Rational Automata Networks: A Non-Markovian Modeling Approach

Authors:
Peter Buchholz;Miklós Telek
Affiliations:
Informatik IV, Technische Universität Dortmund, D-44221 Dortmund, Germany;Department of Telecommunications, Technical University of Budapest, H-1521 Budapest, Hungary
Venue:
INFORMS Journal on Computing
Year:
2013

Citing 14
Cited 1

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Numerical transient analysis of Markov models

Computers and Operations Research
A methodology for solving Markov models of parallel systems

Journal of Parallel and Distributed Computing
BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Superposed stochastic automata: a class of stochastic Petri nets with parallel solution and distributed state space

Performance Evaluation
On the stochastic structure of parallelism and synchronization models for distributed algorithms
Hierarchical Structuring of Superposed GSPNs

IEEE Transactions on Software Engineering
Complexity of Memory-Efficient Kronecker Operations with Applications to the Solution of Markov Models

INFORMS Journal on Computing
Queueing Theory: A Linear Algebraic Approach

Queueing Theory: A Linear Algebraic Approach
On the canonical representation of phase type distributions

Performance Evaluation
Moments Characterization of Order 3 Matrix Exponential Distributions

ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Interactive Markov chains: and the quest for quantified quality

Interactive Markov chains: and the quest for quantified quality
Stochastic Petri nets with matrix exponentially distributed firing times

Performance Evaluation
Continuous System Simulation

Continuous System Simulation

Numerical analysis of rational processes beyond Markov chains

Performance Evaluation

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new class of non-Markovian models is introduced that results from the combination of stochastic automata networks and a very general class of stochastic processes, namely, rational arrival processes, which are derived from matrix exponential distributions. It is shown that the modeling formalism allows a compact representation of complex models with large state spaces. The resulting stochastic process is non-Markovian, but it can be analyzed with numerical techniques like a Markov chain, and the results at the level of the automata are stochastic distributions that can be used to compute standard performance and dependability results. The model class includes stochastic automata networks with phase-type distributed and correlated event times and also includes models that have a finite state space but cannot be represented by finite Markov chains. The paper introduces the model class, shows how the descriptor matrix can be represented in compact form, presents some example models, and outlines methods to analyze the new models.