lowing holds: f
International Journal of Scientific & Engineering Research, Volume 2, Issue 12, December-2011 1
ISSN 2229-5518
ATSERO Method: A Guideline for Business Process and Workflow Modeling within an Enterprise
Roger Atsa Etoundi
Abstract— In the fields of business process and workflows modeling, a wide range of techniques have been defined and used. Despite the popularity of some of them, there is no consensus on the modeling standards and concepts. However, there are many perspectives that need to be taken into consideration for a better management of workflows within an enterprise such as process, organizat ion, information, operation and the quality of service. In this paper, a new approach, so called ATSERO Method, is proposed. The method is based on Formal Method, Domain and Requirement Engineering, is presented. This method describes several salient concepts inherent in the understanding of these perspectives. This method may be considered as a guideline in business process and workflow modeling and also allows organizations to deal with the competitive pressure of the network economy and to improve the quality of service for the satisfaction of different stakeholders.
Index Terms— Business Process Modeling, Process abstraction, Workflows modeling, QoS, Customer satisfaction, Formal method.
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business process typically refers to an enterprise process. Business process modeling (BPM) is one of the core me- thodologies developed to better represent the functional behavior of the information system dealing with the delivery of services to customers within an organization. Existing busi- ness process models are not based on formal approaches in the line of the numerous models such as abstract system, abstract integration, system abstraction and simulation and concrete system. In fact, it rather belongs to the family of informal UML-like models, which seriously limits its theoretical poten-
tial and leaves the door open for new researches [3, 7].
In the domains of business process and workflow modeling, a wide range of techniques have been widely used [2, 3, 13, 15]. Despite the popularity of some of them, there is no consensus on the modeling standards and concepts of business process and workflow in the delivery of services within an organiza- tion. However, there are many perspectives that need to be taken into consideration for a better management of workflows. These perspectives include process, organization, information, operation and the quality of service (QoS). The survey of business process and workflow modeling shows that most researches have been concentrated in the process pers- pective and neglected the other perspectives [13]. As conse- quence, enterprises are not fully productive and have many difficulties to deal with challenges of the network economy.
Focusing on these challenges, researchers have recognized the importance of knowledge in the productivity of organization [25]. Knowledge management allows enterprise to improve
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the quality of services offered to customers, increase custom- ers’ satisfaction, and reduce the cost of maintaining and man- aging services. Knowledge can be found and resides in various places within an organization and out of the organization. This knowledge represents experience, customer’s needs re- lated to services, customer perception of the quality of service, and other valuable management lessons, the functioning and the operation of the organization. Now, because knowledge management aims at the improvement of task processing [19], methodologies that aim at building knowledge management system have to examine the businesses within an enterprise. To this end, the modeling of business process and workflows within an organization must include knowledge abstraction. In the meantime, enterprises face the problem of capacity building of new staff. For the purpose of maintaining the QoS despite the retirement of some staff, human resource manag- ers usually have to send new staff for training, and spend much money to this end. However, the result is not always satisfactory and the manager is obliged to team them with those who are experienced [27], so they can catch up. Some- times, this is not possible due to the fact that, this action gen- erally comes late with respect to the departure for retirement of some staff members. Within this time period, the enterprise pays double for the same workstations; this contributes to a reduction in the income. This situation can be overcome if knowledge concerning the processing procedures is stored for future use and knowledge transfer [19, 25]. Moreover, the process of moving along work-stations that comprises the processing chain, enables new employees to acquire a vast amount of tacit, as well as explicit knowledge. For this reason, it will be very difficult for any employee to present in detail the knowledge required by any work station in the accom- plishment of a specific task. As a result, experienced em- ployees sometimes will provide inaccurate information for knowledge transfer. Although individual employees will not always be accurate or remember specific information regard-
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ing the processing of certain tasks within an enterprise, an enormous amount of knowledge can be obtained from the experience of all the employees who have already handled the processing of such tasks. In order to do so, it is interesting to capture all knowledge concerning the processing of any tasks within an enterprise and store it for future use. The process that can facilitate the capturing and storage of this knowledge for later sharing is the process of managing knowledge [19]. In order to design a management tool within an enterprise, it will require the inclusion of knowledge management process in the design of all business processes and workflows that are supported within an organization. This is one of the chal- lenges that various enterprises have to tackle in order to resist the increasing competitive pressure of global economy if they have to survive.
