Uncertain Marking for Dealing with Partial Parallelization in Business
Leiliane Pereira de Rezende
, St
ephane Julia
and Janette Cardoso
Computing Faculty, Federal University of Uberl
andia - UFU, Uberl
andia, MG, Brazil
DMIA Department, Institut Sup
erieur de l’A
eronautique et de l’Espace - ISAE, Toulouse, France
WorkFlow Net, Possibilistic Petri Net, Deviations, Process Monitoring.
In this paper, an approach based on WorkFlow nets and possibilistic Petri nets is proposed for dealing with flow
deviations in business processes. Routing patterns existing in business processes are modeled by WorkFlow
nets. Possibilistic Petri nets with uncertainty in the marking and the transition firing are considered to express
in a more realistic way the ordering of human activities during real time execution of the process model.
Combining both formalisms, a kind of possibilistic WorkFlow net is obtained. An example of flow deviations
due to human behavior at a process monitoring level is presented.
An organization produces value for its customers by
executing various business processes (BP) which rep-
resent the sequences of activities that have to be ex-
ecuted within an organization to treat specific cases
and to reach well defined goals (van der Aalst and
Hee, 2004). Due to complexity and variety of BP,
contemporary organizations use information technol-
ogy to support activities which may include the au-
tomation of their processes.
A workflow process corresponds to the automa-
tion of a BP, in whole or part, during which docu-
ments, information or tasks are passed from one par-
ticipant to another for a particular form of action, ac-
cording to a set of procedural rules. A Workflow Man-
agement System (WFMS) is a system that completely
defines, manages and executes workflow processes
through the execution of software whose sequence of
activities is driven by a computer representation of the
workflow process logic (Members, 1994).
Many papers have already considered Petri net
theory as an efficient tool for the modeling and anal-
ysis of WFMS (van der Aalst, 1998) (van der Aalst
and Hee, 2004) (Soares Passos and Julia, 2009). The
WorkFlow nets (WF-nets) (acyclic Petri net models
used to represent BP) are defined in (van der Aalst
and Hee, 2004).
The first author received CAPES Scholarship - Proc.
. 99999.001925/2015-06
Soundness property is an important criterion
which needs to be satisfied when treating workflow
processes. In fact, good properties of well-defined
formal models such as WF-nets can easily be proved
when BP are following a rigid structure that does not
allow for deviations from the process description dur-
ing real time execution. Although the explicit or-
dering of activities makes the coordination of activ-
ities relatively easy to understand, even for a non-
technical stakeholder, it was shown that BP do not
easily map to a rigid modeling structure (Kapuruge
et al., 2010). Consequently, they are implemented
such that they “fit the system”, which can cause var-
ious problems (Pesic, 2008). First, considering that
some activities executed in a BP depend on human
resources which do not necessarily respect the rigor-
ous definition of workflow processes, manual inter-
ventions become increasingly frequent as human em-
ployees attempt to manipulate workflow inputs and
outputs to conform with changes in workplace prac-
tices. Second, these manual interventions reduce pro-
ductivity and increase processing time. Since it is un-
dertaken in an ad-hoc manner, manual handling in-
curs an added penalty: the corrective actions under-
taken are not added to organizational memory and, as
a consequence, natural process evolution is not incor-
porated into future iterations of the process (Adams,
Attempts at incorporating a certain level of flex-
ibility in process definition have already been pro-
posed by several authors.
Rezende, L., Julia, S. and Cardoso, J.
Uncertain Marking for Dealing with Partial Parallelization in Business Processes.
In Proceedings of the 18th International Conference on Enterprise Information Systems (ICEIS 2016) - Volume 2, pages 118-125
ISBN: 978-989-758-187-8
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Adams et al., in (Adams et al., 2005) and (Adams
et al., 2006), defined the worklet approach as an
extensible repertoire of self-contained sub-processes
aligned to each task, from which a dynamic runtime
selection is made depending on the context of the par-
ticular work instance. In addition, in (Adams, 2007)
and (Adams et al., 2007), an extensible repertoire
of self-contained exception-handling processes called
“exlets” was incorporated in the worklet approach.
