PN1

1
Business Processes Petri NetsIPA basic course
on formal methods

• Prof.dr.ir. Wil van der Aalst
• Eindhoven University of Technology, Faculty of
  Technology Management,
• Department of Information and Technology, P.O.Box
  513, NL-5600 MB,
• Eindhoven, The Netherlands.

2
Outline

• 10.00 - 11.00 Lecture 1 Petri nets
• 11.00 - 11.15 Break
• 11.15 - 12.00 Exercises 1 Hands-on with CPN
  Tools
• 12.00 - 12.15 Discussion of exercises 1 / demo
• 12.15 - 13.15 Lunch
• 13.15 - 14.15 Lecture 2 Workflow modeling and
  analysis
• 14.15 - 14.30 Break
• 14.30 - 15.15 Exercises 2 Hands-on with Protos
  and Woflan
• 15.15 - 15.30 Discussion of excercises 2 / demo
• 15.30 - 15.45 Break
• 15.45 - 16.15 Wrap-up session Process Mining

3
Lecture 1 Petri netsPetri-nets by example
4
Role of process models in information systems
5
Limitations of classical Petri nets

• Inability to test for zero tokens in a place.
• Models tend to become large.
• Models cannot reflect temporal aspects
• No support for structuring large models, cf.
  top-down and bottom-up design
• (As a result most things are decidable ?)

6
Inability to test for zero tokens in a place
?
t
p
Tricks only work if p is bounded
7
High-level Petri nets

• To tackle the problems identified.
• Petri nets extended with
• Color (i.e., data)
• Time
• Hierarchy
• For the time being be do not choose a concrete
  language but focus on the main concepts.
• We focus on a concrete language CPN.
• We show use CPN Tools.

8
DEMO
9
Exercises 1 Hands-on with CPN Tools
Model and simulate the following cases using CPN
Tools ...
10
Coffee and tea example (1)

• We need to produce 100 cups of tea and 100 cups
  of coffee.
• There are two persons able to manufacture these
  drinks Adam and Eve.
• Assume "random allocation".
• Production times

11
Coffee and tea example (2)

• Simulate the model a couple of times and record
  the makespan.
• Evaluate two control strategies
• Eve just makes tea and Adam just makes coffee.
• Adam makes coffee and Eve can make both.
• Eve makes tea and Adam can make both.
• Why is it diffcult to model priorities/preferences
  ?

12
Coffee and tea example (3)

• Assume a continuous flow of tea and coffee
  drinker, i.e., every 5 minutes there is request
  for tea and every 10 minutes there is a request
  of coffee.
• There are two persons able to manufacture these
  drinks (Adam and Eve) and the production times
  are as before.
• Process the requests in FIFO (first-in-first-out)
  order.

13
Coffee and tea example (4)

• Assume a continuous flow of tea and coffee
  drinker, but now evaluate the following
  alternatives
• LIFO (last-in-first-out) order
• SPT (tea before coffee) order
• FIFO with Eve preferably working on tea and Adam
  on coffee.
• Test also your own strategy.

14
Cheat sheet
15
Lecture 2 Workflow Modeling and Analysis
16
Reference model of the Workflow Management
Coalition
What? When? Who?
17
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18
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20
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21
Focus on "classical" workflow management systems,
but ...

• Four types of "workflow-like" systems
• Information systems with hard-coded workflows
  (process organization specific).
• Custom-made information systems with generic
  workflow support (organization specific).
• Generic software with embedded workflow
  functionality (e.g., the workflow components of
  ERP, CRM, PDM, etc. systems).
• Generic software focusing on workflow
  functionality (e.g., Staffware, MQSeries
  Workflow, FLOWer, COSA, Oracle BPEL, Filenet,
  etc.).

22
Workflow perspectives

• Process perspective (tasks and the routing of
  cases)
• Resource perspective (workers, roles, 4-eyes
  principle, etc.)
• Case/data perspective (process instances and
  their attributes)
• Operation/application perspective (forms,
  application integration, etc.)
• ...

