Dedene, Guido

English

Research Papers in Economics

Tijdschrift voor Economie en Management 
Vol. L, 4, 2005 
 
 
From Conceptual Probabilistic Behavior  
to Operational Measurements 
 
by G. DEDENE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT  
 
This paper discusses a new approach to incorporate probabilistic behavior in 
object-oriented  Business  Models.  Probabilistic  Finite  State  Machines  are 
presented and analyzed in terms of their Dynamic and Static properties. In this 
way,  conceptual  behavior  models  are  translated  in  a  precise  fashion  into 
measures that are very relevant from an operational point of view, for the 
implementation of the conceptual models. The techniques proposed here only 
represent a first step into a new area of Business Modeling.  
Guido Dedene 
KULeuven, Faculty of Economics and 
Management and Universiteit van 
Amsterdam Business School, Amsterdam, 
Nederland  
I.  INTRODUCTION 
 
Traditionally,  Object-oriented  Conceptual  Business  Models,  such  as 
developed in MERODE (Snoeck and Dedene (1998) and Snoeck et al (1999)) 
and various UML-based formalisms, represent the behavior of objects in a 
fairly deterministic way. This paper will explore some possibilities to extend 
these behavior models by including probabilities in the Finite State Machines 
(FSM) that describe the internal behavior of objects. 
This paper is written in honor of Em. Prof. Dr. J. Vandenbulcke, who 
was active particularly in Production, Inventory & Project Management (in the 
Belgian chapter of PICS) and – par excellence – in Database management 
(Vandenbulcke  (2005)).  The  approach  that  is  proposed  in  this  paper  is 
somewhat inspired by “activity on the node” versus “activity on the arrow” 
project models. It is intended as an exploration of new ways to extend the 
current frameworks for modeling the internal behavior of objects. 
The paper starts with a precise definition of the type of probabilistic 
FSM that will be analysed and discussed. Many types of probabilistic FSM 
have  been  studied  in  literature  before,  in  particular  in  Language  Studies 
(Rabiner  (1989)),  Computer  Performance  Modeling  and  in  Artificial 
Intelligence.  Most  of  the  result  which  have  been  developed  there  are  not 
straightforward  applicable  to  Business  Objects.  Hence  some  analysis 
refinements are proposed in the next paragraphs. First the dynamic behavior is 
discussed,  focusing  on  everything  that  is  related  to  events  in  the  object 
lifecycles. A very interesting result is the determination of average lifecycle 
length.  Next  the  static  behavior  is  investigated,  focusing  on  the  static 
relationships which exist in models. These results are particularly interesting 
for database operational measures. The paper concludes with a discussion with 
suggestions for further research. 
 
 
II.  PROBABILISTIC  BEHAVIOR  IN  CONCEPTUAL  BUSINESS 
MODELS 
 
As this paper tries to explore some new ideas, initially a basic example will be 
used to present these ideas. The apparent simplicity of this example should not 
mislead the reader in the applicability of the same type of analysis for larger 
systems.  
  Consider  the  following  specification  for  a  fragment  of  a  Business 
Model, adapted from a reference work on object-oriented Business Models  
(Snoeck et al (1999)): 
 
A funding organization for supporting projects receives gifts. Gifts can 
be allocated in total or partially to projects. Gifts should be certified 
(once, and only once) for tax administration reasons. Projects have a description and a budget, which may be changed from time to time. All 
elements  should  be  archived,  but  allocated parts of gifts cannot be 
archived unless the gift itself is certified 
. 
This  model  is  somewhat  inspired  also  by  a  real-life  example 
(www.cfp.be). A traditional conceptual model for this Business description 
would use the following Class-Association diagram (in UML-notation format): 
 
     
   
 
 
The relationships express that a gift may be allocated (partially) to 
many  projects,  and  projects  may  receive  money  from  various  gifts.  The 
Business events (which can also be considered as the Elementary Business 
Use  Cases)  should  be  consistent  with  this  diagram  (Snoeck  and  Dedene 
(1998)), and results in the following Class-Event Association Table, which 
indicates which classes are participating to what types of events: 
 