However some good properties can be lost due to the
dynamic changes.
In (Pesic and van der Aalst, 2006) and (Pesic et al.,
2007), a declarative constraint-based approach that
allows a process instance to deviate from the origi-
nal behavior at runtime by adding/removing or soft-
ening/hardening the constraints and their mapping to
process definitions is proposed. In (van der Aalst
et al., 2009), an approach based on constraints that
implicitly specifies the execution procedure, i.e., any-
thing is possible as long as it is not explicitly forbid-
den is proposed. The problem with these approaches
is that the sequencing of single activities specified for
a certain process type is only limited to the satisfac-
tion of predetermined constraints.
In (Mohammed et al., 2007), two process models
coexist during the monitoring of the BP. The first one
corresponds to the expected behavior of the process
and the second one, based on the visible actions of
human actors, is built dynamically. The two process
models are then permanently compared and analyzed
in order to detect possible deviations. The problem
in dealing with two models is that the monitoring ac-
tivity can easily be overloaded implying a decrease in
the system’s performance.
In (Zazworka et al., 2009), the deviations and non-
conformities between a planned and executed process
are detected during the development of the software.
In (Thompson and Torabi, 2009), a kind of declar-
ative implicit model, essentially based on rules, is
used to detect inconsistencies (non-conformant states
in the process) and to accept possible deviations (non-
conformant transitions between activities). The limi-
tation of the methodology is that the specified rules
only detect the non-conformance of the process but
do not help in an explicit manner for the real time
process monitoring.
Some authors, such as (Rozinat and van der Aalst,
2008)(Munoz-Gama, 2010)(van der Aalst et al.,
2012), evaluated the level of conformance between
the process model and the execution log of the pro-
cess. For this, they developed metrics for measuring
the relationship between predefined process models
and actual results presented in the form of event logs.
The problem with this approach is that the verification
is carried out after the process execution.
A very promising alternative for dealing with flex-
ibility in BP seems to be those approaches based on
uncertain knowledge as that presented in (Cmpan and
Oquendo, 2000). The model of the process is then
given through fuzzy sets and possibilistic distribu-
tions.The advantage of fuzzy and possibility reason-
ing is the ability to naturally represent uncertain and
imprecise information that exists when activities are
executed by human employees.
One of the first studies which combines fuzzy and
possibilistic representation of information with the
precise structure of a Petri net when considering dis-
crete event systems is that described in (Cardoso et al.,
1999). The main feature of possibilistic/fuzzy Petri
nets is to allow one to reason about the aspects of un-
certainty and change in dynamic discrete event sys-
tems. Most of the examples presented by the authors
of possibilistic Petri net were applied to flexible man-
ufacturing systems.
In this paper, an approach based on WF-nets and
possibilistic Petri nets is proposed to deal with flexi-
bility in BP. In particular, a kind of possibilistic Work-
Flow net will be defined to treat deviations incurred
by manual interventions of the human employees dur-
ing real time execution of the process model.
The remainder of this paper is as follow: in section
2, the definition of WF-nets and soundness correct-
ness criterion are provided. In section 3, an overview
of possibilistic Petri nets is given. In section 4, the
possibilistic WorkFlow net is presented and a sample
business process model illustrates the approach. Fi-
nally, section 5 concludes this work with a short sum-
mary, an assessment based on the approach presented
and an outlook on future work proposals.
A Petri net that models a workflow process is called
a WorkFlow net (WF-net) (van der Aalst and Hee,
2004). A WF-net needs to possess the following prop-
erties (van der Aalst, 1998):
It has only one source place, named Start and only
one sink place, named End. These are special
places, such that the place Start has only outgoing
arcs and the place End has only incoming arcs.
A token in Start represents a case that needs to be
handled and a token in End represents a case that
has been handled.
Every task t (transition) and condition p (place)
should be on a path from place Start to place End.
Uncertain Marking for Dealing with Partial Parallelization in Business Processes
As previously mentioned, a task can be associated
to a transition in a WF-net. However, in order to ex-
plicitly indicate the beginning and the end of each task
in execution, two sequential transitions plus a place
to model a task is used. The first transition represents
the beginning of the task, the place the task, and the
second transition represents the end of the task (Wang
et al., 2009).
