IBM Zurich Research Laboratory | Business Integration Technologies © 2007 IBM Corporation AWPN 2007 September 2007 Analysis of Workflow Graphs through

IBM Zurich Research Laboratory | Business Integration Technologies

© 2007 IBM Corporation

AWPN 2007

September 2007

Analysis of Workflow Graphs through SESE Decomposition

Jussi Vanhatalo, IBM Zurich Research LabHagen Völzer, IBM Zurich Research LabFrank Leymann, University of Stuttgart, IAAS


© 2007 IBM Corporation2 Jussi Vanhatalo, Hagen Völzer, Frank Leymann

Control-flow errors in business process models

Business process models are no longer only for documentation

Increasing importance when models are executed

– Workflow engine

– Realistic business measures through simulation

– Code generation

Our experience [Koehler, Vanhatalo, 2007] & other studies [Mendling et al., 2006]

– Control-flow errors, e.g. deadlocks occur frequently in real models

– Early detection can substantially save costs



Trade off – Speed versus debugging information

Workflow graph

Preprocessor

Workflow graph

Workflow graph = Free-Choice workflow net

Sound workflow graph = no control-flow errors

Known soundness checkers can:

– Check soundness in cubic time

– Produce error trace in exponential time

Our contribution is a preprocessor:

– Speeds up any soundness checker

– Improves debugging information

Soundness checker

Sound? Yes / No

Debugging information



Our contribution

Our preprocessor has two parts:

1) Decomposition of workflow graph

– Into fragments that can be checked in isolation

– Decomposition takes linear time

2) Fast heuristics

– Sort out many fragments occuring in practice

– Takes linear time

Fast heuristics

Decomposition

?

Sound? Yes / No

Workflow graph

Unsound

Sound


Soundness checker



Outline

1. Introduction

– Workflow graphs

– Soundness

2. Decomposition into fragments

3. Heuristics for analyzing soundness

4. Case study

5. Conclusion



Workflow graph

a1

a2

a3

activity

start node stop node

decision

fork join

merge



Soundness of a workflow graph

= Terminal state never becomes dead = (1)+(2):

1. No (local) deadlock

• A join cannot get enough tokens

2. No lack of synchronization

• An edge carries two or more tokens at the same time

a1

a2

a3

a1

a2

a3

Deadlock

a1

a2

a3

Lack of synchronization

Initial state Terminal state

entryedge

exitedge



Outline

1. Introduction


– Fragments

– Decomposition

– Process structure tree


4. Case study

5. Conclusion



Single-entry-single-exit (SESE) fragments

Ca1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

m3

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

j2

f3

j3

A SESE fragment is a connected subgraph that has a single entry edge and a single exit edge.

exitedge

entryedge

fragment



Single-entry-single-exit (SESE) fragments

CJa1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

m3

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

V

j2

f3

j3

SESE fragments are either nested (e.g. J and C), or disjoint (J and V)

SESE fragments do not overlap (essentially)



EA

B

C

D

JZ

Y

F

G

H

IK

L

X

M

a1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

m3

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

N

O

PQ

V R

S

T

U

W

j2

f3

j3

Decomposition into fragments

There is a unique decomposition into SESE fragments

Linear-time algorithm for SESE decomposition known from compiler theory used for discovering the structure of sequential programs [Johnson et al., 1994]



EA

B

C

D

JZ

Y

F

G

H

IK

L

X

M

a1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

m3

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

N

O

PQ

V R

S

T

U

W

j2

f3

j3

Z

X Y

KJ L

C D E F G H I

V W

M N

O P Q R S T U

A B

Process structure tree



Each fragment can be analyzed in isolation

A fragment is sound if and only if

– all its child fragments are sound, and

– the fragment that is obtained by replacing each child fragment with an activity is sound. [Valette, 1979]

a10

a11

f4 j4

d2m2

m3

a12a13 d3

O

PQ

V

d2m2

m3

d3

V

PQ

O

a10

a11

f4 j4O

a12P

a13Q

+

Sound

SoundSound

Sound

Sound



View switch

“Fragment” means the second view in the following

a10

a11

f4 j4

d2m2

m3

a12a13 d3

O

PQ

V

d2m2

m3

d3

V

PQ

O



EA

B

C

D

JZ

Y

F

G

H

IK

L

X

M

a1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

m3

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

N

O

PQ

V R

S

T

U

W

j2

f3

j3

Z

X Y

KJ L

C D E F G H I

V W

M N

O P Q R S T U

A B

Bottom-up analysis



EA

B

C

D

JZ

Y

F

G

H

IK

L

X

M

a1

d1a2

f1 j1

a3

m4

m1

a6

a5 a7

a4 a8

a10

a11

f4 j4

d2m2

a12a13 d3

f7

d4m5

f6

f5

a15

a14

a17

a16j5

j6

f2

a9

N

O

PQ

V R

S

T

U

W

j2

f3

j3

Z

X Y

KJ L

C D E F G H I

V W

M N

O P Q R S T U

A B

Locating an error

m3



Reduction achieved through decomposition

Number of fragments is linear in graph size

Time complexity of the soundness checker is cubic (exponential for error trace)