23
Process perspective Protos (extended Petri nets)
24
Process perspective Staffware
25
Process perspective COSA (Petri nets)
26
Process perspective Baan DEM
27
Process perspective Event driven process chains
(ARIS/SAP)
28
(Oracle) BPEL
ltsequence name"main"gt ltflow name"Flow_1"gt
ltlinksgt ltlink name"receive-to-assess
"/gt ltlink name"receive-to-approval"/gt
ltlink name"approval-to-reply"/gt
ltlink name"assess-to-setMessage"/gt ltlink
name"setMessage-to-reply"/gt ltlink
name"assess-to-approval"/gt lt/linksgt
ltsequence name"sequenceReceive"gt ltsource
linkName"receive-to-assess" transitionCondition"
bpwsgetVariableData('inputVariable','payload','/c
lientLoanApprovalProcessRequest/clientamount')
lt 10000"/gt ltsource linkName"receive-to
-approval" transitionCondition"bpwsgetVariableDa
ta('inputVariable','payload','/clientLoanApproval
ProcessRequest/clientamount') gt 10000"/gt
ltreceive name"receiveInput"
partnerLink"client" portType"clientLoanApproval
" operation"initiate" variable"inputVariable"
createInstance"yes"/gt lt/sequencegt
ltsequence name"sequenceAssess"gt lttarget
linkName"receive-to-assess"/gt ltsource
linkName"assess-to-setMessage"
transitionCondition"bpwsgetVariableData('risk')
'low'"/gt ltsource linkName"assess-to-app
roval" transitionCondition"bpwsgetVariableData('
risk') ! 'low'"/gt ltassign
name"initiateAssessor"gt ltcopygt
ltfrom variable"inputVariable" part"payload"
query"/clientLoanApprovalProcessRequest/clientf
irstName"/gt ltto variable"invokeAssess
or_initiate_InputVariable" part"payload"
query"/ns1AssessorProcessRequest/ns1firstName"/
gt lt/copygt ltcopygt
ltfrom variable"inputVariable" part"payload"
query"/clientLoanApprovalProcessRequest/clientn
ame"/gt ltto variable"invokeAssessor_in
itiate_InputVariable" part"payload"
query"/ns1AssessorProcessRequest/ns1name"/gt
lt/copygt ltcopygt ltfrom
variable"inputVariable" part"payload"
query"/clientLoanApprovalProcessRequest/clienta
mount"/gt ltto variable"invokeAssessor_
initiate_InputVariable" part"payload"
query"/ns1AssessorProcessRequest/ns1amount"/gt
lt/copygt lt/assigngt
ltinvoke name"invokeAssessor" partnerLink"Assesso
r" portType"ns1Assessor" operation"initiate"
inputVariable"invokeAssessor_initiate_InputVariab
le"/gt ltreceive name"receiveAssessor"
partnerLink"Assessor" portType"ns1AssessorCallb
ack" operation"onResult" variable"receiveAssesso
r_onResult_InputVariable" createInstance"no"/gt
ltassign name"completeAssessor"gt
ltcopygt ltfrom variable"receiveAssessor
_onResult_InputVariable" part"payload"
query"/ns1AssessorProcessResponse/ns1level"/gt
ltto variable"risk"/gt
lt/copygt lt/assigngt lt/sequencegt
ltsequence name"sequenceNoApproval"gt
lttarget linkName"assess-to-setMessage"/gt
ltsource linkName"setMessage-to-reply"/gt
ltassign name"setAccepted"gt ltcopygt
ltfrom expression"'Accepted'"/gt
ltto variable"outputVariable" part"payload"
query"/clientLoanApprovalProcessResponse/client
result"/gt lt/copygt lt/assigngt
lt/sequencegt
29
Design-time (a-priori) and run-time
(a-posteriori) questions
Run-time
Design-time
ProM
Woflan
- verification- validation- performance
analysis
- process mining
30
A-priori analysis Woflan
31
A process in Staffware (a similar process could
have been made using BPMN, etc.)
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33
Corresponding WF-net
Not sound!
34
Syntactic sugaring

• Note silent (tau) steps.
• Branching bisimulation is used as an equivalence
  relation to distinguish internal/external choices.

35
Soundness

• A WF-net is sound if and only if
• marking o is reachable from every reachable
  marking (initial marking is i),
• marking o is the only reachable marking marking
  place o, and
• there are no dead transitions.

36
Reachability analysis
37
Place invariants can be used to check detect
errors
end
begin

• There should be a positive place invariant
  assigning positive weights to all places and
  identical weights to begin and end.
• 1.begin 1.end ..... constant

38
Transition invariants can be used to detect errors
short-circuited net
end
begin

• There should be a positive transition invariant
  assigning positive weights to all transitions.

39
Languages/products we can verify

• Event-driven process chains (SAP, ARIS, ARIS
  PPM)
• BPEL (Websphere and Oracle BPEL)
• Staffware
• COSA
• Protos
• YAWL
• PNML (Yasper, ProM, XRL, ...)
• ...

40
Exercises 2 Hands-on with Protos and Woflan
Model the following cases using Protos, export
models to Woflan and verify (make some mistakes
on purpose). You can also start by rebuilding the
example.
41
Insurance company

• Insurance company X processes claims which result
  from traffic accidents with cars where customers
  of X are involved in. Therefore, it uses the
  following procedure for the processing of the
  insurance claims.
• Every claim, reported by a customer, is
  registered by an employee of department CD (CD
  Car Damages). After the registration of the
  claim, the insurance claim is classified by a
  claim handler of rank A or B within CD. There are
  two categories simple and complex claims.
• For simple claims two tasks need to be executed
  check insurance and phone garage. These tasks are
  independent of each other.

42
Insurance company (2)

• The complex claims require three tasks to be
  executed check insurance, check damage history
  and phone garage. These tasks need to be executed
  sequentially in the order specified.
• Both for the simple and complex claims, the tasks
  are done by employees of department CD. After
  executing the two respectively three tasks a
  decision is made. This decision is made by a
  claim handler of rank A and has two possible
  outcomes OK (positive) or NOK (negative).
• If the decision is positive, then insurance
  company X will pay. An employee of the finance
  department handles the payment. In any event, the
  insurance company sends a letter to the customer
  who sent the claim. An employee of the department
  CD writes this letter.

43
Complaints handling

• Each year travel agency Y has to process a lot of
  complaints (about 10.000). There is a special
  department for the processing of complaints
  (department C). There is also an internal
  department called logistics (department L) which
  takes care of the registration of incoming
  complaints and the archiving of processed
  complaints. The following procedure is used to
  handle these complaints.

44
Complaints handling (2)

• An employee of department L first registers every
  incoming complaint. After registration a form is
  sent to the customer with questions about the
  nature of the complaint. This is done by an
  employee of department C. There are two
  possibilities the customer returns the form
  within two weeks or not. If the form is returned,
  it is processed automatically resulting in a
  report which can be used for the actual
  processing of the complaint. If the form is not
  returned on time, a time-out occurs resulting in
  an empty report. Note that this does not
  necessarily mean that the complaint is discarded.
  After registration, i.e., in parallel with the
  form handling, the preparation for the actual
  processing is started.

45
Complaints handling (3)

• First, the complaint is evaluated by a complaint
  manager of department C. Evaluation shows that
  either further processing is needed or not. Note
  that this decision does not depend on the form
  handling. If no further processing is required
  and the form is handled, the complaint is
  archived. If further processing is required, an
  employee of the complaints department executes
  the task process complaint (this is the actual
  processing where certain actions are proposed if
  needed). For the actual processing of the
  complaint, the report resulting from the form
  handling is used. Note that the report can be
  empty. The result of task process complaint is
  checked by a complaint manager. If the result is
  not OK, task process complaint is executed
  again. This is repeated until the result is
  acceptable. If the result is accepted, an
  employee of the department C executes the
  proposed actions. After this the processed
  complaint is archived by an employee of
  department L.