Figure 1: WorkFlow net model of a task.
As shown in figure 1, transition B represents the
beginning of a task execution; E represents the end
of the task execution. Place A
represents the task in
execution. From a reachability analysis perspective,
figure 1 can be reduced to a single transition, which
represents the entire task execution as a single logic
Soundness is a correctness criterion defined for
WF-nets and is related to its dynamics. A WF-net is
sound if, and only if, the following three requirements
are satisfied (van der Aalst and Hee, 2004):
For each token put in the place Start, one and only
one token appears in the place End.
When the token appears in the place End, all the
other places are empty for this case.
For each transition (task), it is possible to move
from the initial state to a state in which that tran-
sition is enabled, i.e. there are no dead transitions.
A method for the qualitative analysis of WF-nets
(soundness verification) based on the proof trees of
linear logic is presented in (Soares Passos and Julia,
2009) and another based on a reachability graph is
presented in (van der Aalst et al., 2011).
Possibilistic Petri nets are derived from Object Petri
nets (Sibertin-Blanc, 2001). As characterized in the
approach presented in (Cardoso, 1999), a possibilis-
tic Petri net is a model where a marked place corre-
sponds to a possible partial state, a transition to a pos-
sible state change, and a firing sequence to a possible
behavior. The main advantage in working with pos-
sibilistic Petri nets is that they allow for the updating
of a system state at a supervisory level with ill-known
information without necessarily reaching inconsistent
A possibilistic Petri net model associates a possi-
bility distribution Π
(p) to the location of an object o,
p being a place of the net. Π
(p) = 1 represents the
fact that p is a possible location of o, and Π
(p) = 0
expresses the certainty that o is not present in place p.
Conventionally, a marking in a possibilistic Petri net
is then a mapping:
M : O × P {0, 1}
where O is a set of objects and P a set of places. If
M(o, p) = 1, there exists a possibility of there being
the object o in place p. On the contrary, if M(o, p) =
0, there exists no possibility of there being o in p. A
marking M of the net allows one to represent:
A certain marking: each token is located in only
one place (well-known state). Then M(o, p) = 1
and p
6= p, M(o, p
) = 0.
An uncertain marking: each token location has a
possibility distribution over a set of places. It can-
not be asserted that a token is in a given place,
but only that it is in a place among a given set
of places. For example, if there exists a possi-
bility at a certain time of having the same ob-
ject o in two different places, p
and p
, then
M(o, p
) = M(o, p
) = 1.
A possibilistic marking will correspond in practice
to knowledge concerning a situation at a given time.
In a possibilistic Petri net, the firing (certain or
uncertain) of a transition t is decomposed into two
Beginning of a firing: objects are put into out-
put places of t but are not removed from its input
End of a firing: that can be a firing cancellation
(tokens are removed from the output places of t)
or a firing achievement (tokens are removed from
the input places of t).
A certain firing consists of a beginning of a firing
and an immediate firing achievement. An uncertain
firing (or a pseudo-firing) that will increase the un-
certainty of the marking can be considered only as
the beginning of a firing (there is no information to
confirm whether the normal event associated with the
transition has actually occurred or not). To a certain
extent, pseudo-firing is a way of realizing forward de-
The interpretation of a possibilistic Petri net is de-
fined by attaching to each transition T an authoriza-
tion function η
defined as follows:
: T {False,Uncertain, True}
where x
, ..., x
are the variables associated with the
incoming arcs of transition T (when considering the
underlying Object Petri net).
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
If o
, ..., o
is a possible substitution for x
, ..., x
for firing t, then several situations can be considered:
t is not enabled by the marking but the associated
interpretation is true; an inconsistent situation oc-
curs and a special treatment process of the net is
t is enabled by a certain marking and the inter-
pretation is true; then a classical firing (with cer-
tainty) of an object Petri net occurs;
t is enabled by a certain marking and the interpre-
tation is uncertain; then the transition is pseudo-
fired and the imprecision is increased;
t is enabled by an uncertain marking; if the inter-
pretation is uncertain, t is pseudo-fired;
t is enabled by an uncertain marking and the inter-
pretation is true: a recovery algorithm, presented
in (Cardoso et al., 1989), is called and a new com-
putation of the possibility distribution of the ob-
jects involved in the uncertain marking is realized
in order to go back to a certain marking.