In this new economy, the difference between enterprises is not only based on the manner in which it tackles the above issues but also on the way they deal with their customers for the sa- tisfaction of their needs. Organizations thus face unprecedent-
cal machinery is important in modeling business process and workflow concepts. This domain of mathematical objects is defined in terms of partially ordered sets, least upper bounds, chains and continuity.
Definition 2.1 (Partially Ordered Set)
Let C be an arbitrary set. A partial order on C is a subset of
CC which satisfies the following for all c1, c2 and c3 in C:
1. c c (reflexivity),
2. if c1 c2 and c2 c3 then c1 c3 (transitivity),
3. if c1 c2 and c2 c1 then c1=c2 (antisymmetry).
In this mathematical domain of objects, we are concerned not only with arbitrary sets with partial order, but also with sets of functions with their ordering. A partial ordering on a set of functions of type C1→ C2 can be derived from the or- derings on C1 and C2.
Definition 2.2 (Sequence)
Let (C, ) be a partially ordered set, c0 ,c1,... , also denoted by
ed competition, forcing them to offer exceptional levels of ser- vice based on the desire of customers, whichever the sector of
ci
is a sequence if and only if for all i N : ci ci1 .
productive business process they find themselves [2, 5, 4, 6]. Thus, enterprises should make efforts in the improvement of the quality of service desired by customers. Customers with the same requirements must receive the same service unde- pendably of the employees involved in the processing of asso-
Definition 2.3 (CPO)
A complete partially ordered (CPO) set is a set C with a partial order which satisfies the following requirements:
1. there is a least element, denoted by , with respect to ,
i.e cC : c ,
ciated tasks. Feedback from the customers should be obtained by the enterprise for the improvement of the quality of the service offered. In the daily life of an enterprise, customers
2. each sequence ci in C has a least upper bound in C.
Definition 2.4 (Continuous Function)
come with new complains and problems, but also with ideas
Let C1,1 , C2 ,2
be two CPO's, the function
f :C1C2 is
and praises. To deal with the satisfaction of customers within
continuous if and only if for each chain
ci i 0 in C, the fol-
an enterprise, not only the quality of the final service or prod-
lowing holds: f
i 0 ci
i 0 f ci .
uct has to be considered but also the quality of various outputs
Fact 1 (Fixed Point Theorem) let C be a CPO and f :CC , if f is
obtained from the execution of tasks should be considered
continuous, then the least fixed point
f exists and is equal
since the final quality of service or product is an aggregation
to i 0 f i , where
of intermediate quality of this artefact. The intermediate quali-
f 0 and f i1 f f i .
ty is the basis in definition of the final QoS. Therefore, QoS
Definition 2.5 (Least Fixed Point)
must be integrated in the modeling of a task and in the model-
Let C , be a CPO,
f : C C and let xC .
ing of business process and workflow. This issue has not yet
been tackled in the research field of BPWM.
x is a fixed point of f if f(x)=x
x is a least fixed point of f if x is a fixed point of f and for
This paper presents a method, so called ATSERO Method, which captures different abstractions of a business process in different levels within an enterprise. The approach is based on
each fixed point y of f, the relation x y
Definition 2.5 (Partial ordering functions)
holds
domain and requirement engineering [24,25], and formal me- thods namely Denotational Semantic [1,14]. The rest of the
Let C1,1 , C 2,2 be two partially ordered sets, C1→ C2 the
set of continuous functions, an ordering on C1→ C2 is de-
paper is organized as follows: section 2 presents part of the
fined as follows, where
f ,gC1C2 :
f g cC1 : f c2 gc .
Denotational Semantics concepts suitable for our modeling
approach, section 3 presents the proposed method for busi-
ness process and workflows modeling, the last section 4 con-
cludes the work and highlights some perspectives and future
Definition 2.7 (Least Upper Bound)
Let C'C . cC is called a least upper bound of
1. c is an upper bound of C' i.e xC' , xc ,
C ' if:
works.
This section gives parts of Denotational Semantics [1,14] that
2. c is a minimal element of the set of upper bounds of C' i.e
yC : (( xC' : x y ) c y ).
The least upper bound of a partially ordered set C' will be de- noted by C' .
Definition 2.8 (Least upper Bound of a Sequence)
are suitable in handling the modeling of business processes
The least upper bound of a sequence
c0 ,c1,... denoted by
and workflows within an enterprise. The resulting mathemati-
i 0 ci or
i 0
is defined as follows:
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ci i0
c|c ci i0where c in 
ci 
i0 means that c is an
element of the sequence
ci i 0 .
if o , then o C
if o , then o C
Fact 2 (CPO of functions) Let C1,1 and C2 ,2 be two CPO's, then C1C2, is a CPO.
