Performance analysis of χ models using discrete-time probabilistic reward graphs

We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and quantitative analysis of timed systems based on the modeling language chi. The extension proposed in this paper is based on timed branching bisimulation reduction followed by a tailored inclusion of probabilities and rewards. The approach is applied in an industrial case study of a turntable drill. The resulting performance measures are shown to be comparable to those obtained by existent methods of the chi environment, viz. simulation and continuous-time Markovian analysis.

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

[2]  J. M. van de Mortel-Fronczak,et al.  Verification of timed chi models using uppaal , 2005, ICINCO.

[3]  J.J.H. Fey,et al.  Design of a fruit juice blending and packaging plant , 2000 .

[4]  S. Sastry,et al.  Hierarchical aggregation of singularly perturbed finite state Markov processes , 1983 .

[5]  Jasen Markovski,et al.  Aggregation Methods for Markov Reward Chains with Fast and Silent Transitions , 2011, MMB.

[6]  Luis G. Vargas.  Review: Marcel F. Neuts, Matrix-geometric solutions in stochastic models, an algorithmic approach , 1983 .

[7]  Gerard J. Holzmann,et al.  The Model Checker SPIN , 1997, IEEE Trans. Software Eng..

[8]  Ronald A. Howard,et al.  Semi-Markov and decision processes , 1971 .

[9]  Anton Wijs,et al.  From Χt to μCRL : Combining performance and functional analysis , 2004 .

[10]  Nikola Trcka,et al.  Verifying chi Models of Industrial Systems with Spin , 2006, ICFEM.

[11]  van Ejj Edgar Campen.  Design of a multi-process multi-product wafer fab , 2001 .

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

[13]  Erik P. de Vink,et al.  Compositionality for Markov Reward Chains with Fast Transitions , 2007, EPEW.

[14]  Jan A. Bergstra,et al.  Discrete time process algebra with silent step , 2000, Proof, Language, and Interaction.

[15]  Wlodzimierz M. Zuberek,et al.  Timed Petri nets and preliminary performance evaluation , 1980, ISCA '80.

[16]  Anton Wijs,et al.  From χt to µCRL: Combining Performance and Functional Analysis , 2005, 10th IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'05).

[17]  Anton Wijs,et al.  Silent steps in transition systems and Markov chains , 2007 .

[18]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[19]  Jos C. M. Baeten,et al.  Process Algebra with Timing , 2002, Monographs in Theoretical Computer Science. An EATCS Series.

[20]  G. Plotkin,et al.  Proof, language, and interaction: essays in honour of Robin Milner , 2000 .

[21]  J. Ben Atkinson,et al.  Modeling and Analysis of Stochastic Systems , 1996 .

[22]  Ka Lok Man,et al.  Syntax and consistent equation semantics of hybrid Chi , 2006, J. Log. Algebraic Methods Program..

[23]  J. Banks,et al.  Discrete-Event System Simulation , 1995 .

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

[25]  Dirk A. van Beek,et al.  Modelling and control of process industry batch production systems , 2002 .

[26]  V Victor Bos,et al.  Formal specification and analysis of industrial systems , 2002 .

[27]  Nikola Trčka.  Verifying % Models of Industrial Systems with SPIN , 2006 .

[28]  V. Kulkarni.  Modeling and Analysis of Stochastic Systems , 1996 .

[29]  Wang Yi,et al.  Uppaal in a nutshell , 1997, International Journal on Software Tools for Technology Transfer.

[30]  Jos C. M. Baeten,et al.  Analyzing a chi model of a turntable system using Spin, CADP and Uppaal , 2005, J. Log. Algebraic Methods Program..

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

[32]  Jan Friso Groote,et al.  µCRL: A Toolset for Analysing Algebraic Specifications , 2001, CAV.