On-the-fly Fluid Model Checking via Discrete Time Population Models

We show that, under suitable convergence and scaling conditions, fluid model checking bounded CSL formulas on selected individuals in a continuous large population model can be approximated by checking equivalent bounded PCTL formulas on corresponding objects in a discrete time, time synchronous Markov population model, using an on-the-fly mean field approach. The proposed technique is applied to a benchmark epidemic model and a client-server case study showing promising results also for the challenging case of nested formulas with time dependent truth values. The on-the-fly results are compared to those obtained via global fluid model checking and statistical model-checking.

[1]  Håkan L. S. Younes,et al.  Numerical vs. Statistical Probabilistic Model Checking: An Empirical Study , 2004, TACAS.

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

[3]  M. Bena.  A Class Of Mean Field Interaction Models for Computer and Communication Systems , 2008 .

[4]  Diego Latella,et al.  On-the-fly Fast Mean-Field Model-Checking , 2013, TGC.

[5]  Diego Latella,et al.  Continuous approximation of collective system behaviour: A tutorial , 2013, Perform. Evaluation.

[6]  Jane Hillston,et al.  Fluid flow approximation of PEPA models , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[7]  Stephen Gilmore,et al.  Scalable Differential Analysis of Process Algebra Models , 2012, IEEE Transactions on Software Engineering.

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

[9]  Enrico Tronci,et al.  Bounded Probabilistic Model Checking with the Muralpha Verifier , 2004, FMCAD.

[10]  Diego Latella,et al.  On-the-fly PCTL fast mean-field approximated model-checking for self-organising coordination , 2015, Sci. Comput. Program..

[11]  Jean-Yves Le Boudec,et al.  A class of mean field interaction models for computer and communication systems , 2008, Perform. Evaluation.

[12]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[13]  Diego Latella,et al.  On-the-fly Probabilistic Model Checking , 2014, ICE.

[14]  Luca Bortolussi,et al.  Fluid Model Checking , 2012, CONCUR.

[15]  Richard Alexander Hayden,et al.  Scalable performance analysis of massively parallel stochastic systems , 2011 .

[16]  Luca Bortolussi,et al.  Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation , 2013, SFM.

[17]  J. Norris,et al.  Differential equation approximations for Markov chains , 2007, 0710.3269.

[18]  Boudewijn R. Haverkort,et al.  A logic for model-checking mean-field models , 2013, 2013 43rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN).

[19]  J. Boudec,et al.  A Generic Mean Field Convergence Result for Systems of Interacting Objects , 2007 .

[20]  T. Kurtz.  Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.