Volume and Entropy of Regular Timed Languages: Discretization Approach
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Volume and Entropy of Regular Timed Languages: Analytic Approach
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Generating functions of timed languages
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Spectral gap in timed automata
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
| Hi-index | 0.00 |
Quantitative evaluation of models allowing multiple concurrent non-exponential timers requires enumeration and analysis of non-Markovian processes. In general, these processes may be not isomorphic to those obtained from the corresponding untimed models, due to implicit precedences induced by timing constraints on concurrent events. The analysis of stochastic Time Petri Nets (sTPNs) copes with the problem by covering the state space with stochastic classes, which extend Difference Bounds Matrix (DBM) theory with a state density function providing a measure of probability for the variety of states collected within a class. In this paper, we extend the theory of stochastic classes providing a close form calculus for the derivation of the state density function under the assumption that all transitions have an expolynomial distribution. The characterization provides insight on how the form of the state density function evolves when transitions fire and the stochastic class accumulates memory and provide the basis for an efficient implementation which drastically reduces analysis complexity.