Fact 3 (Least upper bound of functions) Let C1,1 and
if o1, o2 , then o1 o2 , o1˅ o2 , o1 o2 o C
A condition c can be decomposed into a set of observers +c
whose values are evaluated to true and a set of observers -c
C2 ,2 be CPO's and let
fi i0
be a chain of functions in
that are evaluated to false. The two sets do not have any com-
(C1→ C2), then the function c1.
i0
fi c1
is the least upper
mon element i.e. c c
bound of this chain and therefore
i0 fi c1
i0 fi c1 for all c1C1 .
Given a condition c C and a state s, c is satisfied within the
In the rest of this paper,
f denotes the least fixed point of f
state s if the result of its evaluation is true, i.e. s(c) = true.
where f is a continuous function on a CPO.
This section presents in an incremental manner a model of a business process within an enterprise. The definition of this model starts by the presentation of salient concepts that are suitable for the modeling of a business process and the asso- ciated workflows for the achievement of stakeholders needs according to the related degree of satisfaction.
The environment is considered as a set of different metrics whose value may change [9, 17]. These metrics are primitive Boolean observers denoted by Observer. The associated value of each observer depends on the current state of the environ- ment.
Formally, an environment E is defined as a couple
, S, val
where:
is a non empty set of observers;
S is a non empty set of sates;
val : S Bool is a function which describes the be-
haviour of observers.
In this rest of summary, val(o)(s) is denote by s(o) where s de- notes a state and o an observer, s(o) is the value of the observer o in the state s. Given a state s, the set of observers whose val- ue is true defines the characteristic of s and is represented by
sc o , so true.
Given two states s1 and s2 of the set of states S of the envi- ronment E, the set of observers whose associated values are not the same is defined from the characteristics of the two states. This set is called gap between s1 and s2 and is denoted
by s1 s2 s1c s2c s2c s1c .
Given an environment E, the observers in define the alpha- bet that permits to analyse events that occur on E. The lan- guage defined from this alphabet is denoted by the set of con- ditions or formulae C. A condition cC is an assertion over observers and is defined as a first order formula. The basic elements of C are therefore all the observers of . The ele- ments of C are formed by the following:
3.1.1 State of an Environment
A state is a snapshot of an environment within a time [10, 11,
12]. From this snapshot facts are observed. Some of these facts or features of a state are true or false at this particular time. These facts are represented as some equivalent of predicate calculus formulae. We shall refer, somewhat loosely, to these facts and relations as attributes of a state. In a rigorous man- ner, let F be a set of formulae, and s be a state, then s is a sub- set of F i.e. s F .
In general, let S be a set of states, according to the definition of a state, (S, ) is a partial ordered set. In our work, we are not
dealing with any kind of set of states, we are interested with S execution can be started. This initial state is therefore con- tained in all states of S i.e for all s S , s s . In the meantime, S is required to have a least upper bound s known as a state where the goal of the business process is satisfied.
3.1.2 Knowledge Model
In [20], a goal oriented approach- for the definition of a busi- ness process requirement model, taking into account their lev- el of importance and constraints inherent to these require- ments, is presented. The level of importance of a goal is the credit which the user associates to this goal. Constraints are non-functional requirements related to what this goal must satisfy. The approach that was proposed in [20], revolves around four main activities: requirement elicitation, selection of different goals, transformation of requirements into know- ledge bits and finally the development of the requirement model. It can be shown formally that this approach exhaus- tively describes a business process. To do this, a formalism to model the requirements of a business have been is defined. The model is refinement of the one presented by Farida and Joel Brunet in [26]. The refinement is based on the formal defi- nition of a knowledge bit or expressed requirement. A know- ledge bit is defined as follows k,Ag,Ex,y,w,l,d,v where: k is the name of the knowledge; Ag is the name of the agent who expressed the knowledge; Ex is the experience level of Ag; y the context in which the goal is defined; w is the goal; l the business rule; d execution constraints; v the level of impor- tance of the goal.
