Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Profiles in computing: Allan L. Scherr
Communications of the ACM - Celebrating ACM's 40th anniversary
Computing Poisson probabilities
Communications of the ACM
Journal of the ACM (JACM)
The UltraSAN modeling environment
Performance Evaluation - Special issue: performance modeling tools
Performability modelling tools and techniques
Performance Evaluation
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Model checking
Compositional performance modelling with the TIPPtool
Performance Evaluation - Special issue on modelling techniques and tools for performance evaluation
Performance of Computer Communication Systems: A Model-Based Approach
Performance of Computer Communication Systems: A Model-Based Approach
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
A Software Package for the Analysis of Generalized Stochastic Petri Net Models
International Workshop on Timed Petri Nets
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
TwoTowers: A Tool Integrating Functional and Performance Analysis of Concurrent Systems
FORTE XI / PSTV XVIII '98 Proceedings of the FIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE XI) and Protocol Specification, Testing and Verification (PSTV XVIII)
Parallel State Space Exploration for GSPN Models
Proceedings of the 16th International Conference on Application and Theory of Petri Nets
Model Checking Continuous-Time Markov Chains by Transient Analysis
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
It Usually Works: The Temporal Logic of Stochastic Systems
Proceedings of the 7th International Conference on Computer Aided Verification
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Storage Alternatives for Large Structured State Spaces
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Distributed State Space Generation of Discrete-State Stochastic Models
INFORMS Journal on Computing
A new methodology for calculating distributions of reward accumulated during a finite interval
FTCS '96 Proceedings of the The Twenty-Sixth Annual International Symposium on Fault-Tolerant Computing (FTCS '96)
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Performance Evaluation: = (Process Algebra + Model Checking) × Markov Chains
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Formal modeling and quantitative analysis of KLAIM-based mobile systems
Proceedings of the 2005 ACM symposium on Applied computing
Combining Response Surface Methodology with Numerical Methods for Optimization of Markovian Models
IEEE Transactions on Dependable and Secure Computing
Formal analysis techniques for gossiping protocols
ACM SIGOPS Operating Systems Review - Gossip-based computer networking
Applying formal methods to gossiping networks with mCRL and groove
ACM SIGMETRICS Performance Evaluation Review
Rate-Based Transition Systems for Stochastic Process Calculi
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
On a Uniform Framework for the Definition of Stochastic Process Languages
FMICS '09 Proceedings of the 14th International Workshop on Formal Methods for Industrial Critical Systems
Systematic model-based safety assessment via probabilistic model checking
ISoLA'10 Proceedings of the 4th international conference on Leveraging applications of formal methods, verification, and validation - Volume Part I
Towards model checking stochastic aspects of the thinkteam user interface
DSVIS'05 Proceedings of the 12th international conference on Interactive Systems: design, specification, and verification
| Hi-index | 0.00 |
Markovian models have been used for about a century now for the evaluation of the performance and dependability of computer and communication systems. In this paper, we give a concise overview of the most widely used classes of Markovian models, their solution and application. After a brief introduction to performance and dependability evaluation in general, we introduce discrete-time. Markov chains, continuous-time Markov chains and semi-Markov chains. Stepwisely, we develop the main equations that govern the steady-state and the transient behaviour of such Markov chains. We thereby emphasise on intuitively appealing explanations rather than on mathematical rigor. The relation between the various Markov chain types is explained in detail. Then, we discuss means to numerically solve the systems of linear equations (both direct and iterative ones) and the systems of differential equations that arise when solving for the steady-state and transient behaviour of Markovian models.