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 [SB96b] are an extension of the Formalized Data Flow Diagrams, de ned in [LWBL96]. 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, niteness, liveness, etc.), eventually depending on di erent types of transition times, for the system modeled through the TDFD. In this paper, we consider Markovian transition times for the consumption of in{ ow items and for the production of items on the out{ ow. Moreover, we require the TDFD to be periodic and irreducible and it must have a nite reachability set. For these models, we have been able to apply an aggregation principle of [Sch84], extended for periodic Markov chains by [Woo93], to e ciently determine stationary probabilities, expected waiting times, and limiting process probabilities.