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3.1.3 QoS Model
The quality of service denoted by QoS represents the perfor- mances of the service which determine the projected level of satisfaction for the recipients of these services [16]. The level of satisfaction is defined as a set of properties, criteria, characte- ristics and performances of the services delivered to the cus- tomers. Several works exist in this field, each one defining a specific set of criteria specified in order to measure the QoS. In the literature, there is no consensus yet on the definition of a set of common criteria to evaluate the quality of service deli- vered within the organizations [16,19]. The evaluation criteria are defined according to the objectives and specificities of each
fm:CxPP
g :CxKBx
If c denotes a context of Cx, then c is a restriction of the envi- ronment , that is c . The action of a task within an envi- ronment is to transform its current state into a new one. When
<nt,PP,fm,gm,Cx,KBx> is a task, s a given state where the pre- condition pre(PP) is satisfied i.e s(pre(PP))=true, the action of t in the state s is the new state t(s) which satisfies the post condi- tion post(PP) i.e t(s)(post(PP))=true. In general, the action of a task t within the state s is characterized by the observers of s whose value has been modified.
Definition 3.2 (Task action)
company. The concept also defines an abstract model which
Let
E , S, val
be an environment, s a given state and t a
gives the semantics of the quality of service.
Definition 3.1
Let Cr be a set of criteria considered in the evaluation of the quality of service, Val the set of values that can be assigned to these criteria, and f a map defined by ƒ: C→Val, the QoS is de- fined by (C,Val, ƒ).
Given two QoS q1 and q2 such that q1=(Cr1, Val1, f1) and q2=(Cr2, Val2, f2), q1 and q2 are compatible, denoted by q1∆ q2, if and only if C1=C2 and Val1=Val2. When q1 and q2 are com- patible, q1 is better to q2 and denote q1 q2 if and only if
cC1 ƒ1(c) ≤ ƒ2(c). (ɸ,) is use to denote the partial ordered
set of compatible qualities of services.
3.2 Task Description Model
A task is an atomic activity that cannot be split into smaller
activities [16, 17]. The performance or execution of a task transforms the state of the environment into another state. A task is therefore an action within a state of an environment. Before a task can be executed, the state of the environment should satisfy a specific condition called pre condition, and when this execution is completed another condition, called post condition is satisfied. For a task to be executed within an organization which will be defined later, the knowledge re- quired for its performance is captured. This knowledge de- pends on the context within which the execution can take place. For each of the associated contexts are defined a set of knowledge bits and quality of service to obtain after the execu- tion of a task. A task is formally defined by a tuple
<nt,PP,fm,gm,Cx,KBx,Qx> where nt denotes the name of the task,
PP = Pre×Post where Pre denotes the set non empty set of pre- conditions within which its execution can be carried out, and Post the set of post conditions that are obtained after the ex- ecution, Cx a non empty set of contexts within which the task
task whose pre condition is satisfied in s, then the action of t in
s denoted by ts and is specified by ts o : , so tso.
A task will be represented when there will be no ambiguity by its name t and pre(t) respectively post(t) will denote respective- ly its pre and post conditions. Based on the post condition of a task t, and the state s where s (post(t))=true, we conjecture that ts=+post(t) -post(t).
Definition 3.3 (Conflicting Tasks)
The action of tasks within an environment can be conflicting since many tasks can modify the same observers at the same time [16]. To this end, t1 and t2 are conflicting tasks in the state s, and we denote it by overlap (t1, t2, s), if and only if the con- straints defined in the equation (1) are satisfied:
s pret1s pret2 true
postt post t 0
postt2 post t10
Definition 3.4 (Orthogonal Tasks)
Let t1 = <nt1,PP1,fm1,gm1,Cx1,KBx1,Qx1> and t2=
<nt2,PP2,fm2,gm2,Cx2,KBx2,Qx2> denote two tasks, t1 and t2 are
said to be orthogonal if and only if t1 and t2 require the same knowledge in order to be processed whenever the processing context is differed, i.e Cx1 ≠ Cx2 and KBx1 = KBx2
Definition 3.5 (Shift)
Let SoT be a none empty set of tasks and s a given state, a shift denoted by Shf is a couple Shf =<s, SoT> composed with the state s and the set of non conflicting tasks SoT within s.
Formally, let Shf=<s, SoT> be a shift, the following properties are satisfied:
S T 1
t S T , s pret true2
can be executed, KBx a non empty set of knowledge bits used
for the better understanding and performance of the task, Qx is a quality of service expected after the execution of nt. fm, and gm are maps defined respectively by:
t, t ,
S T , t t ,
overlapt, t , , s
false3
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Let Sht=<s,SoT> be a shift, the simultaneous actions of SoT in s,
denoted by ts(s), is captured by the set of observers whose values are modified within s, that is:
From the definition of the execution path of tasks, we specify
the relation within the set T of tasks based on the set S of states. This relation is denoted by .
o :
S T s
o postt , ti S T
Definition 3.8 (Ordering of Tasks)
i
Definition 3.6 (Chain)
A chain is an execution path of tasks, according to their actions in states and their triggering conditions is denoted by P n Shti , and is specified as a finite sequence of shifts where n represents the length of the sequence.
