Symanzik, Juergen (1997) Stochastic Analysis of Periodic Timed Data Flow Diagrams with Markovian Transition Times. Technical Report TR96-24, Department of Computer Science, Iowa State University.
Stochastic Analysis of Periodic Timed Data Flow Diagrams
with Markovian Transition Times
Timed (or Stochastic) Data Flow Diagrams (TDFD's or SDFD's) introduced
in Symanzik and Baker (1996d) are an extension of the Formalized Data
Flow Diagrams, defined in Leavens et al. (1996). This extension allows us
to assess the quantitative behavior (e. g., performance, throughput,
average load of a bubble, etc.) as well as the qualitative behavior
(e. g., deadlock, reachability, termination, finiteness, liveness, etc.),
eventually depending on different types of transition times, for the
system modeled through the TDFD. In this paper, we consider Markovian
transition times for the consumption of in--flow items and for the
production of items on the out--flow. Moreover, we require the TDFD
to be periodic and irreducible and it must have a finite reachability set.
For these models, we have been able to apply an aggregation principle
of Schassberger (1984), extended for periodic Markov chains by Woo (1993),
to efficiently determine stationary probabilities, expected waiting times,
and limiting process probabilities.
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