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cross-organizational workflow architecture. A Petri-Net-based state transition
approach that binds states of private workflow tasks to their adjacent workflow view-
task was introduced. The concepts are demonstrated by a scenario, run by two ex-
tended workflow management systems. Jiang et al. [17] described a timed colored
Petri net and process-view combined approach to construct cross-organizational
workflows, and a three-model framework was proposed to realize the interoperability
of cross-organizational workflows. Finally, a case study of the collaborative devel-
opment of a motorcycle was presented to verify the validity of our approach. In our
previous work, we formally defined different cross-organizational coordination pat-
terns, including message interaction pattern, resource interaction pattern, task collabo-
ration pattern, service outsourcing pattern, and etc. based on RM_WF_Net in our
precisely work [4], whose correctness is verified by constructing its corresponding
reachability graph. To analyze the property of workflow net systems, the language
description is also an important approach. With the formal language expression, we
can decide and control the fairness, liveness, deadlock and trap for the workflow
processes, which provides an effective solution for the property analysis based on
Petri net. Following this approach, Yan et al. proposed a net reduction rules to pre-
serve languages of workflow net systems, and based on which a generation algorithm
is proposed for the language expression of workflow net systems in [18]. This method
contributes to solve the explosion problem for reachable state space to a certain
degree.
Based on the above-mentioned literature review, we can conclude that most of pre-
vious research on the modeling and analysis of cross-organization workflow net focus
on the modeling and structural analysis, and there is little work on the behavior de-
scription of cross-organization workflow net system. In this paper, we address the
behavior description for a kind cross-organizational workflow with task synchroniza-
tion pattern using Petri net language. As the first complete framework to perform the
behavior description of cross-organizational workflow, we are sure that our work can
improve the state-of-art to a great extent.
3
Preliminaries
Modeling approaches for workflows have been studied for decades, and some excel-
lent models such as, WF-net, XPDL, BPEL, BPMN and etc., have been widely used.
Whatever models are used, the workflow process is totally determined by tasks and
their dependency relations. This work is based on Petri net and its language theory,
WF-net to be more specific. We assume that readers are familiar with the basic con-
cepts of Petri nets [10]-[12] and WF-net [9]. Some of the essential terminologies and
notations are listed as follows.
Definition
3.1.
A
Petri net
is a 4-tuple
=(
P,
T
;
F, M
0
), where: (1)
P
={
p
1
,
p
2
, …
p
m
} is
a finite set of places; (2)
T
={
t
1
,
t
2
, …
t
n
} is a finite set of transitions; (3)
F
ʣ
ↆ
(
P
×
T
)
∪
(
T
×
P
) is a finite set of arcs (flow relation); (4)
M
0
:
P
ₒ
{0,1,2,3,…} is the
initial marking; and (5)
P
∩
T
=
∅
and
P
∪
T
≠∅
.