46
Travel agency

• Consider a fragment of the process of booking
  trips involving six steps register, (booking of)
  flight, (booking of) hotel, (booking of) car,
  pay, and cancel.
• The process starts with task register and ends
  with pay or cancel.
• The tasks flight, hotel and car may succeed or
  fail.
• Let us consider a number of variants

47
Travel agency Variant 1

• Every trip involves a flight, hotel and car and
  these are booked in parallel. If all three
  succeed, the payment follows. Otherwise task
  cancel is executed. Cancel is delayed until all
  three bookings succeed/fail and does not withdraw
  work.

48
Travel agency Variant 2

• Every trip involves a flight, hotel and car and
  these are booked in parallel. If all three
  succeed, the payment follows. Otherwise task
  cancel is executed. Task cancel can be executed
  the moment the first task fails and withdraws
  work-items waiting for remaining booking tasks.

49
Travel agency Variant 3

• Every trip may involve a flight, hotel and/or car
  and these are booked in parallel. A trip should
  involve at least a flight, hotel or car but may
  be any combination of the three bookings, e.g., a
  flight and car but not a hotel. If all bookings
  succeed, the payment follows. Otherwise task
  cancel is executed. Task cancel can be executed
  the moment the first task fails and withdraws
  work-items waiting for remaining booking tasks.

50
Travel agency Variant 4

• Every trip may involve a flight, hotel and/or car
  and these are booked in parallel. A trip should
  involve at least a flight, hotel or car but may
  be any combination of the three bookings, e.g., a
  flight and car but not a hotel. If all bookings
  succeed, the payment follows. Otherwise task
  cancel is executed. Task cancel can be executed
  the moment the first task fails and withdraws
  work items waiting for remaining booking tasks.
  All bookings that have completed successfully
  need to be compensated.

51
Wrap-up Process mining
52
from languages and systems to analysis ...
53
Design-time (a-priori) and run-time
(a-posteriori) questions
Run-time
Design-time
ProM
- verification- validation- performance
analysis
- process mining
54
A-posteriori analysis ProM
55
(No Transcript)
56
Process discovery Reversing the process
process discovery
1
57
Conformance testing
2
58
Log based verification
formula four_eyes_principle (a1activity,a2activi
ty) forallpperson (!(execute(p,a1)) \/
!(execute(p,a2)))
3
59
ProM
Outlook
CPN Tools
ARIS/ARIS PPM
YAWL
Caramba
60
XML format
61
ProM architecture
62
Demo
63
Conclusion

• Petri nets have and strong theoretical basis and
  are close to languages used in practise.
• The workflow/process mining domain offers many
  research challenges!

useful links

• www.processmining.org
• www.workflowpatterns.com
• is.tm.tue.nl/research/woflan/

• www.workflowcourse.com
• BPMcenter.org
• www.yawl-system.com

64
Reference slides
65
Petri netsClassical Petri nets The basic model

• Prof.dr.ir. Wil van der Aalst
• Eindhoven University of Technology, Faculty of
  Technology Management,
• Department of Information and Technology, P.O.Box
  513, NL-5600 MB,
• Eindhoven, The Netherlands.

66
Process modeling

• Emphasis on dynamic behavior rather than
  structuring the state space
• Transition system is too low level
• We start with the classical Petri net
• Then we extend it with
• Color
• Time
• Hierarchy

67
Classical Petri net

• Simple process model
• Just three elements places, transitions and
  arcs.
• Graphical and mathematical description.
• Formal semantics and allows for analysis.
• History
• Carl Adam Petri (1962, PhD thesis)
• In sixties and seventies focus mainly on theory.
• Since eighties also focus on tools and
  applications (cf. CPN work by Kurt Jensen).
• Hidden in many diagramming techniques and
  systems.

68
Elements
69
Rules

• Connections are directed.
• No connections between two places or two
  transitions.
• Places may hold zero or more tokens.
• First, we consider the case of at most one arc
  between two nodes.

70
Enabled

• A transition is enabled if each of its input
  places contains at least one token.

enabled
Not enabled
Not enabled
71
Firing

• An enabled transition can fire (i.e., it occurs).
• When it fires it consumes a token from each input
  place and produces a token for each output place.

fired
72
Play Token Game

• In the new state, make_picture is enabled. It
  will fire, etc.

73
Remarks

• Firing is atomic.
• Multiple transitions may be enabled, but only one
  fires at a time, i.e., we assume interleaving
  semantics (cf. diamond rule).
• The number of tokens may vary if there are
  transitions for which the number of input places
  is not equal to the number of output places.
• The network is static.
• The state is represented by the distribution of
  tokens over places (also referred to as marking).

74
Non-determinism
Two transitions are enabled but only one can fire
75
Example Single traffic light
76
Two traffic lights
OR
77
Problem
78
Solution
How to make them alternate?
79
Playing the Token Game on the Internet

• Applet to build your own Petri nets and execute
  them http//www.tm.tue.nl/it/staff/wvdaalst/Downl
  oads/pn_applet/pn_applet.html
• FLASH animations http//www.tm.tue.nl/it/staff/wv
  daalst/courses/pm/flash/

80
Exercise Train system (1)

• Consider a circular railroad system with 4
  (one-way) tracks (1,2,3,4) and 2 trains (A,B). No
  two trains should be at the same track at the
  same time and we do not care about the identities
  of the two trains.

