Realizability of Schedules by Stochastic Time Petri Nets with Blocking Semantics
Abstract
This paper considers realizability of expected schedules by production systems
with concurrent tasks, bounded resources that have to be shared among tasks,
and random behaviors and durations. Schedules are high level views of desired
executions of systems represented as partial orders decorated with timing con-
straints. Production systems (production cells,train networks. . . ) are modeled as
stochastic time Petri nets STPNs with an elementary (1-bounded) semantics. We
detail their interleaved operational semantics, and then propose a non-interleaved
semantics through the notion of time processes. We then consider boolean re-
alizability: a schedule S is realizable by a net N if S embeds in a time process
of N that satisfies all its constraints. However, with continuous time domains,
the probability of a time process with exact dates is null. We hence consider
probabilistic realizability up to α time units, that holds if the probability that N
realizes S with constraints enlarged by α is strictly positive. Upon a sensible
restriction guaranteeing time progress, boolean and probabilistic realizability
of a schedule can be checked on the finite set of symbolic prefixes extracted
from a bounded unfolding of the net. We give a construction technique for these
prefixes and show that they represent all time processes of a net occurring up to
a given maximal date. We then show how to verify existence of an embedding
and compute the probability of its realization.
Origin : Files produced by the author(s)
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