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Graph-Based Methods for the Representation and Analysis of Business Workflows

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  1. Graph-Based Methods for theRepresentation and Analysis ofBusiness Workflows Amitava Bagchi Indian Institute of Management Calcutta

  2. References • Mukherjee Arindam, Sen Anup K and Bagchi Amitava (2004), Information analysis in workflows represented as task-precedence metagraphs, Proc WITS-2004, Workshop on Information Technology and Systems, Seattle, WA, USA, pp 32-37 • Mukherjee Arindam, Sen Anup K and Bagchi Amitava (2005), Representation, Analysis and Verification of Business Processes: A Metagraph-Based Approach, Working Paper WPS-552, Indian Institute of Management Calcutta (http://www.iimcal.ac.in) ISI_Dec_05

  3. Outline • Business Process & Workflow • Metagraphs & Information Elements • Task Precedence Metagraphs (TPMGs) • Information Analysis: Graphical Algorithm • Functional & Organizational Perspectives • Workflow Verification ISI_Dec_05

  4. Objectives • To describe an AND/OR graph representation scheme for business workflows • To present a graph traversal algorithm for the analysis of information flow in such workflows • To extend the above method to task and resource analyses • To outline how the structural correctness of workflows can be verified ISI_Dec_05

  5. Business Process & Workflow • Abusiness process consists of a set of related tasks in one or more functional areas (such as finance or marketing), which, when performed in any one of several permissible orders, enables an organization to achieve a business goal. • Ex: A loan appraisal system used in a bank ISI_Dec_05

  6. Loan Appraisal: Business Process Example ISI_Dec_05

  7. Legend (see fig p 6) • PD applicant’s property data • CD data on comparable properties • AC applicant’s account data • APD loan application data • AV appraised value of property • CR applicant’s credit rating • LA loan amount • RLA revised loan amount • LR risk level of loan • AR, MR, BR the loan risk level is acceptable, marginally bad, bad • BP current portfolio of bank’s loans • RE bank’s current loan exposure • YES the application is approved • NO the application is rejected ISI_Dec_05

  8. Business Process & Workflow • Workflow (or Workflow Instance): A specific instance of flow of control in a business process; it is a sub-graph of the given process graph • In practice, the terms business process and workflow are often used interchangeably. ISI_Dec_05

  9. Workflow Instance 1 ISI_Dec_05

  10. Workflow Instance 2 ISI_Dec_05

  11. Workflow Instance 3 ISI_Dec_05

  12. Business Process Modeling:Existing Approaches • Petri Nets & Related Formalisms • Petri Nets (van der Aalst & van Hee 2002) • Workflow Management Coalition (WfMC) Guidelines (http://www.wfmc.org) • Metagraph-Based Formalisms • Metagraphs (Basu & Blanning 2000, 1999, 1994) ISI_Dec_05

  13. Petri Nets & Related Formalisms • Main focus is on the precedence relationships between tasks • Flow of information plays a subsidiary role • Commercial products such as IBM’s MQSeries have adopted this convention • Widely used, and quite suitable for engineering applications ISI_Dec_05

  14. Metagraph-Based Formalisms • A metagraph is a directed (hyper-)graph. It can be viewed as a special type of AND/OR graph. • A metagraph is typically small in size (at most a few hundred nodes) and is explicitly available, i.e., the entire graph is supplied as input to a search algorithm. So the expansion of a node just means moving to its immediate successors. • In (implicit) game trees, new nodes actually get added to the graph as they get created. ISI_Dec_05

  15. Metagraph-Based Formalisms • Each node in a metagraph contains one or more information elements (items). • In Information Analysis, an input set of items is supplied at start, specifying the business information initially available. • Another set of items, called the output set, contains the target set of items that are desired as output. ISI_Dec_05

  16. Metagraph-Based Formalisms • Each arc represents a task that converts one set of items to another set of items. • The objective is to start from the input set of items, perform the tasks in the given order of precedence and derive all the items in the output set. ISI_Dec_05

  17. Metagraph-Based Formalisms • The metagraph convention puts more emphasis on the flow of information, so has an advantage over Petri Nets for business applications. • However, it is not widely used in practice because it suffers from certain shortcomings. ISI_Dec_05

  18. e Metagraph for Loan Evaluation Process 1 Calculate Account Credit Data (AC) Rating Credit Rating (CR) Marg . Bad e e 4 k 8 s i Risk (MR) R l Calculate a Applicant n t n i g e r m a s s M e Loan s Data (APD) s A Risk Loan Risk (LR) A e c A B c s a 9 e Appr .Value s A d p p r o v e p e R s e t t h i e (AV) e L s a s o a Loan n k b m 7 1 l 0 A e Approved e s d n s e e e s t R s i (YES) s a 5 i y r s t m w n e L o a n r p C a l c u l a t e a e k e e 2 p n p A t o o u n t A m r e t P a Accept f l o u c e l Risk (AR) Loan u a l Bad C a V Amt . (LA) Risk (BR) R e e e j A 6 e 1 p L c e t a 1 l c u t l p a o C l Property Risk t a i k h c s n i R s ’ k e n a a B Data (PD) Exposure i t e r u o s o p x E n (RE) Loan Comparables Bank’s Rejection Data (CD) Portfolio (NO) (BP)