81
Exercise Train system (2)

• Consider a railroad system with 4 tracks
  (1,2,3,4) and 2 trains (A,B). No two trains
  should be at the same track at the same time and
  we want to distinguish the two trains.

82
Exercise Train system (3)

• Consider a railroad system with 4 tracks
  (1,2,3,4) and 2 trains (A,B). No two trains
  should be at the same track at the same time.
  Moreover the next track should also be free to
  allow for a safe distance. (We do not care about
  train identities.)

83
Exercise Train system (4)

• Consider a railroad system with 4 tracks
  (1,2,3,4) and 2 trains. Tracks are free, busy or
  claimed. Trains need to claim the next track
  before entering.

84
WARNINGIt is not sufficient to understand the
(process) models. You have to be able to design
them yourself !
85
Multiple arcs connecting two nodes

• The number of arcs between an input place and a
  transition determines the number of tokens
  required to be enabled.
• The number of arcs determines the number of
  tokens to be consumed/produced.

86
Example Ball game
87
Exercise Manufacturing a chair

• Model the manufacturing of a chair from its
  components 2 front legs, 2 back legs, 3 cross
  bars, 1 seat frame, and 1 seat cushion as a Petri
  net.
• Select some sensible assembly order.
• Reverse logistics?

88
Exercise Burning alcohol.

• Model C2H5OH 3 O2 gt 2 CO2 3 H2O
• Assume that there are two steps first each
  molecule is disassembled into its atoms and then
  these atoms are assembled into other molecules.

89
Exercise Manufacturing a car

• Model the production process shown in the
  Bill-Of-Materials.

car
subassembly2
engine
2
chair
subassembly1
4
chassis
wheel
90
Formal definition

• A classical Petri net is a four-tuple (P,T,I,O)
  where
• P is a finite set of places,
• T is a finite set of transitions,
• I P x T -gt N is the input function, and
• O T x P -gt N is the output function.
• Any diagram can be mapped onto such a four tuple
  and vice versa.

91
Formal definition (2)

• The state (marking) of a Petri net (P,T,I,O) is
  defined as follows
• s P-gt N, i.e., a function mapping the set of
  places onto 0,1,2, .

92
Exercise Map onto (P,T,I,O) and s
93
Exercise Draw diagram

• Petri net (P,T,I,O)
• P a,b,c,d
• T e,f
• I(a,e)1, I(b,e)2, I(c,e)0, I(d,e)0, I(a,f)0,
  I(b,f)0, I(c,f)1, I(d,f)0.
• O(e,a)0, O(e,b)0, O(e,c)1, O(e,d)0, O(f,a)0,
  O(f,b)2, O(f,c)0, O(f,d)3.
• State s
• s(a)1, s(b)2, s(c)0, s(d) 0.

94
Enabling formalized

• Transition t is enabled in state s1 if and only
  if

95
Firing formalized

• If transition t is enabled in state s1, it can
  fire and the resulting state is s2

96
Mapping Petri nets onto transition systems

• A Petri net (P,T,I,O) defines the following
  transition system (S,TR)

97
Reachability graph

• The reachability graph of a Petri net is the part
  of the transition system reachable from the
  initial state in graph-like notation.
• The reachability graph can be calculated as
  follows
• Let X be the set containing just the initial
  state and let Y be the empty set.
• Take an element x of X and add this to Y.
  Calculate all states reachable for x by firing
  some enabled transition. Each successor state
  that is not in Y is added to X.
• If X is empty stop, otherwise goto 2.

98
Example
(3,2)
(3,1)
(3,0)
(1,3)
(1,2)
(1,1)
(1,0)
Nodes in the reachability graph can be
represented by a vector (3,2) or as 3 red 2
black. The latter is useful for sparse states
(i.e., few places are marked).
99
Exercise Give the reachability graph using both
notations
100
Different types of states

• Initial state Initial distribution of tokens.
• Reachable state Reachable from initial state.
• Final state (also referred to as dead states)
  No transition is enabled.
• Home state (also referred to as home marking) It
  is always possible to return (i.e., it is
  reachable from any reachable state).
• How to recognize these states in the reachability
  graph?

101
Exercise Producers and consumers

• Model a process with one producer and one
  consumer, both are either busy or free and
  alternate between these two states. After every
  production cycle the producer puts a product in a
  buffer. The consumer consumes one product from
  this buffer per cycle.
• Give the reachability graph and indicate the
  final states.
• How to model 4 producers and 3 consumers
  connected through a single buffer?
• How to limit the size of the buffer to 4?

102
Exercise Two switches

• Consider a room with two switches and one light.
  The light is on or off. The switches are in state
  up or down. At any time any of the switches can
  be used to turn the light on or off.
• Model this as a Petri net.
• Give the reachability graph.

103
Modeling

• Place passive element
• Transition active element
• Arc causal relation
• Token elements subject to change
• The state (space) of a process/system is modeled
  by places and tokens and state transitions are
  modeled by transitions (cf. transition systems).

104
Role of a token

• Tokens can play the following roles
• a physical object, for example a product, a part,
  a drug, a person
• an information object, for example a message, a
  signal, a report
• a collection of objects, for example a truck with
  products, a warehouse with parts, or an address
  file
• an indicator of a state, for example the
  indicator of the state in which a process is, or
  the state of an object
• an indicator of a condition the presence of a
  token indicates whether a certain condition is
  fulfilled.

105
Role of a place

• a type of communication medium, like a telephone
  line, a middleman, or a communication network
• a buffer for example, a depot, a queue or a post
  bin
• a geographical location, like a place in a
  warehouse, office or hospital
• a possible state or state condition for example,
  the floor where an elevator is, or the condition
  that a specialist is available.

106
Role of a transition

• an event for example, starting an operation, the
  death of a patient, a change seasons or the
  switching of a traffic light from red to green
• a transformation of an object, like adapting a
  product, updating a database, or updating a
  document
• a transport of an object for example,
  transporting goods, or sending a file.