The size of the largest fragment is the most important factor for worst-case running time

Sound? Yes / No


8000 vs. 800

1 048 576 vs. 340

Decomposition

Workflow graph

Largest

Soundness checker

20

46

82



Outline

1. Introduction



– Heuristic for sound fragments

– Heuristic for unsound fragments

4. Case Study

5. Conclusion



Heuristic for sound fragments – Well-structured fragments

All sound, and all recognized in linear time

DA B C

Well-structured sequence

Well-structured cycle

Well-structured alternative branching

Well-structured concurrent branching

G

F

E

MK

O

N

L



Heuristic for sound fragments – Pure fragments

No forks, no joins

No concurrency

No decisions, no merges

No cycles

Pure alternative branching(State machine)

Pure concurrent branching(Marked graph)

d2m2

m3

d3

O

PQ

V

E

F

G

H

IK

f2 j2

f3

j3

All sound, and all recognized in linear time



Complex fragments

Not well-structured, nor pure

Mixes of forks/joins with decisions/merges

Sound or unsound

Soundness checker required

m4

d4m5

f6

f5j5R

S

T

U

W

C

B

A

Sound complex fragment Unsound complex fragment

Deadlock



Outline

1. Introduction



– Heuristic for sound fragments

– Heuristic for unsound fragments

4. Case study

5. Conclusion



Heuristic for unsound fragments

D

C

A

B

L

K

I

J

G

E

F

P

O

M

N

At least one join, but no forks At least one fork, but no joins

At least one merge, but no decisions At least one decision, but no merges

All unsound, and all recognized in linear time

H

DeadlockLack of synchr.

Lack of synchr.

Deadlock



Heuristic for unsound fragments – Cyclic Fragments

G

H

G

G

H

H

A cycle, but no merges A cycle, but no decisions

A cycle, but no merges and no decisions

All unsound, and all recognized in linear time

Deadlock

Lack of synchr.

Deadlock



Outline

1. Introduction



4. Case study

– Reductions achieved with the decomposition

– Applicability of the heuristics

5. Conclusion



Case study

More than 340 process models:

– Industrial business process models

– Modeled with the IBM WebSphere Business Modeler

Library 1:

– More than 140 process models

Library 2:

– More than 200 process models

– Experimental extension of Library 1

Average analysis time per workflow graph is less than 0.1 seconds

– Excluding the soundness checker

Fast heuristics

Decomposition

?

Sound? Yes / No

Workflow graph

Unsound

Sound


Soundness checker



Reductions achieved with the decomposition

Fast heuristics

Decomposition

Workflow graph

Largest


Library 1

Reduction factor = Graph size / size of largest fragment

– Average 2.8

– (min: 1.0, max: 9.0)

Average size: 67 edges(min: 11, max: 215)

Average size of the largest fragment: 24 edges(min: 11, max: 51)

Sound? Yes / No

140 x

Soundness checker

?Unsound

Sound



Reduction increases as the graph size increases

Upper boundary for the largest fragment size seems to be independent of graph size

0

10

20

30

40

50

60

0 50 100 150 200 250

Number of edges in the workflow graph

Num

ber

of e

dges

in th

e la

rges

tfr

agm

ent o

f th

e w

orkf

low

gra

ph



Applicability of the heuristics

Fast heuristics

Decomposition

?

Workflow graph

Largest

Unsound

Sound


100 %0 %

0 %

Sound? Yes / NoAll sound

140 x

Fragment category Percentage of fragments

1) Well-structured (sound) 54.8 %

2) Pure (sound) 45.2 %

3) Complex 0.0 %

3a) Complex (not sound) 0.0 %

3b) Complex (soundness unknown)

0.0 %

Library 1

Soundness checker



Applicability of the heuristics

Fast heuristics

Decomposition

Soundness checker

?

Workflow graph

Largest

Unsound

Sound


80.3 %5.4 %

14.3 %

200 x

Fragment category Percentage of fragments

1) Well-structured (sound) 65.4 %

2) Pure (sound) 14.9 %

3) Complex 19.7 %

3a) Complex (not sound) 5.4 %

3b) Complex (soundness unknown)

14.3 %

Library 2

Sound? Yes / ? / No



Outline

1. Introduction



4. Case study

5. Conclusion



Conclusion

Our preprocessor has two parts:

1) Decomposition of workflow graph

– Divide-and-conquer technique– Linear time algorithm

2) Fast heuristics

– Resolves many fragments occurring in practice

– Linear time algorithm

Fast heuristics

Decomposition

?

Sound? Yes / No

Workflow graph

Unsound

Sound


Soundness checker



Future work

Integrate our prototype to a soundness checker

– Compare the analysis times

Use cases for the SESE decomposition:

– Browsing and constructing large processes

– Discovery of reusable subprocesses

– Code generation

Documents

IBM Zurich Research Laboratory | Business Integration Technologies © 2007 IBM Corporation AWPN 2007 September 2007 Analysis of Workflow Graphs through