  19. Metagraphs • The existing metagraph model for workflows has three main shortcomings: • Flow of control is not displayed with clarity and the diagram appears cluttered • The analysis makes use of symbolic matrices which are not easy to manipulate • A clear distinction is not always drawn between OR joins & AND joins (or even between OR splits & AND splits) ISI_Dec_05

  20. Task Precedence Metagraphs (TPMGs) • A TPMG is a modified form of metagraph. • It is visually more appealing and is more like an AND/OR graph in appearance. • It is less cluttered so the flow of control is discerned more easily. • A TPMG is more general than a WfMC graph in that AND & OR splits and joins are not always required to be matched in pairs. ISI_Dec_05

  21. Terminology • Tasks & Propagation Edges • Init Nodes & Prop Nodes • OR Nodes & AND Nodes • Split Nodes & Join Nodes ISI_Dec_05

  22. Task Precedence Metagraphs (TPMGs) • Edges are of two types: • Tasks: shown as bold arrows; a task converts the set of items at its start to another set of items, which cannot be obtained from any other task • Propagation Edges: shown as lightly drawn arrows; a propagation edge conveys an item from the outgoing end of a task to the incoming end of another task. ISI_Dec_05

  23. Task Precedence Metagraphs (TPMGs) • Nodes are also of two types • Init Nodes • An init node has a single outgoing edge corresponding to a task • Is shown as a bold oval • Prop Nodes • A prop node can have multiple outgoing edges, all of which are propagation edges • Is shown as a lightly drawn oval ISI_Dec_05

  24. Task Precedence Metagraphs (TPMGs) • Init and Prop Nodes • On every directed path, init nodes alternate with prop nodes, i.e., a TPMG is a directed bipartite graph, just like a Petri net. ISI_Dec_05

  25. Task Precedence Metagraphs (TPMGs) • Nodes are of two types, OR and AND. • An OR node (identified with a + sign) shows alternate paths for flow of control. • An AND node (identified with a • sign) indicates that flow of control takes place along all the edges at the same time. • An OR (or AND) node is either a split node or a join node. ISI_Dec_05

  26. Task Precedence Metagraphs (TPMGs) • Split & Join Nodes • A split node is a node at which multiple paths begin. It is always a prop node. • A join node is a node at which multiple paths end. It is always an init node. ISI_Dec_05

  27. Task Precedence Metagraphs (TPMGs) • However, a TPMG differs from a Petri Net in that every node has an associated subset of labeled items. This underscores the role of business information in a business process. ISI_Dec_05

  28. Information Analysis • Given a workflow, we seek answers to questions of the following type: • Suppose a set A of items is supplied. Starting from A, can we produce all the items in another given set B? • Is item ‘a’essential for producing item ‘b’? • These can be formulated as graph search problems. ISI_Dec_05

  29. Information Analysis • But a standard AND/OR graph search algorithm such as AO* (Nilsson 1980) is not appropriate for our purpose because a TPMG differs from an AND/OR graph in some ways: • TPMG: Multiple start nodes AND/OR Graph: One start node ISI_Dec_05

  30. Information Analysis • TPMG: Both AND joins and OR joins AND/OR Graph: Only OR joins • TPMG: Can have directed cycles AND/OR Graph: AO* assumes it is cycle-free • Note that a project scheduling network has only AND splits/joins and no OR splits/joins ISI_Dec_05

  31. Algorithm InfAnalysis • Algorithm InfAnalysis is an iterative graph search algorithm • Given: • An explicit TPMG • An input set of items • An output (target) set of items • Determines whether all the items in the output set can be derived. ISI_Dec_05

  32. Algorithm InfAnalysis • Algorithm InfAnalysis has some similarities with A* and AO* and makes use of an edge-marking method. • We think of the given TPMG as representing a business process, and the marked solution sub-graph produced by InfAnalysis as a workflow instance. ISI_Dec_05

  33. Algorithm InfAnalysis Makes use of four lists: • ITEMSET: initially contains the input set of items; new items get added as nodes get expanded • TARGET: contains the items desired as output • FRONTIER: only holds init nodes; initially holds those that have all their items in ITEMSET • STACK: needed for processing OR nodes; remembers which OR alternative should be processed next ISI_Dec_05

  34. Algorithm InfAnalysis • An active node is an init node in FRONTIER with all its items in ITEMSET. • At each iteration, InfAnalysis looks for an active node in FRONTIER, processes the correspond-ing task, and updates ITEMSET & FRONTIER. ISI_Dec_05