Concepts concerning possibilistic Petri nets will
be illustrated through a practical example in section
If a Petri net is used as a model for Business Pro-
cesses in a WFMS, transitions will represent the state
changes of the process. In particular, each event oc-
curring during the execution of the process (begin-
ning and ending of activities) will be associated with
a transition as a boolean variable. Such a variable will
be essentially seen as an external value corresponding
to a message received from an activity (or send to an
activity). Possibly, internal values depending on cer-
tain token attributes will enable some transitions too.
Petri net models can be directly executed using a
specialized inference mechanism called token player
algorithm” that allows for a simplified monitoring of
the represented process model. A classical token
player algorithm”, as the one defined in (Cardoso and
Valette, 1997), is only based on events under those
conditions normally expected. If an unexpected event
occurs, the process stops or needs to be repaired man-
As pointed out in the introduction, the explicit
ordering of activities makes the coordination of ac-
tivities relatively easy to understand even for a non-
technical stakeholder, however, due to rigid structure
of workflow processes, several manual interventions
have become increasingly frequent as human employ-
ees attempt to manipulate workflow inputs and out-
puts to conform with changes in workplace practices.
From this, some deviations may occur between the
model of the process and the real process execution.
A classic deviation may be the initialization of an ac-
tivity before the end of a previous one due to a dead-
line for example.
If inevitable system changes are handled haphaz-
ardly without being added to organizational memory
in order that they be considered part of the evolution-
ary process, they can lead to major work disruptions
increasing dissatisfaction to a point at which the entire
system implementation is considered as a failure. In
order to handle the changes during real process execu-
tion and register them in the organizational memory,
a model of the process based on the routing structure
of WF-nets and on uncertain marking along with the
firing of possibilistic Petri nets is proposed for dealing
with the deviations incurred by manual interventions
by human employees during its real time execution.
A simple ordering process, presented in (Weske,
2007), will be used to illustrate the approach. This
process features a sequence of activities. Firstly, the
order is stored. After, the inventory is checked, the
invoice is sent, the funds are received and the ship-
ment is prepared. Finally, the goods are shipped and
the process terminates with the archiving of the or-
der. The possibilistic WF-net with objects in Figure 2
represents such a model.
< c > is an object belonging to the class “Order”,
as well as variable x and all the model’s places. Each
transition has an interpretation and an action attached
to it defined by the designer. The interpretation is
used to manage the occurrence of each event in the
system by imposing restrictions on the firing of tran-
sitions. The action is an application that involves the
attributes or methods of formal variables associated
with incoming arcs allowing for the modification of
some specific attributes. However, in the model pre-
sented, the actions are not represented given that they
do not interfere in understanding the approach. The
true and uncertain interpretations are represented, re-
spectively, by the letters T and U. Note that when the
representation of the uncertain interpretation is omit-
ted in the model, such interpretation is always evalu-
ated as false. On the other hand, the false interpreta-
tion is evaluated as true when both the true interpreta-
tion and the uncertain interpretation are evaluated as
false. The element τ represents the current time.
The conditions correspond to the folloing interpre-
Uncertain Marking for Dealing with Partial Parallelization in Business Processes
Figure 2: A BP model using possibilistic WF-net.
sgBA1”, sgBA2”, sgBA3”, sgBA4”, sgBA5”,
sgBA6” and “sgBA7” represent, respectively, the
beginning of the tasks “store order”, “check in-
ventory”, “send invoice”, “receive funds”, “pre-
pare shipment”, “ship goods” and “archive”;
sgEA1”, sgEA2”, sgEA3”, sgEA4”,
sgEA5”, sgEA6” and sgEA7” represent,
respectively, the end of the tasks “store order”,
“check inventory”, “send invoice”, “receive
funds”, “prepare shipment”, “ship goods” and
, t
and t
are maximum points
in the timescale associated to a specific activity
which indicate the maximum time allowed for the
initialization of a task;
, t
, t
and t
are maximum
points in the timescale associated to a specific ac-
tivity, which indicates the maximum time allowed
to begin the conclusion of a task.
