Petri Nets with Discrete Phase Type Timing:
A Bridge Between Stochastic and Functional Analysis
Andrea Bobbio,András Horváth
Abstract:
The addition of timing specification in Petri Nets (PN) has followed
two main lines: intervals for functional analysis or stochastic
durations for performance and dependability analysis. The present
paper proposes a novel technique to analyze time or stochastic PN
models based on discretization. This technique can be seen as a bridge
between the world of functional analysis and the world of stochastic
analysis. The proposed discretization technique is based on the
definition of a new construct called Discrete Phase Type Timing -
DPT that can represent a discrete cumulative density function (cdf)
over a finite support (or a deterministic cdf) as well as an interval
with non-deterministic choice (or a deterministic duration). In both
views, a preemption policy can be assigned and a strong (the
transition must fire when the interval expires) or a weak (the
transition can fire when the interval expires) firing semantics. The
paper introduces the DPT construct and shows how the expanded state
space can be built up resorting to a compositional approach based on
Kronecker algebra. With this technique a functional model can be
quantified by adding probability measures over the firing intervals
without modifying the (compositional) structure of the PN model.
Postscript
András Horváth, 2008-06-25