Let P be a path of length n>1, and
Let T be a set of tasks, and t1 and t2 be two tasks of T, we write t1 t2 if and only if for all chain CH such that if nt1 and nt2 denote respectively the maximum range of t1 and t2 in CH,
then nt1nt2 . This relation has the following properties:
1. reflexivity: t t this simply means that the task t belongs to the chain CH;
2. antisymetric: if t1 t2 and t2 t1 in the chain D then t1 = t2.
shk
sk , stk
, shk 1 
sk 1, stk 1
notes respectively the shift in
By convention, there will always exist a path from each
the range k and k+1, the state sk+1 is the resulting state after the
task to itself;
execution of the set of tasks stk i.e
sk 1 stk sk . When there
3. transitivity: obviously if in the chain CH, t1 t2 and t2 t3
will be no ambiguity, the shift of the range k of the path P will
be denoted by Pk .
then t1 t3.
Let
Shtk
Sk , S Tk
and
Shtk 1
Sk 1, S Tk 1
be two shifts
Lemma 3.4
where Shtk S Tk sk , the difference between the states sk and
The set of tasks T associated with the relation previously de- fined , i.e. T , , forms a complete partial ordered set.
sk+1 is denoted by
sk sk 1 S Tk sk .
Lemma 3.1
sk sk 1
and is defined as follows:
3.2.1 Palette
Let E be an environment, and S be a set of different states that
E may reach according to the actions of tasks T, then a palette
Let p be an execution path and
t S T pk with
P is a couple <E,S→S>. The set of functions S→S will be de-
k lengthp then there will always exist m such that m>k and
S(p(m))(post(t))=false.
Lemma 3.2
Let p be an execution path then S T plength p .
Definition 3.7 (State ordering)
noted by T, the set of tasks of the palette. P(E) and P(E) will denote when there will be no ambiguity, the environment and the set of tasks of the palette P respectively.
The actions of the set of tasks T of the palette P in the envi- ronment E are to change at least once the value of each ob- server of in E. Hence, the consecutive actions of a non empty
Let P be a path of length n>1, and
Shtk Sk ,S oTk
and
set of tasks within an environment may not modify all the ob-
Shtk 1 Sk 1,S oTk 1
be two consecutive shifts in P with k<n
servers in this environment. The set of observers whose value are not changed during the execution of any given none emp-
then
Sk Sk 1 specifies the fact that the set of observers
ty set of tasks will be abstracted from all the possible states of
modified in Sk after the actions of SoT are contained in the set
of observers of Sk+1 with the same values.
Lemma 3.3
Let P be an execution path, S the set of states of P, then S ,
is completed partial ordered where the least upper bound state in the last state of P and the least state is the first state of P.
The defined modeling approach has to ensure that the execu- tion of a task t will stop at a certain time. In order to do so, the set of observers that should be modified by t must contain
the environment, i.e.
t1T ,o postt1
o or
t2T ,o postt2
Given a palette P, according to the environment changes with- in organizations and the different processing of tasks that can take place, different ways in which tasks can be executed have to be captured. SPP is use to specify the set of processing paths that can be obtained from a palette P.
Lemma 3.5
partially or totally the observers forming its pre condi-
Let P be a palette,
sS P
a given state of the environment
tion pret pret postt postt .
E(P) of P, there will always exist a processing path
p SPP such that
of the path p.
s S p , where S p denotes the set of states
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Lemma 3.6
Let P=<E,T> be a palette, and
t T , there will exist an execu-
This approach reduces the number of patterns to be used in
order to capture various ways tasks can be ordered. This is the
tion path chSPP
where SPP denotes the set of possible
main difference between the proposed modeling approach
processing paths of T, chn
sn ,S Tn
3.3 Task processing
such that t S Tn .
and other BPM theory papers presented in the literature. In
these works, the Workflow Management Coalition [18] has identified four basic control structures for workflows: OR-
Based on the planning and scheduling of tasks processing done by the resource manager within an organization for the achievement a given customer goal, employees process these assigned tasks based on their own experience and knowledge associated to these tasks. According to the context within which the performance of the tasks is taking place, processing can be done straightforward if the knowledge related to the task is adequate for its processing within this context. The processing sometime will not be done straightforward as the knowledge related to the performance of the task is not enough. When it is the case, the employee will use his tacit knowledge, or that received from more experienced em- ployees, in order to process the task. In order to keep track of this new way of carrying out this task, the defined information should be stored for further use. For this end, the knowledge of the so called task should be updated. In order to take this into consideration, the modeling of workflow must take into account the processing of tasks by employees. Let tk be a task that is processed by an employee using the knowledge kb in the context cx, the task tk changes state after its performance based on the fact that, the knowledge associated to this context is updated by the knowledge used for its processing i.e gm(cx,tk)=gm(cx,tk’)kb where gm(cx,tk) denotes the set of knowledge required for the processing of the task tk.
