Computing Degree of Parallelism for BPMN Processes
. . .
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Outline • Motivating example • BPMN model and our technical problems • Compute the peak workload demand § Homogenous processes § Acyclic choice-less processes § Asynchronous processes
• Conclusion and future work Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Business Process Management Notation Task Insurance
Parallel-join gateway
(1 Day) Apartment Purchase Application
Payment
Issue Certificate
Public Notification
(1 Day)
(1 Day)
(1 Day)
(3 Days)
Start node
Parallel-split gateway
Document Archive
(1 Day)
End node
Duration (positive integer)
X Dec 2011
Exclusive-merge gateway
X
Computing Degree of Parallelism for BPMN Processes
Exclusive-choice gateway
4
The Problem to Solve • To compute the degree of parallelism under eager
scheduling policy § Maximum number of running tasks at the same time § The next task will start as soon as the previous one finishes The degree of parallelism is 3
Insurance
(1 Day)
Apartment Purchase Application
Payment
Issue Certificate
Public Notification
(1 Day)
(1 Day)
(1 Day)
(3 Days)
Document Archive
(1 Day)
Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Summary of Results Sub-Class of processes Homogenous
Complexity
O(n×log(n))
Acyclic Choice-less O(m×log(n) + m×L)
Asynchronous
Exponential If with constant number of cycles: O(L2)
* n: number of nodes; m: number of edges; L: sum of all tasks’ durations Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Outline • Motivating example • BPMN model and our technical problems • Processes with different classes § Homogenous processes § Acyclic choice-less processes § Asynchronous processes
• Conclusion and future works Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Homogenous Processes • Parallel
• Choice
+
X § Cannot generate new threads § The degree of parallelism is always one
Dec 2011
• Parallel gateways can fork threads § How to compute?
Computing Degree of Parallelism for BPMN Processes
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Parallel-Homogenous Processes Compute the Degree: Simulation O(nlog(n)) n: number of gateways and tasks
Priority Queue
2
0
2
1
2
1
1
...
4
3
9 g4
t3 e1
t1
t2
(2 Days)
(1 Day)
g1
g2
(3 Days)
(3 Days)
t5
g5
e2
(1 Day)
t6 (1 Day)
t4
g3
t7
t8 (1 Day)
(1 Day) Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Outline • Motivating example • BPMN model and our technical problems • Compute the peak workload demand § Homogenous processes § Acyclic choice-less processes § Asynchronous processes
• Conclusion and future work Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Acyclic Choice-less Processes
+
+
X
X
* This example is in the paper Dec 2011
Computing Degree of Parallelism for BPMN Processes
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g2
Process Decomposition • Step 1: Decompose a
process by merge/join X +
e1
g7 g5
g2
g7
e1
g5
Property: each sub-process only has one entry Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Compute degree for Sub-Processes • Step 2:
§ Treat + X as start or end nodes § Similar to parallel-homogenous process t2 e1
g2
1 Day
2 Days
g4
e1
Dec 2011
0
3 Days
2 Days
2
1 3 t2
1 Day
g5
6
g4 g5 g4 g2
Computing Degree of Parallelism for BPMN Processes
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Restore the Whole Process • Step 3: Combine all the lists to one e1
2 0
g2 g7
Dec 2011
3 t2
6
7 g5 t10
1 1
t7
3
2
12
g4 g4 g2
2 0
24
1
9
t7 g5 t9 g7
g5 g5
1 10 t10
12 t9 g7
2 0
1 1 t10
t9
3
g7
Empty
Computing Degree of Parallelism for BPMN Processes
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Complexity • O(m×log(n) + m×L) § m: number of edges § n: number of nodes § L: sum of all durations of tasks
Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Outline • Motivating example • BPMN model and our technical problems • Compute the peak workload demand § Homogenous processes § Acyclic choice-less processes § Asynchronous processes
• Conclusion and future work Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Asynchronous Processes
+ Data Archive Evaluation Application
(2 Hours)
Apartment Assessment
Data Analysis
(1 Hour)
(1 Hour)
(1 Hour) Comment & Review
(1 Hour)
X
Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Degree May Be Infinite • The degree of parallelism is finite if and only if no two cycles are connected (*) • Compute the degree for asynchronous processes § With at most one cycle: O(L3) • L: sum of all tasks’ durations § General: open
• In this paper § With at most one cycle: O(L2) § General: exponential complexity
* [Potapova-Su WS-FM 2010] Dec 2011
Computing Degree of Parallelism for BPMN Processes
Computing Degree of Parallelism for BPMN Processes
t5
t2 t3
t2
t4 t5 . . . . . .
The degree of parallelism is 4 19
Outline • Motivating example • BPMN model and our technical problems • Compute the peak workload demand § Homogenous processes § Acyclic choice-less processes § Asynchronous processes
• Conclusion and future work Dec 2011
Computing Degree of Parallelism for BPMN Processes
20
Summary of Results Sub-Class of processes Homogenous
Complexity
O(n×log(n))
Acyclic Choice-less O(m×log(n) + m×L)
Asynchronous
Exponential If with constant number of cycles: O(L2)
* n: number of nodes; m: number of edges; L: sum of all tasks’ durations Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Conclusions and Future Work
• Compute the peak workload demand • Focus on 3 sub-classes of BPMN processes • Future work § Produce histogram for resource planning • (Can be done with the existing algorithms) § With non-eager scheduling § Durations are intervals Dec 2011
Computing Degree of Parallelism for BPMN Processes
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Q&A
Dec 2011
Computing Degree of Parallelism for BPMN Processes
