Modified Petri Nets for Workflow Process Modeling

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Modified Petri Nets for Workflow Process Modeling

• Haidong Bi
• AI Lab PhD Seminar
• May 10, 2002

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Workflow

• Workflow (WFMC, 1999)
• automation of business processes
• documents, information or tasks are passed from
  one participant to another for action
• a set of procedural rules
• Workflow Management System (WFMS) (WFMC, 1999)
• a system that defines, creates and manages the
  execution of workflows through the use of
  software

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Four Perspectives of Process Modeling (Curtis, et
al. 1992 Jablonski Bussler 1996)

• Informational perspective
• information and data
• generated, manipulated, and consumed
• Organizational perspective
• relationship between a WFMS and an organization
• resources and roles involved to each activity
• Functional perspective
• functions delivered and applications accomplished
• Control flow perspective
• activities
• ordering, relationships, when to take place

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Control Flow Modeling

• The most fundamental perspective (Aalst et al.
  2000)
• Major modeling tasks process constructs

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Current Status of PM

• Like DBMS before relational data model and ERD
  were invented in early 1970s (Sheth et al. 1999
  Basu Kumar 2002)
• More than 250 workflow products
• No unifying workflow modeling standard

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Modeling Issues

• Is the process modeling language graph-based?
• Does the modeling language have a formal base to
  support computation and analysis?
• Is the modeling language capable of modeling
  various scenarios of control flows?
• Can the modeling language capture and model the
  states of activities and processes?
• Can the modeling language model the relationships
  between activities, especially the global
  relationships between activities?
• If the language can meet various modeling
  requirements, is it intuitive, simple, and
  user-friendly?

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Existing Modeling Approaches

• Workflow Management Coalition (WFMC, 1999)

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Existing Modeling Approaches

• 2. Petri nets (Murata 1989 Aalst 1998, 1999
  Adam et al. 1998)

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Existing Modeling Approaches

• 3. StateCharts (Harel 1987 Wodtke Weikum 1997)

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Existing Modeling Approaches

• 4. Logic-based approaches (Emerson 1990 Bonner
  Kifer 1994 Kifer 1996 Davulcu et al. 1998)
• Use logic expressions to represent process
  transitions
• e.g. A v B ? C

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Comparison of Existing Modeling Approaches
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Petri nets (PN)

• Three basic elements
• Transitions (rectangles )
• Places (circles )
• Directed arcs (?)
• Formalism for analysis and verification
• Token-based state representation to trace control
  flows
• Strictly separate activities (transitions) and
  states (places)

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Incidence Matrix

• The incidence matrix U uij,
• W(tj, pi), transition j --gt place i
• uij -W(pi, tj), place i --gt transition j
• 0, otherwise
• where place i 1, 2, , m
• transition j 1, 2, , n

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State Equation

• M M0 UV?
• where
• M -- final marking to be obtained
• M0 -- initial marking
• U -- incidence matrix
• ? -- a firing sequence of transitions
• V? -- counting vector of ?, V? v1, v2, , vn,
  
• where vj is the number of times tj
  included in ?

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Limitations of PN

• Less expressive and difficult to learn and use
  (Jablonski Bussler 1996 Wodtke Weikum 1997)
• Do not do a good job in modeling the activities
  connectivity and interactions (Basu Blanning.
  2000)
• Cant model global relationships between
  non-directly connected transitions (Davulcu et
  al. 1998)

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Modified Petri nets (MPN)

• Four basic elements
• Transitions (rectangles )
• ID, description
• Control flow constructs (circles )
• token, ID, incoming/outgoing control flow symbols
• Directed arcs ( 4 )
• weight
• Constraints (dotted hexagon
  )
• ID, description

a1 Receive order
c1 End(a5) gt Start(a6)
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MPN
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MPN

• Seven Types of control flows
• Sequence (SEQ)
• AND-Split (AND-S)
• AND-Join (AND-J)
• XOR-Split (XOR-S)
• XOR-Join (XOR-J)
• OR-Split (OR-S)
• OR-Join (OR-J)
• Two special symbols
• Start
• End

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MPN

• Map MPN graph into four tables
• Transition table
• Control flow construct table
• Link table
• Constraint table

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Modeling Example of PN

• Scenario and graph

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Incidence Matrix

• Initial marking
• M0

• Incidence Matrix
• 12 x 9 108 entries
• U

t1 t2 t3 t4 t5 t6
t7 t8 t9
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State Equation

• Suppose the firing sequence
• t1 t2 t4 t5 t7 t8 t6 t9
• Thus, Counting vector V?
• Final marking
• M M0 UV?
  

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Modeling Example of MPN

• Scenario and graph

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Incidence Matrix

• Initial marking
• M0

• Incidence Matrix
• 6 x 9 54 entries
• U

t1 t2 t3 t4 t5 t6
t7 t8 t9  
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State Equation

• Suppose the same firing sequence
• t1 t2 t4 t5 t7 t8 t6 t9
• Thus, the same Counting vector V?
• Final marking
• M M0 UV?
  

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MPN Transition Table
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MPN Construct Table
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MPN Link Table
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MPN Constraint Table
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Similarities

• Both PN and MPN have
• Transitions, places (constructs), and directed
  arcs
• Token-based state representation

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Differences

• Petri nets (PN)
• Information of control flows is implicitly given
  by the relative positions among transitions and
  places
• Weight of all arcs 1
• Number of incoming/outgoing flows to/from some
  transitions gt1

• Modified Petri nets (MPN)
• Information of control flows is explicitly
  represented by the control flow constructs
• Weight of some arcs gt 1
• Number of incoming/outgoing flows to/from all
  transitions 1
• Constraints on transitions and constructs

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Summary

• MPN inherits PNs powers in process modeling
• Explicitly separate transitions and states
• Token-based state representation supports formal
  analysis and verification
• All analysis methods are still applied to MPN

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Advantages of MPN

• 1. MPN models various scenarios of control flows
  more effectively than PN does

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Advantages of MPN

• MPN 2-Out-of-3 Join
• 4 transitions
• 1 construct
• 1 constraint

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Advantages of MPN

• 2. MPN can model global relationships between
  transitions

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Advantages of MPN

• 3. MPN has strong computational capabilities by
  supporting modeling and implementing
• Graphs
• Tables
• 4. MPN reduces computational complexity
• 5. MPN is more intuitive, simple, and
  user-friendly

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Q A

• Thank you very much!