3.4 Business Process Model
A business process is a collection of activities or tasks de-
signed to produce a specific output for customers [16, 17, 19].
SPLIT, OR-Join, AND-Split, and AND-Join. More control struc-
tures have been identified by Van der Aalst in [15].
Lemma 3.7
There will always exist a state Slub such that when it is reached, other states cannot be reached. This state is called a least up- per bound state of the associated business process.
Lemma 3.8
There will always exist a state Sini from which the execution of the business process starts. This state is called a least state of the associated business process.
For each service associated to a given business process, a set of qualities of service is defined to deal with the daily work and the competitive pressure of the network economy.
Definition 3.10 (Well Defined Business Process)
Let, BP=< P,G> be a business process, BP is well defined if and only if all the observers that form its goal (service) are con- tained in the set of observers of the environment E i.e.
G G E
Definition 3.11 (Well Formed Business Process)
Let BP=< P,G> be a business process, BP is said to be well formed if and only if each execution chain SCH reaches the least upper bound state slub which satisfies the service G i.e.
ch SCH , nch N , slu b S
nch lengthch
slu b
It implies a strong emphasis on how work is done within an
organization in order to deliver a particular service. A process
lu b
G true
is thus a specific order of work activities across time and space, with a beginning, an end, and clearly defined inputs and outputs. The output is the reason the organization does
More formally, let SCH be the non empty set of different
chains that can be obtained from a business process BP, and
CH SCH with the length nCH such that the nth state slub of CH
this work and is defined in terms of the benefits this process has for the organization as a whole.
Definition 3.9 (A service)
A service is the characteristic of a business process and is de- fined as a composition of a set of criteria that characterize what is delivered within an organization, where each criterion is represented by an observer [16, 17, 19].
The model of a business process is defined as a couple <P, G> where P is a palette and G the service to be achieved. Accord- ing to the definition of the palette, the ordering of tasks is cap- tured explicitly by their pre conditions and the states of the environment within which their execution is being carried out.
satisfies G i.e. slub=true.
Definition 3.12 (Deadlock- and Livelock-Free)
Let BP be a business process, BP is deadlock- and livelock-free if and only if it guarantees that every execution chain reaches its least upper bound state satisfying the goal of the business process BP.
Theorem 3.1
Let BP denote a business process such that BP is well defined and well formed, then BP is deadlock-free and livelock-free.
Proof: By the definitions of well formedness and well defi- nedness of a business process which states that the least upper bound of the state of a business process is reached and that
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this least upper bound state satisfied the goal of the business,
the described business process model is deadlock and live lock free.
All the execution paths of a business process start from the same state denoted by Sini. It can be easily being shown that the set of states SBP associated with the ordering relation as defined previously is completed partially ordered.
3.5 Human Actor Model
There are many types of agents participating in the processing of tasks within an enterprise for the achievement of customers’ needs. The enterprise system dealing with the processing of tasks is a hybrid system including hardware components with embedded software, the human actors interacting with the hardware and the organization. An organization is an ar- rangement of human actors purposefully organized to carry out a certain mission, which, in its turn, adds a dimension to the quality of service [16]. The hardware components have been designed to play specific roles and functions in the process chain, and can hardly be moved among different roles in the enterprise as it is done for human actors. The proposed modeling approach is not dealing with hardware but with human actors who can significantly influence the quality of service according to their skills and associated experiences. We model the skill of a human actor by (Sk,Tks,mch) where Sk is the set of competences, Tks the set of tasks and mch a map that gives for each competence cp Sk the set of tasks mch(cp)
Tks that can be processed based on cp with mch(cp) ≠. The structure (Sk,Tks,mch) will be represented by Sk when there
will be no ambiguity. Based on the organization put in place, the set of tasks assigned to a human actor are kept in a diary.
A diary is described by the set of tasks and the set of time in- tervals within which they are processed [16]. It is important that the set of time intervals in the agenda be defined such that it does not allow the overlapping of time intervals.