Due to the somewhat cautious policy realized by
the BP, the normal expected behavior of the process
is to execute all activities in sequence such that for an
activity to start, it must wait for the end of the previ-
ous one. For example, the activity “prepare shipment”
) starts only after receiving the funds (activity A
In consequence, BP instances based on this process
model might suffer from long processing times, re-
sulting in insufficient customer satisfaction.
An abnormal behavior will happen if, disregarding
the rigid sequencing of the activities but considering
a maximum time allowed to start or finish an activ-
ity, the activities A
and A
, for example, start before
the end of the activity A
, allowing a lower processing
time and sufficient customer satisfaction. In this case,
some pseudo-firing will have to occur and the impre-
cision linked to some objects will increase. In doing
so, some of the sequential activities, specified through
the rigid structure of the sequential WF-net of figure
2, will be partially executed in parallel.
The general behavior of a WFMS contingent on
possibilistic WF-net models will be based on the pos-
sibilistic token player given by the activity diagram in
Figure 3.
To illustrate a possible abnormal behavior, the fol-
lowing values are considered: t
= 24, t
25, t
= 49, t
= 50, t
= 74, t
75 and t
= 90. In addition, it is assumed that the
conditions become true on the following dates: sgBA
at τ = 0, sgEA
at τ = 4, sgBA
at τ = 7, sgEA
τ = 19, sgBA
at τ = 20, sgEA
at τ = 23, sgBA
τ = 24, sgEA
at τ = 85, sgBA
at τ = 86, sgEA
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
Figure 3: Possibilistic token player algorithm.
τ = 87, sgBA
at τ = 88, sgEA
at τ = 89, sgBA
τ = 90 and sgEA
at τ = 100.
Taking into consideration the values defined above
(the maximum points and the conditions), the follow-
ing scenario will occur:
at the following times τ = 0, τ = 4, τ = 7, τ = 19,
τ = 20, τ = 23 and τ = 24, the transitions B.A
, B.A
, E.A
, B.A
, E.A
and B.A
are re-
spectively fired with certainty given that they are
enabled by a certain marking and the interpreta-
tion attached to them is true (η
(t) = true). The
resulting state of the process after this firing se-
quence is shown in Figure 4(a).
at current time τ = 49, the transition E.A
is en-
abled by a certain making and its interpretation is
uncertain (η
) = uncertain). Then, E.A
is pseudo-fired (Figure 4(b));
at the following times τ = 50, τ = 74 and τ = 75,
the transitions B.A
, E.A
and B.A
are respec-
tively pseudo-fired given that they are enabled by
uncertain markings and the interpretation attached
to them is uncertain (η
(t) = uncertain). The
resulting state of the process after this firing se-
quence is shown in Figure 4(c);
at current time τ = 85, the transition E.A
is en-
abled by an uncertain marking and its interpreta-
tion becomes true (η
) = true). This situ-
ation occurs because the notification of the receipt
of the funds arrived late and the activities A
started before it ended, so as not to increase
the processing time of the process such that cus-
tomer satisfaction is not affected. Consequently,
the recovery algorithm described in Algorithm 1
is called to cancel some pseudo-fired transitions.
After the execution of the recovery algorithm, the
transition E.A
can be fired with certainty given
that it is enabled by a certain marking (Figure
4(d)) and its interpretation is true. It is important
to note that if the marking is not certain after the
processing of the algorithm, the transition E.A
cannot be fired with certainty and the process in-
stance must wait for a new event in order that the
τ = 24
τ = 49
τ = 75
τ = 85
τ = 100
Figure 4: Simulation results of the scenario.
process state can go back to a certain marking;
finally, at the following times τ = 86, τ = 87,
τ = 88, τ = 89, τ = 90 and τ = 100, the transitions
, E.A
, B.A
, E.A
, B.A
and E.A
are re-
spectively fired with certainty given that they are
enabled by certain markings and the interpretation
attached to them is true (η
(t) = true). The
resulting state of the process, after this firing se-
quence, is shown in Figure 4(e).
