Lumpable continuous-time stochastic automata networks

Stochastics and Statistics Lumpable continuous - time stochastic automata networks

The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When the...

Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

Stochastic automata networks (SANs) have been developed and used in the last 15 years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we concentrate on the not so much emphasized discrete-time SANs. First, we remodel and extend an SAN that arises in wireless communications. Second, for an SAN with functional transitions, we deriv...

Fuzzy completion time for alternative stochastic networks

In this paper a network comprising alternative branching nodes with probabilistic outcomes is considered. In other words, network nodes are probabilistic with exclusive-or receiver and exclusive-or emitter. First, an analytical approach is proposed to simplify the structure of network. Then, it is assumed that the duration of activities is positive trapezoidal fuzzy number (TFN). This paper com...

Stochastic Automata Networks

Automata over continuous time

The principal objective of this paper is to lift basic concepts of the classical automata theory from discrete to continuous (real) time. It is argued that the set of nite memory retrospective functions is the set of functions realized by /nite state devices. We show that the /nite memory retrospective functions are speed-independent, i.e., they are invariant under ‘stretchings’ of the time axi...