107
Typical network structures

• Causality
• Parallelism (AND-split - AND-join)
• Choice (XOR-split XOR-join)
• Iteration (XOR-join - XOR-split)
• Capacity constraints
• Feedback loop
• Mutual exclusion
• Alternating

108
Causality
109
Parallelism
110
Parallelism AND-split
111
Parallelism AND-join
112
Choice XOR-split
113
Choice XOR-join
114
Iteration 1 or more times
XOR-join before XOR-split
115
Iteration 0 or more times
XOR-join before XOR-split
116
Capacity constraints feedback loop
AND-join before AND-split
117
Capacity constraints mutual exclusion
AND-join before AND-split
118
Capacity constraints alternating
AND-join before AND-split
119
We have seen most patterns, e.g.
Example of mutual exclusion
How to make them alternate?
120
Exercise Manufacturing a car (2)

• Model the production process shown in the
  Bill-Of-Materials with resources.
• Each assembly step requires a dedicated machine
  and an operator.
• There are two operators and one machine of each
  type.
• Hint model both the start and completion of an
  assembly step.

car
subassembly2
engine
2
chair
subassembly1
4
chassis
wheel
121
Modeling problem (1) Zero testing

• Transition t should fire if place p is empty.

?
t
p
122
Solution

• Only works if place is N-bounded

t
Initially there are N tokens
N input and output arcs
p
p
123
Modeling problem (2) Priority

• Transition t1 has priority over t2

t1
?
t2
Hint similar to Zero testing!
124
A bit of theory

• Extensions have been proposed to tackle these
  problems, e.g., inhibitor arcs.
• These extensions extend the modeling power
  (Turing completeness).
• Without such an extension not Turing complete.
• Still certain questions are difficult/expensive
  to answer or even undecidable (e.g., equivalence
  of two nets).
• Turing completeness corresponds to the ability
  to execute any computation.

125
Exercise Witness statements

• As part of the process of handling insurance
  claims there is the handling of witness
  statements.
• There may be 0-10 witnesses per claim. After an
  initialization step (one per claim), each of the
  witnesses is registered, contacted, and informed
  (i.e., 0-10 per claim in parallel). Only after
  all witness statements have been processed a
  report is made (one per claim).
• Model this in terms of a Petri net.

126
Exercise Dining philosophers

• 5 philosophers sharing 5 chopsticks chopsticks
  are located in-between philosophers
• A philosopher is either in state eating or
  thinking and needs two chopsticks to eat.
• Model as a Petri net.

127
Preview Analysis (Chapter 8)

• Various types of analysis techniques
• Simulation (repeatedly playing the token game)
• Reachability analysis (constructing the
  reachability graph)
• Markovian analysis (reachability graph with
  transition probabilities)
• Invariants place invariants and transition
  invariants (conservation of tokens and sequences
  without effect)
• Role of models (1) insight, (2) analysis, and
  (3) specification.

128
Place invariant Example
waitbeforeaftergone freeoccupied
129
Transition invariant Example
entermake_pictureleaveaccident
130
CPNA concrete language for high-level Petri nets

• Prof.dr.ir. Wil van der Aalst
• Eindhoven University of Technology, Faculty of
  Technology Management,
• Department of Information and Technology, P.O.Box
  513, NL-5600 MB,
• Eindhoven, The Netherlands.

131
CPN (Colored Petri nets)

• CPN is the language developed by Kurt Jensen.
• CPN supports the extensions with time, color and
  hierarchy.
• CPN is based on standard ML.
• CPN is supported by Design/CPN and CPN Tools.
• First, we only consider the extensions with color
  and time.
• For more information http//www.daimi.au.dk/CPnet
  s/

132
Values and types

• Syntax is needed to type places and give values
  (colors) to tokens.
• Adopted from Standard ML
• Outline
• Basic types int, string, bool, (real), and unit.
• Type constructors with, product, record, list.
• Defining constants.

133
Basic types

• Integers (int), e.g., 5, 34234, 32423.
• Reals (real), e.g., 34.34, 23.0, 7e3, 4e2.
• Strings (string), e.g., "Hallo", "28-02-2003".
• Booleans (bool) true and false.
• unit type with just one value ()
• 32423 means -32423
• 23.0 means 23, 7e3 means 7000.0, and 4e2
  means 0.04
• unit is used to represent black (i.e., uncolored)
  tokens
• Reals are no longer supported.

134
Basic operators

• for the unary minus
• and for reals and integers
• (multiplication) for reals and integers
• / (division) for reals
• div and mod for integers (28 div 10 2, 28 mod
  10 8)
• , gt, lt, gt, lt, ltgt for comparing things (note
  the notation for gt (greater than), lt (smaller
  than), and ltgt (not equal)).
• for strings (concatenation "AA""BB" "AABB")

135
Logical operators

• not (for negation)
• andalso (for logical AND)
• orelse (for logical OR)
• if then else (choice based on Boolean argument,
  the then and else part should be of the same
  type)
• not(11) results in false
• (11) andalso not(0gt1 orelse 2gt3) results in true
• if "X""X" then 3 else 4 results in 3

136
Exercise Give type and value of each result

• if (4gt4) then ("Hello" " " "World") else "X"
• if true then 20 div 8 else 20 mod 8
• not (11 orelse 12)
• not (11 andalso 12)
• if ("Hello" " " "World" "X") then 20 else 3

137
Color set declarations

• A color set is a type that is defined using a
  color set declaration color ... ... , e.g.,
• color I int
• color S string
• color B bool
• color U unit
• Once declared, it may be used to type places.
• Newly defined types like I,S,B,U may be used in
  other color set declarations.

