieter Katoen,et al.  The Ins and Outs of the Probabilistic Model Checker MRMC , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[68]  Frits W. Vaandrager,et al.  Cost-optimization of the IPv4 zeroconf protocol , 2003, 2003 International Conference on Dependable Systems and Networks, 2003. Proceedings..

[69]  Salem Derisavi,et al.  A Symbolic Algorithm for Optimal Markov Chain Lumping , 2007, TACAS.

[70]  Prakash Panangaden,et al.  Labelled Markov Processes , 2009 .

[71]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..