Discrete-Time Rewards Model-Checked

This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and succinct way. Algorithms to efficiently analyze such formulae are introduced. The approach is illustrated by model-checking a probabilistic cost model of the IPv4 zeroconf protocol for distributed address assignment in ad-hoc networks.

[1]  Kishor S. Trivedi,et al.  SPNP: stochastic Petri net package , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

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

[3]  Christel Baier,et al.  On the Logical Characterisation of Performability Properties , 2000, ICALP.

[4]  William H. Sanders,et al.  Reward Model Solution Methods with Impulse and Rate Rewards: An Algorithm and Numerical Results , 1994, Perform. Evaluation.

[5]  Insup Lee,et al.  Modeling and Analysis of Power-Aware Systems , 2003, TACAS.

[6]  B. Nordstrom.  FINITE MARKOV CHAINS , 2005 .

[7]  Kishor S. Trivedi,et al.  Performability Analysis: Measures, an Algorithm, and a Case Study , 1988, IEEE Trans. Computers.

[8]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[9]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[10]  Marco Bernardo,et al.  An Algebra-Based Method to Associate Rewards with EMPA Terms , 1997, ICALP.

[11]  Jeroen Voeten,et al.  Performance evaluation with temporal rewards , 2002, Perform. Evaluation.

[12]  Stephen Gilmore,et al.  Specifying Performance Measures for PEPA , 1999, ARTS.

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

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

[15]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

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

[17]  Stuart Cheshire,et al.  Dynamic Configuration of IPv4 Link-Local Addresses , 2005, RFC.

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

[19]  Christel Baier,et al.  Model checking performability properties , 2002, Proceedings International Conference on Dependable Systems and Networks.

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

[21]  Kishor S. Trivedi,et al.  Transient analysis of cumulative measures of markov model behavior , 1989 .

[22]  Luca de Alfaro,et al.  How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems , 1998, LICS.

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

[24]  William H. Sanders,et al.  State-Space Support for Path-Based Reward Variables , 1999, Perform. Evaluation.