Let ds=(TI,,∩, ∆) be a set of time intervals such that (TI,) is a partial ordered set with ∂ the smallest time interval, ∩ and ∆ be two maps defined as follows ∩ : TI ×TI → TI and ∆ :TI ×TI
→Boolean, t1 and t2 be two time intervals of TI, p1 and p2 over-
lapped if and only if there exists a time interval p3 such that:
p3p1p3p2 p1p2t3
p3p1p3p2
where and ∆ define respectively the intersection and the overlapping relationship. The set of time intervals is represented when there is no ambiguity, by Pds. Based on the concepts of tasks and time interval, the diary concept is mod- eled by <Tks,Pds,g> where Tks is the set of tasks, Pds the set of associated time intervals, and g a map defined by g: Tks Pds such that t1, t2Tks, t1≠ t2 (g(t1)∆g(t2)).
Definition 3.12 (Human Actor)
A human actor is defined by <Sk,Ex,f,Dy,Id> where Sk is its set
of skills, Ex the set of associated experiences, Id his identifica- tion, Dy his associated diary, and f a map which defines for each skill sk Sk its associated experience f(sk) Ex.
3.6 Workflow modeling
A workflow is defined by (Ts, Es,Ps,h,fem, Q)+ where Ts is the set of none conflicting tasks, Es the set of employees dealing with the processing of Ts within the time intervals Ps to obtain the quality of service Q, h is the map Ts Ps which defines for each task t, its time interval h(t) within which it is processed, and f a map that gives for each task t the employee fem(t) who is charge of its processing . The two maps h and f are required to be two isomorphism as each task is required to be associated to a time interval within which its execution will take place, and should also be assigned to a specific employee for its per- formance. The quality of service Q is such that:
n
Q qi where qi is the quality of service obtain after the ex-
i1
ecution of task ti Ts and n the number of task in Ts.
Based on the fact that the satisfaction of customers is one of the challenges that enterprises are required to guarantee, in the modeling of the workflow, we require that employees who are involved in the processing of tasks have the necessary knowledge to carry out these tasks. Therefore, if t is a task to be carried out by the employee fem(t), and kbem(t, fem(t)) his knowledge associated for the processing of t, there will exist at least a context c within which t can be processed such that the knowledge bk(t,c) required for its processing verifies the fol- lowing constraint bk(t,c) kbem(t, fem(t)).
3.7 Enterprise Model
An enterprise is a structure dealing with the service delivery of customers based on a certain quality of service. This struc- ture is organized in terms of business processes that are car- ried out, employees in charge of the processing of the asso- ciated tasks, and the resulting workflows.
Definition 3.13 (WorkStation)
A workstation wk is a position within an enterprise defined by (Tks,KBs,ωtk,ωpk) where Tks is the set of tasks to be carried out by a human actor appointed at this position, KBs is the set of knowledge bits required for the performance of tasks Tks, and ωtk is a map which gives for each task tk, the tacit knowledge ωtk(tk) acquired by the former employees in this position, ωpk(tk) defined the critical knowledge required for the processing of tk based on the execution context.
In the proposed modeling approach, A workstation wk
=(Tks,KBs,ωtk,ωpk) with an empty set of knowledge bits related to its given task is not accepted, i.e.tkTks, ω(tk)≠Ø. Moreo- ver, if wk denotes a workstation, tasks(wk) denotes its asso- ciated set of tasks.
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International Journal of Scientific & Engineering Research, Volume 2, Issue 12, December-2011 8
ISSN 2229-5518
Definition 3.14 (Enterprise)
An enterprise Org is modeled by (Io,BPs,Emps,WFs, WKs,fewk) where Io is its identification, BPs is the set of its business processes that can be run, Emps its set of employees who parti- cipated in the processing of tasks defined in various business processes, WFs its set of workflows defined for the achieve- ment of customer’s needs, WKs the associated workstations, and fewk denotes a map which gives for each employee ag Emps, the position fewk(ag) that he is appointed to.
Definition 3.15 (Strong well-Definedness staff)
Given an enterprise Org=(Io,BPs,Emps,WFs,WKs,fewk), the as- sociated employees are said to be strong well-definedness if and only if each employee ag appointed to a given work sta- tion has the required profile, that is if ag=<Sk,Ex,,Dy,Id>Emps with Ex=<TEx,KBs,β> and fewk(ag)=wk where wk is a workstation wk=(Twk,KBwk,tk,pk) then Twk TEx, and ag has the necessary knowledge to process all the tasks that is, if tk Twk, then pk(tk) β(tk).