138
Creating subtypes using the "with" clause

• color Age int with 0..130
• color Temp int with 30..40
• color Alphabet string with "a".."z"
• color YN bool with (no,yes)
• color BlackToken unit with null

139
Creating new types using the "with" clause

• color Human with man woman child
• color ThreeColors with Green Red Yellow

140
Creating new types using product, record, and
list constructors

• color Coordinates product I I I
• color HumanAge product Human Age
• color CoordinatesR record xI yI zI
• color CD record artistsS titleS
  noftracksI
• color Names list S
• color ListOfColors list ThreeColors

141
Possible values (colors)

• Coordinates (1,2,3), (4,66,0), ...
• HumanAge (man,50), (child,3), ...
• CoordinatesR x1, y2, z3, x4, y66, z0,
  y2, x1, z3, ...
• CD artists"Havenzangers", title"La La",
  noftracks10, ...
• Names "John", "Liza", "Paul", , ...
• ListOfColors Green, Red, Yellow, ...
• Note the difference between products and records.

142
Example

• color Driver string
• color Lap int with 1..80
• color TimeMS real with 0..10000000
• color LapTime product Lap TimeMS
• color LapTimes list LapTime
• color DriverResults record dDriver
  rLaptimes
• color Race List DriverResults

143
Example (2)

• A possible color of type Race is
• d"Jos Verstappen", r(1,31000),(2,33400),(3,32
  800),
• d"Michael Schumacher", r(1,32200),(2,31600),(3
  ,30200),(4,29600),
• d"Rubens Barrichello", r(1,34500),(2,32600),(3
  ,37200),(4,42600)

144
Operations on lists and records

• denotes the empty list
• concatenates two lists, e.g., 1,2,34,5
  evaluates to 1,2,3,4,5
• adds an element in front of a list, e.g.,
  "a""b","c" evaluates to "a","b","c"
• extracts a field of a record xx1,y2
  evaluates to 1

145
Constants

• It is possible to define constants, e.g.,
• val jv "Jos Verstappen" Driver
• val lap1 1 Lap
• val start 0 Time
• val seven 7 int

146
Example

• Determine the value of constant Monaco
• val jv "Jos Verstappen" Driver
• val r1jos (1,31000) LapTime
• val r2jos (2,33400) LapTime
• val r3jos (3,32800) LapTime
• val r123jos ((1,31000)(2,33400))(3,32800)
  LapTimes
• val jos djv,r123jos DriverResults
• val michael d"Michael Schumacher",
  r(1,32200),(2,31600),
• (3,30200),(4,29600)DriverResults
• val rubens d"Rubens Barrichello",
  r(1,34500),(2,32600),(3,37200),
  (4,42600)DriverResults
• val Monaco jos (michaelrubens) Race

147
Exercise

• Determine the value of the following constants
• val e1 r1jos
• val e2 d(michael)
• val e3 r(jos)r(Rubens)

148
So what?
149
We can now type and initialize places!
declarations
name of place
type of place
initial marking
150
Multi-sets

• To initialize places with multiple tokens but
  also for various other purposes we need
  multi-sets also referred to as bags.
• In CPN multi-sets are denoted using the following
  notation x1v1 x2v2 ... xnvnwhere v1
  is a value and x1 the number of times this
  element appears in the multi-set, etc.
• E.g., 4"Red" 2"Green" 1"Blue" is a
  multi-set containing 7 elements

151
Initialization expressions
one token
no tokens
six tokens
152
Arc inscriptions

• Arc inscriptions are used to define input-output
  behavior.
• Arc inscriptions may use variables.
• Variables are typed and need to be declared

153
Example

• Give final marking.

154
Binding

• Given a transition t with variables x1, x2, ...,
  xn on its input and output arcs, a binding of t
  allocates a concrete value to each of these
  variables. These values should be of the
  corresponding type.
• A binding is enabled if there are tokens matching
  the values of the arc inscriptions.
• If a binding is enabled, it can occur, i.e., the
  transition fires while consuming and producing
  the corresponding tokens.
• The pair (t1,ltx1v1,x2v2, ...xnvngt) is called a
  binding element.

155
Example

• Two binding elements (t1,ltx2gt) and (t1,ltx3gt)

156
Example

• Binding element (t1,ltx0gt). After it occurred
  (t1,ltx1gt), etc.

157
Example
No binding possible!
(t2,ltx1,y2gt)
(t2,ltx1,y3gt)
158
Exercise

• Give all possible binding elements and final
  markings

159
Exercise

• Give all possible binding elements and final
  markings

160
Exercise

• Give all possible binding elements and final
  markings

161
Exercise

• Give all possible binding elements and a final
  marking

162
Exercise

• Give all possible binding elements and a final
  marking

163
Exercise

• Give all possible binding elements and a final
  marking

164
Example Voting
165
Exercise Bank

• Consider a simple banking system. There are 1000
  accounts numbered from 1 to 1000. People can
  deposit or withdraw money. Only amounts between 1
  EURO and 5000 EURO can be deposited or withdrawn.
  The account may have a negative balance.
• Model this in terms of a CPN model.

166
Exercise Article database

• Consider a database system where authors can
  submit articles. The articles are stored in such
  a way that it is possible to get a sequential
  list of articles per author. The list is ordered
  in such a way that the oldest articles appear
  first.
• Note that the system should support two actions
  submit articles (with name of author and article)
  and get articles of a given author.
• We assume that each article has a single author
  and that only authors already registered in the
  database can submit articles.
• Model this in terms of a CPN model.

167
Exercise (2)

• Extend the CPN model such that each article can
  have multiple authors, i.e., the article is
  stored once for each author, and that there is an
  explicit action to add authors to the database.