  35. Algorithm InfAnalysis • If all items in TARGET belong to ITEMSET then a solution has been found (success). • If there is no active node in FRONTIER then the next OR alternative in STACK must be pursued. • If STACK is also empty then failure. ISI_Dec_05

  36. Algorithm InfAnalysis • Thus the algorithm traverses the given TPMG exhaustively, looking for a workflow instance that generates, for the given input set, a set of items that contains the given output set. • When traversing a workflow instance, the edges in the instance get marked (say by colouring red). ISI_Dec_05

  37. Algorithm InfAnalysis • When the next workflow instance is examined, the marking at the corresponding OR split node is changed. • The advantage of marking is that each instance need not be traversed from scratch; the work done earlier can be remembered and partly reused. • The algorithm assumes that the TPMG is structurally valid. ISI_Dec_05

  38. Algorithm InfAnalysis • Example: For the loan appraisal process, we want to know whether, given the set of items S = { LA, PD, CD, AC, APD, BP } as input, we can produce the item YES as output. • A graph search algorithm is appropriate for such problems. To keep the algorithm simple, we do not indicate the edge markings. ISI_Dec_05

  39. Algorithm InfAnalysis initialize ITEMSET, FRONTIER, STACK; do while (TARGET is not a subset of ITEMSET) { if (there is an active node n in FRONTIER) then { remove n from FRONTIER; expand n, entering its init successors in FRONTIER, OR split nodes in ORLIST, and new items in ITEMSET; } // else examine next workflow instance else if (STACK is not empty) then { take next init successor p of OR node m on top of STACK; enter p in FRONTIER adding its items to ITEMSET; if (m has no other successors) then pop m; } else { announce “failure”; exit; } } // no remaining workflow instances announce “success”; exit; ISI_Dec_05

  40. Algorithm InfAnalysis: Observations • Works correctly on the example shown earlier (TPMG for loan appraisal) • But for more complex TPMGs containing OR split nodes that are not descendants of each other, the STACK must be replaced by a more flexible data structure ISI_Dec_05

  41. Functional Perspective • Queries that relate to the execution of tasks rather than to the flow of information: • Which other tasks must be completed before a given task t can start? • If a task t cannot be executed, which other tasks become inoperable? ISI_Dec_05

  42. Functional Perspective • Algorithm InfAnalysis can be modified in a simple way to answer such queries. • For example, to find the tasks that must be completed before task t can start, consider the set S of items contained in the init node that immediately precedes t. Run InfAnalysis with the given inputs and with S as the target set; the required set of tasks are those in the marked sub-graph. ISI_Dec_05

  43. Organizational Perspective • Queries that relate to resources (i.e., the executors of tasks, whether human agents or machines): • If a resource r is unavailable, some tasks will not get performed. As a result, some other resources might become idle. Which are the resources that will become idle? ISI_Dec_05

  44. Organizational Perspective • Again, Algorithm InfAnalysis can be modified in a simple way to answer such queries. • For example, to determine the other resources that become idle when resource r is unavailable, first find the set T of tasks that r executes. We can determine which other tasks get held up because the tasks in T cannot be executed. This will tell us whether any resources have become completely idle. ISI_Dec_05

  45. Temporal Constraints • The control structure of a workflow imposes temporal constraints on tasks. If a task precedes another task, it must be performed earlier. • If temporal information, such as the duration of tasks, is supplied, then issues arise similar to those in project scheduling. • However, the presence of directed cycles in workflows causes additional complications. ISI_Dec_05

  46. Structural Verification • A valid workflow always serves a business goal. • Given a business process W supplied in the form of a TPMG, how do we tell whether W is valid? • To ensure the validity of W, some structural (i.e., syntactic) constraints must be imposed on W. • We now give examples of such structural constraints. ISI_Dec_05

  47. Structural Problem: Deadlock • Deadlock:Caused when an OR split node is nested with an AND join node. • In the figure, only one of the two outgoing edges at the OR split node 2 can be marked at any time. So execution cannot proceed beyond the AND join node 7. • A valid workflow must not have any deadlocks. ISI_Dec_05

  48. Structural Problem: Lack of Synchronization • Lack of Synchronization:Caused when an AND split node is nested with an OR join node. • In the figure, since both the outgoing edges at the AND split node 2 will get marked, the task (7,8) will be executed twice. • A valid workflow must not suffer from lack of synchronization. ISI_Dec_05

  49. Structural Problem: Non-Terminating Cycle • Non-Terminating Cycle: Caused when control cannot exit from a directed cycle. • This problem can be avoided when every directed cycle is well-formed, i.e., it has an OR join node lying on it through which control can enter, and an OR split node lying on it through which control can exit (see loan appraisal example). ISI_Dec_05

  50. Other Structural Errors • Examples of other structural errors that must be eliminated: • Dangling Nodes: It should be ensured that if a node in a TPMG contains items that are not target items, then the node has a successor task. ISI_Dec_05