Figure 5(a) depicts the possibility distributions of
instance < c > as functions of time relative to the sce-
nario described above(the black lines represent a pos-
sibility equal to 1 and the bright lines a possibility
equal to 0). Note that the activities A
and A
after the
execution of the recovery algorithm do not spend all
the processing time predefined because they have al-
ready been initialized. In addition, observing the pos-
sibility distributions of instance < c >, it is easy to
verify that the activities A
, A
and A
were pseudo-
parallelized during the time period between 49 and 85
even with the fact that in the process model they are
strictly described in a pure sequential way.
In order to show the difference in the processing
time spent when the process model is strictly executed
Uncertain Marking for Dealing with Partial Parallelization in Business Processes
(a) Pseudo-parallelized (b) Strictly sequential
Figure 5: Possibility distributions of object location < c >.
Algorithm 1: Recovery algorithm.
WN: WF-net with an uncertain marking
t: transition
WN: WF-net with a new marking
1. if t was pseudo-fired
2. then LP (t)
3. cancel the firing of t
2. else LP φ
4. while LP 6= φ do
5. p LL[0]
6. while t
(p) | t
was pseudo-fired do
7. LP LP (t
8. cancel the firing of t
sequentially, Figure 5(b) depicts the possibility distri-
butions of instance < c > as functions of time consid-
ering the same processing time that each task spent
during its execution in the scenario described above.
Comparing both figures (Figure 5(a) and 5(b)), it is
easy to see that the processing time spent by the first
is 33% lower than the second one.
Considering the change patterns suitable for pro-
viding flexibility in time execution proposed by We-
ber et al. in (Weber et al., 2008), the proposed ap-
proach incorporates, during real time execution, the
adaptation pattern “Parallelize Process Fragments”.
In this article, a possibilistic WorkFlow net model was
presented with the purpose of dealing with deviation
situations in BP. Combining the routing structure of
WF-nets and the uncertain reasoning of possibilistic
Petri nets, the authors presented an approach that can
deal with deviation situations that can be reached dur-
ing the real time execution when human behaviour is
considered. Such an approach was applied to an ex-
ample of a simple ordering process.
Other studies that deal with the problem of devia-
tions in workflow processes create new structures dur-
ing the execution process, which can lose the good
properties of the process or only detect the devia-
tions after the conclusion of the process. Comparing
these studies with the approach presented in this pa-
per, the main advantage is that the good properties of
the model will be preserved because the structure in
the process (the different routing patterns) will not be
altered during the real time execution. Some devia-
tions will be allowed and recorded in the organiza-
tional memory for being posteriorly considered in the
process evolution. However, the allowed deviations
will be limited due to the possibilistic behavior.
As a future work proposal, it will be interesting to
deal with fuzzy time information in an explicit way
in the structure of a WF-net as the one presented in
(Cardoso, 1999). The use of fuzzy dates can allow
a flexible control of a time schedule describing the
causality relations between the events and improving
the updating process. Such an approach should be
interesting at the monitoring level in order to diminish
the imprecision of human intervention.
In addition, in order to validate experimentally
such an approach, the model of the possibilistic Work-
Flow net will have to be implemented on a Petri net
software tool allowing for the programming of transi-
tion pseudo firing. It seems that the CPN Tools soft-
ware resources (Beaudouin-Lafon et al., 2001) should
be able to implement in a simple way some of the ba-
sic behaviors of a possibilistic token player given that
they combine advanced interaction techniques into a
consistent interface for editing, simulating, and ana-
lyzing Coloured Petri Nets. Such an implementation
should prove the gain in the overall process perfor-
The authors would like to thank Coordenac¸
de Aperfeic¸oamento de Pessoal de N
ıvel Superior
(CAPES), Fundac¸
ao de Amparo a Pesquisa do Estado
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
de Minas Gerais (FAPEMIG) and Conselho Nacional
de Desenvolvimento Cientfico e Tecnolgico (CNPq)
for financial support.
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