Dynamic Workflow Modeling and Analysis J Wang and

Dynamic Workflow Modeling and Analysis J. Wang and R. Rosca Department of Software Engineering Monmouth University June 8, 2006 Dynamic Workflow Modeling and Analysis 1

Outline • • • Motivation An intuitive and formal workflow model Well-formed workflows Verification Tool support Conclusion and future work June 8, 2006 Dynamic Workflow Modeling and Analysis 2

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 June 8, 2006 Dynamic Workflow Modeling and Analysis 3

WIFA Workflow Definition A workflow is WF = (T, P, C, A, S 0), where • T = {T 1, T 2, …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(T 1), A(T 2), …, 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. • S 0 {0, 1, 2, 3}m is the initial state of the workflow. June 8, 2006 Dynamic Workflow Modeling and Analysis 4

Example T 2 T 6 T 4 T 1 T = {T 1, T 2, …, T 8}, T 5 T 7 T 8 , T 3 June 8, 2006 A(T 1) = Ø, A(T 2) = {{T 1}, {T 6}}, A(T 3) = {{T 1}}, A(T 4) = {{T 2}}, A(T 5) = {{T 4}}, A(T 6) = A(T 7) = {{T 5}}, A(T 8) = {{T 3, T 7}}. S 0 = (1, 0, 0, 0, 0). Dynamic Workflow Modeling and Analysis 5

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. June 8, 2006 Dynamic Workflow Modeling and Analysis 6

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. June 8, 2006 Dynamic Workflow Modeling and Analysis 7

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. 0 June 8, 2006 1 2 3 Dynamic Workflow Modeling and Analysis State value change of a task 8

State Transition Rules • Example T 4 T 2 T 5 T 7 T 1 T 6 T 3 c 23 = 1 S 0 =(1, 0, 0, 0) S 1 =(2, 1, 1, 0, 0) S 2 =(2, 2, 0, 1, 0, 0, 0) S 3 =(2, 0, 0, 1, 0) …… June 8, 2006 Dynamic Workflow Modeling and Analysis 9

Modeling Power • • • Sequential execution Conflict (decision making) Concurrency Synchronization Loop T 2 T 6 T 4 T 1 T 5 c 23 = 0 c 67 = 1 A(T 2) = {{T 1}, {T 2}} A(T 8) = {T 3, T 7} T 7 T 8 T 3 June 8, 2006 Dynamic Workflow Modeling and Analysis 10

(1 0 0 0 0) T 1 Reachability Tree (2 1 1 0 0 0) T 2 T 3 (2 2 1 1 0 0) (2 1 2 0 0 0) T 2 T T 3 (2 2 2 1 0 0) (2 2 1 0 0 0) T 3 T 5 T 4 4 (2 2 1 1 0) T 6 (2 2 2 1 1 0) T 7 T 6 (2 3 1 2 2 2 0 0) T 2 T 3 (2 3 2 2 0 0) T 2 (2 2 2 0 2 1) T 8 (2 2 1 3 2 2 0 0) T 4 T 6 T 3 (2 2 2 3 2 2 0 0) T 4 (2 2 2 0 2) (2 2 1 2 3 2 0 0) T 5 T 3 (2 2 3 2 0 0) T 5 (2 2 1 2 2 3 1 0) T 7 T 3 (2 2 2 3 1 0) T 7 (2 2 1 2 2 0) June 8, 2006 T 3 (2 2 2 2 1) T 8 (2 2 2 2 2) Dynamic Workflow Modeling and Analysis T 6 T 3 11

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 June 8, 2006 Dynamic Workflow Modeling and Analysis 12

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 June 8, 2006 AND-In-AND-Out XOR-In-and-Out AND-In-XOR-Out XOR-In-XOR-Out Dynamic Workflow Modeling and Analysis 13

Workflow Dynamics • A couple of theorems developed for quick on-the-fly wellformedness 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, wellformed properties. – Theorems for changing business rules that express task dependencies June 8, 2006 Dynamic Workflow Modeling and Analysis 14

Lemma 1 • Given a workflow WFA = (T, P, C, A, S 0) with Tk T. As shown in Fig, WFB = (T’, P’, C’, A’, S’ 0) is obtained by replacing Tk with Tk 1 and Tk 2, such that –*Tk 1 = *Tk, Tk 2* = Tk*, Tk 1* = {Tk 2} and * Tk 2 = {Tk 1}, –A’ (Tk 1) = A(Tk); –C’(Ti, Tj) = C(Ti, Tj) for Ti, Tj Tk*, Then WFB is confusion-free well-formed iff WFA is confusion-free wellformed. Tk Tk 1 WFA June 8, 2006 Tk 2 WFB Dynamic Workflow Modeling and Analysis 15

Lemma 2 • Let WFA = (T, P, C, A, S 0) be a well-formed confusion-free workflow with Tk 1, Tk 2 T, Tk 1* = * Tk 2 = , and Tk 2 is not a predecessor of Tk 1. As shown in the figure, WFB = (T’, P’, C’, A’, S’ 0) is obtained by introducing precedence constraint between Tk 1 and Tk 2 such that Tk 1 is an immediate predecessor of Tk 2. Then WFB is also well-formed and confusion-free. Tk 1 WFA June 8, 2006 Tk 2 Tk 1 Tk 2 WFB Dynamic Workflow Modeling and Analysis 16

Adding a new task Ti WF Tk Ti Tk *Tk ≠ , Tk* = Tk WF *Tk = , Tk* ≠ WF *Tk ≠ , Tk* ≠ June 8, 2006 Dynamic Workflow Modeling and Analysis 17

Changing dependency T 6 T 3 T 1 T 4 T 2 June 8, 2006 T 3 T 5 T 7 T 8 T 4 T 5 T 7 T 1 T 8 T 2 Dynamic Workflow Modeling and Analysis 18

Deleting a task T 6 T 3 T 1 T 4 T 2 June 8, 2006 T 3 T 5 T 7 T 8 T 1 T 5 T 4 T 7 T 8 T 2 Dynamic Workflow Modeling and Analysis 19

Tool Support for Editing, Validation and Enactment of WFs June 8, 2006 Dynamic Workflow Modeling and Analysis 20

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 June 8, 2006 Dynamic Workflow Modeling and Analysis 21

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 June 8, 2006 Dynamic Workflow Modeling and Analysis 22

Future Work • • Data dependency Decision support Inter-organizational workflows Tool enhancement June 8, 2006 Dynamic Workflow Modeling and Analysis 23