Dynamic Workflow Modeling and Analysis

1
Dynamic Workflow Modeling and Analysis

• J. Wang and R. Rosca
• Department of Software Engineering
• Monmouth University

2
Outline

• Motivation
• An intuitive and formal workflow model
• Well-formed workflows
• Verification
• Tool support
• Conclusion and future work

3
Motivation

• Driven by workflow design for incident command
  systems
• Frequent changes of the course of action dictated
  by incoming events
• Calls for on-the-fly verification of the workflow
  correctness
• Predominantly volunteer-based workforce
• Needs intuitive features for the description and
  modification of the WF
• High stake
• Needs formal approach (no ambiguity, allows
  analysis)
• We introduced the Workflow Intuitive Formal
  Approach (WIFA) to meet the needs

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WIFA Workflow Definition

• A workflow is WF (T, P, C, A, S0), where
• T T1, T2, Tm is a set of tasks, m 1.
• P (p)mxm is the precedence matrix of the task
  set. If Ti is the direct predecessor of Tj, then
  pij 1 otherwise, pij 0.
• C (c)mxm is the conflict matrix of the task
  set. cij ? 0, 1 for i 1, 2, m and j 1, 2,
  m.
• A (A(T1), A(T2), , A(Tm)) defines
  pre-condition set for each task. ?Tk ? T, A(Tk)
  Tk ? . Let set A ? A(Tk). Then Ti ? A
  implies pik 1.
• S0 ? 0, 1, 2, 3m is the initial state of the
  workflow.

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Example
T T1, T2, , T8,
A(T1) Ø, A(T2) T1, T6, A(T3) T1,
A(T4) T2, A(T5) T4, A(T6) A(T7)
T5, A(T8) T3, T7. S0 (1, 0, 0, 0, 0,
0, 0, 0).
,
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Individual Task State Values

• S(Ti) 0 means Ti is not executable at state S
  and not executed previously.
• S(Ti) 1 means Ti is executable at state S and
  not executed previously.
• S(Ti) 2 means Ti is not executable at state S
  and executed previously.
• S(Ti) 3 means Ti is executable at state S and
  executed previously.

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State Transition Rules

• A set of rules to guide workflow execution
• Denote by Sa(Ti)Sb that task Ti is executed under
  state Sa, and the new state after the execution
  is Sb.
• Rules ? Tj ? T,
• If Tj Ti then Sb(Tj) 2. (Tj is just executed)
• If Sa(Tj) 0
• If pij 1 and ?A ? A(Tj) such that Sb(Tk) 2
  for any Tk ?A, then Sb(Tj) 1
• otherwise Sb(Tj) 0.

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State Transition Rules

• Sa(Tj) 1
• If cij 0 then Sb(Tj) 1 otherwise Sb(Tj) 0.
• Sa(Tj) 2
• If pij 1 and ?A ? A(Tj) such that Sb(Tk) 2
  for any Tk ?A, then Sb(Tj) 3 otherwise Sb(Tj)
  2.
• Sa(Tj) 3
• If cij 0 then Sb(Tj) 3 otherwise Sb(Tj) 2.

State value change of a task
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State Transition Rules

• Example

T4
T2
T5
T7
T1
c23 1
T6
T3
S0 (1, 0, 0, 0, 0, 0, 0) S1 (2, 1, 1, 0, 0, 0,
0) S2 (2, 2, 0, 1, 0, 0, 0) S3 (2, 0, 2, 0, 0,
1, 0)
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Modeling Power

• Sequential execution
• Conflict (decision making)
• Concurrency
• Synchronization
• Loop

c23 0 c67 1 A(T2) T1,T2 A(T8) T3,
T7
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Reachability Tree
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Well-Formed Workflows

• All reachable states form reachable set R
• A workflow is well-formed if and only if the
  following two behavior conditions are met
• There is no dangling task
• Given any reachable state, there is always an
  execution path leading the workflow to finish
• Validation of a WF being well-formed requires the
  reachability analysis of the WF

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Confusion-Free Workflows

• To simplify workflow modeling and verification
• A confusion-free workflow
• Is a well-formed workflow
• Either all tasks triggered by the same task are
  in conflict, or no pairs of them are in conflict
• A task becomes executable either when all of its
  predecessor tasks are executed, or when any one
  of them is executed

XOR-In-and-Out
AND-In-AND-Out
AND-In-XOR-Out
XOR-In-XOR-Out
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Workflow Dynamics

• A couple of theorems developed for quick
  on-the-fly well-formedness verification
• Theorem for adding new tasks to a WF, such that
  the new WF can preserve the confusion-free,
  well-formed properties (in the paper).
• Theorem for deleting a task from the WF such that
  the new WF can preserve the confusion-free,
  well-formed properties.
• Theorems for changing business rules that express
  task dependencies

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Lemma 1

• Given a workflow WFA (T, P, C, A, S0) with Tk ?
  T. As shown in Fig, WFB (T, P, C, A, S0)
  is obtained by replacing Tk with Tk1 and Tk2,
  such that
• Tk1 Tk, Tk2 Tk, Tk1 Tk2 and Tk2
  Tk1,
• A (Tk1) A(Tk)
• C(Ti, Tj) C(Ti, Tj) for ?Ti, Tj ? Tk,
• Then WFB is confusion-free well-formed iff WFA is
  confusion-free well-formed.

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Lemma 2

• Let WFA (T, P, C, A, S0) be a well-formed
  confusion-free workflow with Tk1, Tk2 ? T, Tk1
  Tk2 ?, and Tk2 is not a predecessor of Tk1.
  As shown in the figure, WFB (T, P, C, A,
  S0) is obtained by introducing precedence
  constraint between Tk1 and Tk2 such that Tk1 is
  an immediate predecessor of Tk2. Then WFB is also
  well-formed and confusion-free.

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Adding a new task
Tk
Ti
WF
Tk
Ti
Tk
Tk ? ?, Tk ?
WF
Tk ?, Tk ? ?
WF
Tk ? ?, Tk ? ?
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Changing dependency
T6
T3
T5
T4
T8
T7
T1
T2
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Deleting a task
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Tool Support for Editing, Validation and
Enactment of WFs
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Tool Features

• Saving workflow in XML or as an image
• Drag and Drop interface
• Dynamically change tasks/workflow properties
• Zooming in and out to focus on specific sections
  of the workflow
• Validate workflow
• Visually step through workflow in design window
• Step forward/backward through the simulation
• Auto-play speed adjustment
• Audit log for post incident analysis

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Conclusion

• Introduced a new formalism to support dynamic
  workflow modeling and verification
• Developed a set of theorems to validate the
  on-the-fly workflow changes
• Implemented a tool to allow easy workflow
  construction, modification, verification and
  execution

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Future Work

• Data dependency
• Decision support
• Inter-organizational workflows
• Tool enhancement