Analysis and Composition of Partially-Compatible Web Services - Business and Scientific Workflows - page 92

2. For each outgoing message place p i 2 P M1 [ P M2 with

p i Þ¼ 1
2.1 If k i ¼ Dð

Cð

1
2.1.1 Add a mediation transition t i in

C ð p i ÞÞ >

M :

T m ¼ T m [f t i g , add places f p i1 ; p i2 ; ... ; p ik i g in M :

P m ¼ P m [f p i1 ; p i2 ; ... ; p ik i g

2.1.2 F m ¼ F m [fð p i ; t i Þ; ð t i ; p i1 Þ; ð t i ; p i2 Þ; ... ; ð t i ; p ik i Þg

3. For each incoming message place p j 2 P M1 [ P M2 with

1
3.1 If k j ¼ Dð

Cð p j Þ¼þ

1
3.1.1 Add a mediation transition t j in

C ð p j ÞÞ >

M :

T m ¼ T m [f t j g , and add place f p j1 ; p j2 ; ... ; p jk j g in M :

P m ¼ P m [f p j1 ; p j2 ; ... ; p jk j g

Þg
4. For each active data mapping rule without transformation, and
the source and target message places are p i and p j , respectively,
Merge

3.1.2 F m ¼ F m [fð t j ; p j Þ; ð p j1 ; t j Þ; ð p j2 ; t j Þ; ... ; ð p jk j ; t j

p i ; p j Þ
5. For each active data mapping rule with transformation, and
the source and target message places p i and p j , respectively,
AddTransformation ð

ð

p i ; p j Þ

6. Return M ¼ð P m ; T m ; F m ; S m ; C m Þ

p i ; p j Þ In Algorithm 4.2, two functions, that is, Merge ð and

p i ; p j Þ p i ; p j Þ

AddTransformation ð are used. Merge ð is to merge a place

p i Þ with a place p jk 2 ð p j Þ .Ifp i and/or p j p ik 2ð is null, use p i and/or

p i ; p j Þ

p j instead of p jk and p jk . AddTransformation ð is to add a transition

p i Þ and a place p jk 2 ð p j Þ t ikj between a place p ik 2ð ,thatis,T m ¼

.Ifp i and/or p j

T m [f t ikj g ,andF m ¼ F m [fð p ik ; t ikj Þ; ð t ikj ; p jk Þg is

p i Þ > null, use p i and/or p j instead of p ik and p jk .Notethatif ð 1or

ð p j Þ >

1, choose a different k each time these two functions are invoked
such that each place in p i Þ willmergewith a different place in ð p j Þ ,and

each newly added transition will have different source and target places in
ð

ð

p i Þ and ð p j Þ .

With the proposed method, a mediator between eBay and TPC is
generated as shown in Figure 4.12. The mediation transitions are denoted
with black rectangles to differentiate them from operation transitions
belonging to eBay and TPC services. With the generated mediator M ,the