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If two different organizations need to synchronize to finish a certain task, i.e., each
organization shoulders parts of this task, in this way, there exists a task synchroniza-
tion pattern between these two organizations. The formal definition of task synchroni-
zation pattern and the cross-organization workflow net with task synchronization
pattern are defined in Definitions 4.1-4.2.
Definition 4.1. Let W 1 =( P 1 , T 1 ; F 1 , M 01 ) and W 2 =( P 2 , T 2 ; F 2 , M 02 ) be the WF-net of
two workflow processes. A task synchronization pattern exist between them if (1)
P 1
P 2 =
; and (2) T 1
T 2 ≠∅
.
Definition 4.2. Let W 1 =( P 1 , T 1 ; F 1 , M 01 ) and W 2 =( P 2 , T 2 ; F 2 , M 02 ) be the WF-net of
two workflow processes. W CW =( P , T ; F , M 0 ) is the cross-organization workflow net
with task synchronization pattern, short for CWF-net, if: (1) P = P 1
P 2 ; (2) T = T 1
T 2 ;
(3) F = F 1
F 2 ; and (4) M 0 = M 01
M 02 .
4.2
A Typical Cross-Organization Workflow Case
A typical scenario of cross-organization medical diagnosis workflow process at least
involves the surgical organization and the cardiovascular organization. For more in-
formation please refer to the case study in [6]. Part of this scenario is described as: (1)
When a patient arrives, the outpatient medical staff performs pre-examination triage;
(2) Then the patient information is generated based on the pre-examination result and
sent to the surgical medical staff; (3) The surgical medical staff takes admissions and
presents the reservation application, and then generates the reservation form; (4) The
surgeon diagnoses this patient and determine if he needs a consultation with the car-
diovascular internists; (5) If a consultation is needed, then the surgeon applies consul-
tation by sending consultation form to the cardiovascular internists; (6) If there is no
need to perform a consultation, the surgeon will give prescription based on the patient
symptom; (7) The internists receive the consultation request and begin to arrange the
consultation; (8) Surgeons and internists conduct the consultation and finally to give a
prescription together; (9) The internists make the consultation summary; and (10) The
patient takes the medicine and then leaves.
This cross-organization medical diagnosis workflow process involves two organi-
zations, i.e., the surgical organization and the cardiovascular organization. More spe-
cifically, the surgical organization contains tasks, such as pre-examination triage ( t 1 ),
admissions ( t 2 ), reservation application ( t 3 ), diagnosis ( t 4 ), consultation application
( t 5 ), give prescription ( t 6 ) and etc. The cardiovascular organization mainly consists of
tasks like receive consultation request ( t 7 ), consultation arrangement ( t 8 ), consultation
summary ( t 11 ) and file archive ( t 12 ). These two organizations need to collaborate to
finish certain tasks, including consultation ( t 9 ) and give prescription ( t 10 ). Thus, there
exists a task synchronization pattern between them.
According to the former business description, we obtain the WF-net s of the sur-
gical organization ( W s ) and the cardiovascular organization ( W C ) which is shown in
Figs. 1-2.
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