A characterization of independence for competing Markov chains with applications to stochastic Petri nets

1994 ◽  
Vol 20 (7) ◽  
pp. 536-544 ◽  
Author(s):  
R.J. Boucherie
Keyword(s):  
Markov Chains ◽  
Petri Nets ◽  
Stochastic Petri Nets

Markov Chains and Stochastic Petri Nets for Availability and Reliability Modeling

2019 ◽  
pp. 127-151
Author(s):  
Paulo Romero Martins Maciel ◽  
Jamilson Ramalho Dantas ◽  
Rubens de Souza Matos Júnior
Keyword(s):  
Markov Chains ◽  
Petri Nets ◽  
Stochastic Petri Nets ◽  
Reliability Modeling

Extended Stochastic Petri Nets: Applications and Analysis.

1984 ◽  
Author(s):  
J. B. Dugan ◽  
K. S. Trivedi ◽  
R. M. Geist ◽  
V. F. Nicola
Keyword(s):  
Petri Nets ◽  
Stochastic Petri Nets

Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities

2020 ◽  
Vol 52 (4) ◽  
pp. 1249-1283
Author(s):  
Masatoshi Kimura ◽  
Tetsuya Takine
Keyword(s):  
Markov Chains ◽  
Stationary Distribution ◽  
Continuous Time ◽  
State Transition ◽  
Convex Polytope ◽  
Linear Inequalities ◽  
Systems Of Linear Inequalities ◽  
Free Sets ◽  
Practical Implications

AbstractThis paper considers ergodic, continuous-time Markov chains $\{X(t)\}_{t \in (\!-\infty,\infty)}$ on $\mathbb{Z}^+=\{0,1,\ldots\}$ . For an arbitrarily fixed $N \in \mathbb{Z}^+$ , we study the conditional stationary distribution $\boldsymbol{\pi}(N)$ given the Markov chain being in $\{0,1,\ldots,N\}$ . We first characterize $\boldsymbol{\pi}(N)$ via systems of linear inequalities and identify simplices that contain $\boldsymbol{\pi}(N)$ , by examining the $(N+1) \times (N+1)$ northwest corner block of the infinitesimal generator $\textbf{\textit{Q}}$ and the subset of the first $N+1$ states whose members are directly reachable from at least one state in $\{N+1,N+2,\ldots\}$ . These results are closely related to the augmented truncation approximation (ATA), and we provide some practical implications for the ATA. Next we consider an extension of the above results, using the $(K+1) \times (K+1)$ ( $K > N$ ) northwest corner block of $\textbf{\textit{Q}}$ and the subset of the first $K+1$ states whose members are directly reachable from at least one state in $\{K+1,K+2,\ldots\}$ . Furthermore, we introduce new state transition structures called (K, N)-skip-free sets, using which we obtain the minimum convex polytope that contains $\boldsymbol{\pi}(N)$ .

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

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