168
Guard

• A guard is a Boolean expression attached to a
  transition. Only binding elements which evaluate
  to true are enabled.
• Denoted by square brackets.

guard evaluates to false for binding
(t1,ltx1,y2gt)
169
Example

• Give all enabled binding elements and the final
  marking

170
Exercise

• Give all enabled binding elements and the final
  marking

171
Exercise

• Give all enabled binding elements and all
  possible final marking

172
Exercise

• The CPN model assumes that an account could have
  a negative balance. Change the model such that
  the balance cannot become negative, i.e., do not
  accept transactions which lead to a negative
  balance.

173
Function declarations

• color INT int
• fun fac(xINT) if xgt1 then xfac(x-1) else 1
• fun fib(xINT) if xlt2 then 1 else fib(x-1)
  fib(x-2)
• color L list INT
• fun odd(xL) if x then else
  hd(x)even(tl(x))
• fun even(xL) if x then else odd(tl(x))
• Calculate fac(fib(3)) and modify odd and even
  such that the odd lines are returned in reversed
  order.

174
Example
175
Questions

• Is it possible to have multiple arcs connecting a
  place and a transitions?
• Is it possible to have multi-sets as arc
  inscriptions on input arcs?
• Is it possible to use constants or other
  expressions without variables as arc
  inscriptions?
• Is it possible to use records, lists, etc. with
  variables (e.g., ax,by and xy) in arc
  inscriptions?

4x
176
Example Multiple arcs
177
Example Multi-sets and constants
178
Example Records
179
Example Lists
180
Requirement
It should be possible to bind variables to
concrete token values!!
181
Time in CPN

• Tokens are either untimed (are always available)
  or timed (bear a timestamp).
• Color sets can be made timed color sets by adding
  the keyword timed.
• A delay is modeled by v_at_d as arc expression on
  an outgoing arc where v is the value and d is the
  delay of the produced token.
• Delays may depend on the values of tokens to be
  consumed (i.e., through the binding of variables).

182
Example
183
Exercise

• Determine a possible final state.

184
Exercise

• Modify the left-hand side such that for positive
  values of y the delay is 10 while for other
  values the delay is 20.
• Modify the right-hand side such that the delay
  for "Hi'' is 10 while for other values the delay
  is y.

185
Overview of CPN (with color and time)
186
Coffee and tea example (1)

• We need to produce 100 cups of tea and 100 cups
  of coffee.
• There are two persons able to manufacture these
  drinks Adam and Eve.
• Assume "random allocation".
• Production times

187
Coffee and tea example (2)

• Simulate the model a couple of times and record
  the makespan.
• Evaluate two control strategies
• Eve just makes tea and Adam just makes coffee.
• Adam makes coffee and Eve can make both.
• Eve makes tea and Adam can make both.
• Why is it diffcult to model priorities/preferences
  ?

188
Coffee and tea example (3)

• Assume a continuous flow of tea and coffee
  drinker, i.e., every 5 minutes there is request
  for tea and every 10 minutes there is a request
  of coffee.
• There are two persons able to manufacture these
  drinks (Adam and Eve) and the production times
  are as before.
• Process the requests in FIFO (first-in-first-out)
  order.

189
Coffee and tea example (4)

• Assume a continuous flow of tea and coffee
  drinker, but now evaluate the following
  alternatives
• LIFO (last-in-first-out) order
• SPT (tea before coffee) order
• FIFO with Eve preferably working on tea and Adam
  on coffee.
• Test also your own strategy.

190
Example revisited Punch card desk
191
Improved color sets

• color Name string
• color Street string
• color Number int
• color Town string
• color Address record sStreet nNumber
  tTown
• color Day int with 1..31
• color Month with Jan Feb Mar Apr May
  Jun
• Jul Aug Sep Oct Nov
  Dec
• color Year int with 0..2100
• color Date record dDay mMonth yYear
• color Gender with male female
• color Pat record nameName addressAddress
• birthdateDate genderGender
  timed

192
Improved color sets (2)

• color EmpNo int with 100000..999999
• color Emp record empnoEmpNo experienceYear
  timed
• color EP product Pat Emp timed
• var pPat
• var eEmp
• val Klaas name"Klaas",
• addresss"Plein",n10,t"Unknown",
  
• birthdated13,mDec,y1962,
• gendermalePat
• val Ann empno641112, experience7Emp
• fun d(xEmp) if experience(x) gt 5 then 3 else
  4

193
Example revisited Stock keeping system
194
Store

• Place stock is a so-called store, i.e., it will
  always contain a single token.
• Only the value of the token matters (not its
  presence).
• Stores that aggregate elements are always of type
  list.
• Drawback complex functions/inscriptions
• Advantage easy to query the individual items as
  a whole, e.g., taking the sum of things ...

195
Function "totalstock"

• fun totalstock(sStock)
• if s
• then 0
• else (number(hd(s)))totalstock(tl(s))

196
Alternative model
Note the simplicity/elegance of the arc
inscriptions.
197
Example Signing documents

• Documents need to be signed by persons.
• Four persons Tim, Sue, Clare and John.
• Each document requires three signatures.
• No two signatures of the same person.
• Work in progress is limited to five documents.

198
Signing documents Declarations
199
Signing documents Network structure
200
WARNINGIt is not sufficient to understand the
(process) models. You have to be able to design
them yourself !
201
Exercise

• Replace place free by a place always holding one
  token.

202
Example Thermostat system

• At any point the room has a temperature
  (initially 15 degrees centigrade).
• There is a heater to warm up the house and there
  is a door which opens every hour such that part
  of the warmth escapes.
• When the door opens the temperature in the room
  suddenly drops by three degrees centigrade.
• The heater has a capacity of heating the room 1
  degree centigrade every 15 minutes.
• When the heater would be switched on the whole
  time the temperature would continue to rise by 1
  degree per hour. Therefore, there is a control
  system, i.e., the thermostat, which switches off
  the heater. The thermostat uses the following
  rules.
• If the temperature drops below 18, the heater is
  switched on.
• If the temperature rises above 22, the heater is
  switched off.

