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3
Net Models of Distributed
Systems and Work
f
ows
3.1 INFORMAL INTRODUCTION TO PETRI NETS
In 1962 Carl Adam Petri introduced a family of graphs, called PlaceTransition (P/T),
nets, to model dynamic systems [25]. P/T nets are bipartite graphs populated with
tokens that
f
ow throughthe graph. A
bipartite graph
is one with two classes of nodes;
arcs always connect a node in one class with one or more nodes in the other class. In
the case of P/T nets the two classes of nodes are
places
and
transitions
; arcs connect
one place with one or more transitions or a transition with one or more places.
To model the dynamic behavior of systems, the places of a P/T net contain tokens;
F
ring of transitions removes tokens from some places, called input places, and adds
them to other places, called output places. The distribution of tokens in the places of
a P/T net at a given time is called the
marking
of the net and re
f
ects the state of the
system being modeled.
P/T nets are very powerful abstractions and can express both concurrency and
choice. P/T nets are used to model various activities in a distributed system; a transi
tion may model the occurrence of an event, the execution of a computational task, the
transmission of a packet, a logic statement, and so on. The
input places
of a transition
model the preconditions of an event, the input data for the computational task, the
presence of data in an input buffer, the preconditions of a logic statement. The
output
places
of a transition model the postconditions associated with an event, the results
of the computational task, the presence of data in an output buffer, or the conclusions
of a logic statement.
P/T nets, or Petri nets (PNs), as they are commonly called, provide a very useful
abstraction for system analysis and for system speci
F
cation, as shown in Figure 3.1.
137
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NET MODELS OF DISTRIBUTED SYSTEMS AND WORKFLOWS
M; Petri Net
Model of
System S
Modeling
Translation
MP;
Model
Properties
SP; System
Properties
System
Analysis
Static
Analysis of
the Net
Model
Dynamic
Analysis of
the Net
Model
Remapping
(a)
Translation
MP;
Model
Properties
Dynamic
Analysis of
the Net
Static
Analysis of
the Net
(b)
S; Reallife
System
M; Petri Net
Description of
a Software
System S
S; Software
System
Fig. 3.1
Applications of Petri nets. (a) PNs are often used to model complex systems that
are dif
f
cult or impossible to analyze by other means. In such cases one may construct a PN
model of the system,
, then carry out a static and/or dynamic analysis of the net model and
from this analysis infer the properties of the original system
.I
f
is a software system one
may attempt to translate it directly into a PN rather than build a model of the system. (b) A
software system could be speci
f
ed using the PN language. The net description of the system
can be analyzed and, if the results of the analysis are satisfactory, then the system can be built
from the PN description.
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This note was uploaded on 02/15/2012 for the course COP 5611 taught by Professor Staff during the Spring '08 term at University of Central Florida.
 Spring '08
 Staff

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