Definition 3.16 (Weak well-Definedness Staff)
Given an enterprise Org=(Io,BPs,Emps,WFs,WKs,fewk), the as- sociated employees are said to be weakly well defined if and only if each employee ag appointed to a given workstation has the required profile, that is if ag=<Sk,Ex,,Dy,Id>Emps with Ex=<TEx,KBs,β> and fewk(ag)=wk where wk is a workstation wk=(Twk,KBwk,tk,pk) then Twk TEx.
Definition 3.17 (Well organized workstation)
Given an enterprise Org=(Io,BPs,Emps,WFs,WKs,fewk), the as- sociated workstations are said to be well organized if and only if each workstation wk, there exits an employee ag appointed to this position, that is wk =fewk(ag).
Definition 3.18 (Strong well-definedness enterprise)
Given an enterprise Org=(Io,BPs,Emps,WFs, WKs,fewk), Org is said to be strongly well defined if and only if (i) the worksta- tions are well organized, and (ii) the employees are strongly defined that is they all have the public and tacit knowledge required for their respective positions in the organization.
Definition 3.19 (Weak well-definedness enterprise)
Given an enterprise Org=(Io,BPs,Emps,WFs,WKs,fewk), Org is said to be weak well defined if and only if (i) the workstations are well organized, and (ii) there exists at least one employee who has only the public knowledge required by his position.
Based on the human actors working in a given enterprise and their availability and the services required by customers, em- ployees involved in different workflows associated to a busi- ness process will not necessary be the same. Thus, according to their skills, the quality of service delivered may be different. The criteria for the evaluation of the quality of service will
then some time be associated with minimum values when
tasks will be processed by staff with minimum experience. More-over these values will be maximal when staff with max- imum experience has been involved in the processing of tasks. The set of quality of service associated to a given business process will therefore have two specific qualities of service Qmin and Qmax which have the following properties.
Lemma 3.9 Let Qmin = (C,Val,fqmin), and Qmax = (C,Val,fqmax), be minimal and the maximal quality of service of a business process (P, ɸ) then p = (C,V,fp) ɸ, c C , fqmin(c) ≤ fp(c), and
q = <C,V,fq> ɸ, c C , fq(c) ≤ fqmax(c).
Conclusion
The main technical content of this paper is to present a novel methodology for the modelling of business processes and workflows within an enterprise. The model is defined formally using the denotational semantics. The defined me- thodology is based on the domain and requirement engineer- ing. These two approaches enable the determination of salient concepts that are suitable for the abstraction of a problem. Hence, concepts like the environment, the context of execution of a task, the resources required for the performance of a task, the knowledge bit needed for the processing of a task by a human actor, and the quality of service expected by consumer stakeholders. These core concepts and others have been de- fined formally using the denotational semantics in order to model a business process, a workflow and enterprise.
This novel approach differs from the existing one as it does not explicitly define the dependency among tasks. Based on the task model, the relation between tasks is obtained straightforward. Another contribution of this work is the defi- nition of a link between the processing of tasks and the quality of service. This was not obvious in the former approaches de- spite the fact that the quality of service is one of the factors that allows enterprises to be competitive and to deal with chal- lenges of the network economy.
Moreover, based on the fact that, human actors are groping out of the process while others are entering, whereas those groping out, most of the time, have acquired knowledge in the processing of tasks, as a result enterprises are then forced to train the new actors in order to maintain the same level of the quality of the service. This requires additional expenditure and a decrease in productivity during the training period. In order to deal with this problem, the modeling of a business process should take into consideration knowledge suitable for tasks processing. The existing approaches for business process modeling have neglected this issue, and it becomes very diffi- cult to integrate this requirement in the resulting model. The proposed ATSERO Method tackles this issue by proposing in the definition of a knowledge repository within an enterprise based on human actors in charge of tasks processing.
Based on the notion of chain, the processing path of a busi- ness process has been laid out. Each of these paths is required to reach the least upper bound state of the environment which satisfies the associated goal of a business process. This goal is
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defined as a set of criteria that are assigned for the quality of service evaluation. From the chain concept, the well- formedness and well definedness properties of a business process have been defined. These definitions are used to show that a business process is deadlock and livelock free. The modeling is completed by giving an abstract representation of an enterprise based on business processes and human actors who deal with the processing of associated tasks in order to deliver a given quality of service. The defined models can serve as a guideline for business process and workflow model- ing within various organizations. In future works, more inves- tigations based on case studies for practical issues shall be car- ried out, after which a support tool shall be developed.
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