203
CPN model of thermostat system
204
Exercise

• Describe the room temperature in time starting in
  the initial state shown, i.e., play a timed,
  colored token game''.
• Extend the model such that there is a day program
  and a night program. From midnight to 8am, the
  thermostat tries to keep the temperature between
  14 and 18 degrees centigrade. (If the temperature
  drops below 14 the heater is switched on. If the
  temperature rises above 18 the heater is switched
  off.) From 8am to midnight, the temperature is
  kept between 18 and 22 degrees, like before.

205
Exercise Train system

• 7 sectors (tracks)
• 2 trains A and B
• When moving to a new sector both this sector and
  the next one should be empty.
• Trains drive in one direction.

• Model as a classical Petri net.
• Model in terms of CPN without folding the tracks.
• Model as a CPN with folding the tracks (i.e.,
  only two places).

206
Exercise Philosophers

• 5 philosophers
• 5 chopsticks
• Each philosopher is either thinking or eating.
• For eating two chopsticks are needed.
• Chopsticks need to be shared among neighbors.
• Both chopsticks are taken and released at the
  same time.

• Model as a classical Petri net.
• Model in terms of CPN using only three places and
  two transitions.

207
Exercise Philosophers (2)

• 5 philosophers
• 5 chopsticks
• Each philosopher is either thinking or eating.
• For eating two chopsticks are needed.
• Chopsticks need to be shared among neighbors.
• First the right chopstick is taken. Then the
  second one is taken.
• The two chopstick are released in reversed order.

• Model in terms of CPN.
• Are deadlocks possible?

208
Exercise Philosophers (3)

• 5 philosophers
• 5 chopsticks
• Each philosopher is either thinking or eating.
• For eating two chopsticks are needed.
• Chopsticks need to be shared among neighbors.
• First the one chopstick (either left or right) is
  taken. Then the other one is taken.
• Also released in arbitrary order.

• Model in terms of CPN.
• Are deadlocks possible?

209
More on functions Recursion

• fun fac(xINT) if xgt1 then xfac(x-1) else 1
  is a recursive function since the function is
  expressed in terms of itself.
• Two cases
• fac(x) xfac(x-1)
• fac(1) 1
• fac(10)10fac(9)109fac(8)1098fac(7)
  10987654321 3628800

210
Recursion (1)
color Product string color Number int color
StockItem record prodProduct
numberNumber color Stock list StockItem fun
totalstock(sStock) if s then 0 else
(number(hd(s)))totalstock(tl(s))
Recursion in length of list
211
Recursion (2)
Instead of sum the maximum is taken
fun maxstock(sStock) if s then 0 else
if (number(hd(s))) gt maxstock(tl(s)) then
number(hd(s))
else maxstock(tl(s))
212
Recursion (3)
Function calls other function
fun maxstockname(sStock) if s then "no
product found" else if (number(hd(s)))maxstock
(tl(s)) then prod(hd(s))
else maxstockname(tl(s))
213
Recursion (4)
Function has two arguments
fun enoughstock(sStock,nNumber) if s
then else if (number(hd(s)))gt n then
hd(s)enoughstock(tl(s),n)
else enoughstock(tl(s),n)
214
Recursion (5)
Length of list rather than list itself
fun enoughstockn(sStock,nNumber) if s
then 0 else if (number(hd(s)))gt n then
1enoughstockn(tl(s),n)
else enoughstockn(tl(s),n)
215
More on functions Pattern matching
fun lenlist1(sStock) if s then 0 else
1lenlist(tl(s))
base case
induction step
fun lenlist2() 0 lenlist2(sis)
1lenlist2(s)
No explicit typing!!!
216
Pattern matching (1)
fun totalstock(sStock) if s then 0 else
(number(hd(s)))totalstock(tl(s))
fun totalstock(Stock) 0
totalstock(sis) (number(si))totalstock(s)
217
Pattern matching (2)
fun maxstock(sStock) if s then 0 else
if (number(hd(s))) gt maxstock(tl(s)) then
number(hd(s))
else maxstock(tl(s))
fun maxstock(Stock) maxstock(sis)
if (number(si))gtmaxstock(s) then number(si)
else
maxstock(s)
218
Pattern matching (3)
fun incrs(xStockItem,Stock) x incrs
(x,(sis)) if (prod(si))(prod(x))
then prod(prod(si)),number((number(si))(num
ber(x)))incrs(x,s) else (siincrs(x,s))
219
Pattern matching (4)
fun reverse() reverse(xy)
reverse(y)x fun odd() odd(xy)
xeven(y) fun even() even(xy)
odd(y)
220
More information

• About Standard ML
• Robin Milner, Mads Tofte, Robert Harper, and
  David MacQueen.The Definition of Standard ML
  Revised 1997. The MIT Press, 1997.
• J. D. Ullman. Elements of ML Programming (ML 97
  edition). Prentice-Hall, 1998.
• About CPN
• K. Jensen Coloured Petri Nets. Basic Concepts,
  Analysis Methods and Practical Use. Volume 1,
  Basic Concepts. Monographs in Theoretical
  Computer Science, Springer-Verlag, 1997.
• K. Jensen Coloured Petri Nets. Basic Concepts,
  Analysis Methods and Practical Use. Volume 2,
  Analysis Methods. Monographs in Theoretical
  Computer Science, Springer-Verlag, 1997.
• K. Jensen Coloured Petri Nets. Basic Concepts,
  Analysis Methods and Practical Use. Volume 3,
  Practical Use. Monographs in Theoretical Computer
  Science, Springer-Verlag, 1997.
• K. Jensen and G. Rozenberg (eds.) High-level
  Petri Nets. Theory and Application.
  Springer-Verlag, 1991.