Efficient Checking of Individual Rewards Properties in Markov Population Models

In recent years fluid approaches to the analysis of Markov populations models have been demonstrated to have great pragmatic value. Initially developed to estimate the behaviour of the system in terms of the expected values of population counts, the fluid approach has subsequently been extended to more sophisticated interrogations of models through its embedding within model checking procedures. In this paper we extend recent work on checking CSL properties of individual agents within a Markovian population model, to consider the checking of properties which incorporate rewards.

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

[2]  Allan Clark,et al.  Performance Specification and Evaluation with Unified Stochastic Probes and Fluid Analysis , 2013, IEEE Transactions on Software Engineering.

[3]  Luca Bortolussi,et al.  Model checking single agent behaviours by fluid approximation , 2015, Inf. Comput..

[4]  Boudewijn R. Haverkort,et al.  Comparison of the Mean-Field Approach and Simulation in a Peer-to-Peer Botnet Case Study , 2011, EPEW.

[5]  Jan J. M. M. Rutten,et al.  Mathematical techniques for analyzing concurrent and probabilistic systems , 2004, CRM monograph series.

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

[7]  Jeremy T. Bradley,et al.  Mean-Field Analysis of Markov Models with Reward Feedback , 2012, ASMTA.

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

[9]  Bruno Gaujal,et al.  A mean field model of work stealing in large-scale systems , 2010, SIGMETRICS '10.

[10]  Jean-Yves Le Boudec Performance Evaluation of Computer and Communication Systems , 2010, Computer and communication sciences.

[11]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

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

[13]  W. Ebeling Stochastic Processes in Physics and Chemistry , 1995 .

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

[15]  P. Billingsley,et al.  Convergence of Probability Measures , 1970, The Mathematical Gazette.

[16]  Luca Bortolussi On the Approximation of Stochastic Concurrent Constraint Programming by Master Equation , 2008, Electron. Notes Theor. Comput. Sci..

[17]  Stephen Gilmore,et al.  Fluid Rewards for a Stochastic Process Algebra , 2012, IEEE Transactions on Software Engineering.

[18]  Luca Bortolussi,et al.  Hybrid performance modelling of opportunistic networks , 2012, QAPL.

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

[20]  M. Benaïm,et al.  A class of mean field interaction models for computer and communication systems , 2008, 2008 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops.

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

[22]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[23]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[24]  Luca Bortolussi,et al.  Model Checking Markov Population Models by Central Limit Approximation , 2013, QEST.

[26]  Diego Latella,et al.  Scalable context-dependent analysis of emergency egress models , 2012, Formal Aspects of Computing.

[27]  Harold R. Parks,et al.  A Primer of Real Analytic Functions , 1992 .

[28]  Ronald A. Howard,et al.  Dynamic Probabilistic Systems , 1971 .

[29]  D. Vere-Jones Markov Chains , 1972, Nature.

[30]  J. Norris Appendix: probability and measure , 1997 .

[31]  Vipul Periwal,et al.  System Modeling in Cellular Biology: From Concepts to Nuts and Bolts , 2006 .

[32]  Hong Qian,et al.  Single-molecule enzymology: stochastic Michaelis-Menten kinetics. , 2002, Biophysical chemistry.

[33]  Peter Buchholz,et al.  On the Numerical Analysis of Inhomogeneous Continuous-Time Markov Chains , 2010, INFORMS J. Comput..

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

[35]  R. W. R. Darling Fluid Limits of Pure Jump Markov Processes: a Practical Guide , 2002 .

[36]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[37]  Jean-Yves Le Boudec,et al.  On Mean Field Convergence and Stationary Regime , 2011, ArXiv.

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