1991
DOI: 10.1016/0743-7315(91)90007-v
|View full text |Cite
|
Sign up to set email alerts
|

A methodology for solving markov models of parallel systems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
75
0

Year Published

1995
1995
2016
2016

Publication Types

Select...
5
1
1

Relationship

0
7

Authors

Journals

citations
Cited by 100 publications
(75 citation statements)
references
References 4 publications
0
75
0
Order By: Relevance
“…This is the form of the Kronecker representation in hierarchical Markovian models [3], where rectangularity of the smaller matrices is possible due to the product state space of the modelled system being larger than its reachable state space [9]. When the product state space is equal to the reachable state space, the smaller matrices turn out to be square as in stochastic automata networks [19,20].…”
Section: Introductionmentioning
confidence: 99%
“…This is the form of the Kronecker representation in hierarchical Markovian models [3], where rectangularity of the smaller matrices is possible due to the product state space of the modelled system being larger than its reachable state space [9]. When the product state space is equal to the reachable state space, the smaller matrices turn out to be square as in stochastic automata networks [19,20].…”
Section: Introductionmentioning
confidence: 99%
“…Given that a 1 k corresponds to the matrix element A 1i; j , then R k is deÿned similarly as the rearrangement of the block matrix R i; j . The ÿnal equality comes from the fact that a third-order tensor 3 (R) is actually m 1 n 1 second-order tensors and thus the sum of squares of the third-order tensor is the same as the sum of the m 1 n 1 sums of squares of the second-order tensors.…”
Section: Finding Higher-order Nkp For a General Matrixmentioning
confidence: 99%
“…This information regarding the automata and their types of transitions provides all the information needed to formally deÿne a SAN, as Atif and Plateau have done [2]. While this infrequent interaction (synchronizing transitions and functional transition rates) does complicate SANs, Plateau and her co-workers have shown that the SAN can still be represented in compact form as a sum of Kronecker products, known as the SAN descriptor [1,3,4]. Of course, too much interaction may complicate the SAN model to the point that all savings have been lost.…”
Section: Introductionmentioning
confidence: 99%
“…However, such computations rely on the underlying Markov chain of the Petri net model, so that Petri nets by themselves do not simplify the computation of statistics. In [10,11], however, particular structures of the transition matrix associated to certain Markov chains are used to decompose the statistical analysis of the system under consideration. Clearly, many real applications have been tackled by employing approaches developed within the Petri net community, and software products are available.…”
Section: Such Applications Require the Following Functionsmentioning
confidence: 99%