GraphBased Methods for the Representation and Analysis of Business Workflows

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)

3
Outline

• Business Process Workflow
• Metagraphs Information Elements
• Task Precedence Metagraphs (TPMGs)
• Information Analysis Graphical Algorithm
• Functional Organizational Perspectives
• Workflow Verification

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

5
Business Process Workflow

• A business 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

6
Loan Appraisal Business Process Example
7
Legend (see fig p 6)

• PD applicants property data
• CD data on comparable properties
• AC applicants account data
• APD loan application data
• AV appraised value of property
• CR applicants 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 banks loans
• RE banks current loan exposure
• YES the application is approved
• NO the application is rejected

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.

9
Workflow Instance 1
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Workflow Instance 2
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Workflow Instance 3
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Business Process ModelingExisting 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)

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 IBMs MQSeries have
  adopted this convention
• Widely used, and quite suitable for engineering
  applications

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.

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.

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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.

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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.

18
e
Metagraph for Loan Evaluation Process
1
Calculate
Account
Credit
Data (AC)
Rating
Credit
Rating
(CR)
Marg
. Bad
e
e
k
4
8
s
Risk (MR)
i
R

l
Calculate
a
Applicant
n
t
n
i
g
e
r
m
a
s
M
s
e
Loan
s
Data (APD)
s
A
Risk
Loan
Risk (LR)
A
e
c
A
B
c
s
a
9
Appr
.Value
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s
A
d
p
p
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o

v
p
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R
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(AV)
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L
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Loan
a
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7
1

0
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A
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Approved
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(YES)
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Exposure
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(RE)
Loan
Comparables
Banks
Rejection
Data (CD)
Portfolio
(NO)
(BP)
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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)

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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.

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Terminology

• Tasks Propagation Edges
• Init Nodes Prop Nodes
• OR Nodes AND Nodes
• Split Nodes Join Nodes

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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

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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

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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.

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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.

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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

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.

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.

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).

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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.

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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.

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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

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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

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?

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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.

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?

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.

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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.

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.

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.

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.

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).

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.

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Structural Verification

• The structural verification algorithm TPMG_SYN
  traverses the workflow instances in the given
  TPMG one by one looking for structural problems.
• As soon as it locates a problem it terminates
  with an appropriate error message.
• If TPMG_SYN does not find a problem, the given
  TPMG models a valid business process.

52
Structural Verification

• TPMG_SYN has many similarities with Algorithm
  InfAnalysis.
• TPMG_SYN assumes for convenience that there is
  one start node and one goal node. If this does
  not hold for the given TPMG, an AND split node
  can be added at the top and an OR join node at
  the bottom.

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Algorithm TPMG_SYN

• 1 initialize ITEMSET, FRONTIER, STACK finish
  false
• 2 do while (finish false)
• 3 if (there is a non-goal active node n in
  FRONTIER) then
• 4 remove n from FRONTIER
• 5 expand n, entering its init successors in
  FRONTIER,
• 6 OR split nodes in ORLIST, and new items
  in ITEMSET
• 7
• 8 else if (there is a goal node in FRONTIER)
  then
• 9 announce one workflow instance scanned
• 10 else if (STACK is not empty) then
• 11 take next init successor p of OR node m
  on top of STACK
• 12 enter p in FRONTIER adding its items to
  ITEMSET
• 13 if (m has no other successors) then pop
  m
• 14
• 15 else finish true
• 16
• 17 announce the given TPMG is valid exit

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TPMG_SYN Detection of Errors

• Illegal cycles and lack of synchronization can
  both be detected at line 5 when node n is
  expanded. We can just check whether as a result
  of the expansion an OR join node has two marked
  incoming edges. This would be illegal in general,
  but in some situations it can indicate the
  presence of a legal directed cycle.

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TPMG_SYN Detection of Errors

• Deadlock can be detected at line 8 when a goal
  node is not found but inactive nodes are present
  in FRONTIER.
• Dangling nodes can also be detected at line 5
  when node n is expanded.

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Workflow Verification

• Note that some semantic constraints are imposed
  by the meanings of the items contained in the
  TPMG nodes.
• TPMG_SYN when appropriately modified can perform
  certain types of semantic verification of TPMGs.

57
Workflow Verification

• A similar verification procedure can be devised
  for workflows drawn using Petri Nets or any other
  WfMC convention.

58

• Thank You!