 
 
 
 Each event has a number of participating object types, where a C 
indicates that a new object is created, a M denotes a (potential) modification 
of an object and an E indicates that this event terminates the life-cycle of an 
object.  
From  this  table  the  life-cycle  models  follow  in  a  straightforward 
fashion. Allocation and Project have trivial life-cycles: they are created and 
ended as show in the previous table. The life-cycle of a Gift is somewhat more 
complicated, due to the certification event, which may only happen once, and 
the particular situation on the archiving of Allocations. 
  Using stratified Finite State Machines, the life-cycles for the different 
Business objects are the following: 
 
 
 
 
 
 
 
 
One  way  these  lifecycle  models  can  be  improved  with  additional 
information is by means of adding probabilities to the state transitions. In first 
instance the lifecycle of Gift will be dressed with probabilities now. Suppose 
the following probabilities for the other state transitions are known:  
 
 
 
The probabilities should be interpreted as follows. In the first state, 
the  probability  of  occurrence  of  a  “certify”-event  is  0.4  whereas  the 
probability of an “allocate”-event is 0.6. It is clear that the sum of all outgoing 
probabilities should be equal to 1 for any given state. In this example the 
probabilities are fairly arbitrary although not unlogical, as will be seen clearly 
from  other  analysis  results  in  this  paper.  It  is  clear  that  more 
“archiveAllocation”-events  occur  after  the  “certify”-event  happened  than 
before it happened. However the numbers have deliberately been kept simple, 
just to present the ideas. 
The above probabilistic FSM can also be seen as a Markov chain, but 
it is quite different from the type of Markov chains that are used in Computer 
Performance Evaluation, for example. The main reason is the appearance of 
an explicit “start” state, which is actually not a really state, because it is the 
“nill” state before an object exists. So actually, an object is never in that state, 
but it is an explicit part of the FSM. Also Business Object lifecycles typically 
have a clear end-state. Many of the traditional Markov and Hidden Markov 
Chain analysis techniques are less applicable to this type of model. The next  
paragraphs will explore how operational measures can be derived from the 
above probabilistic FSM. 
 
 
III.  DYNAMIC OPERATIONAL MEASURES 
 
The first type of analysis is related to the event behavior of the objects. In this 
way it can be seen as a dynamic operational view. For the sake of analysis, the 
FSM will be made somewhat more abstract, renaming the states and the events 
as follows: 
  
 
A.  Steady State Probabilities 
 
If pi denotes the steady state probability of being in a state i, and aij denotes 
the probability associated with the state transition from state i to state j in the 
FSM, the steady state probabilities are the solution of the following equations: 
 
   ´ =
j
ji j i a p p   (state balance equations) 
  1 = 
i
i p     (normalization condition) 
 
In this case the transition probability matrix is the following: 
 
 












=
0 0 0 0
3 . 0 7 . 0 0 0
0 3 . 0 7 . 0 0
0 0 1 0
ij a    
 
The steady state solutions in this case are given by the following vector:  
 
    [ ] 115 . 0 385 . 0 385 . 0 115 . 0 = p  
 
So far this is a classical Markov chain analysis. However in this case 
the state  p0 is not relevant since it is the state in which the object must still be 
created.  The  other  states  are  the  real  “existing”  states  of  the  object  Gift. 
Observe  that  the  last  state  p3  probability  is  equal  to  the  first  state  p0 
probability, which is logical. It should also be clear that in a conceptual model 
an  object  that  finished  its  lifecycle  is  ready  to  be  deleted,  but  should  not 
necessarily  be  deleted.  This  aspect  will  be  covered  again  in  the  database 
related measures.  One solution consists of renormalizing the state probabilities for all 
the  states  different  from  the  start  state.  In  this  case,  the  relevant  state 
probabilities are given by: 
 
    [ ] 130 . 0 435 . 0 435 . 0 = p  
 
which shows that there are as many Gifts certified as not certified yet.  
 
 
A.  Event visit models 
 
The next kind of analysis requires a transformation of the probabilistic FSM 
into an event visit model, which shows the “events on the nodes” instead of 
“on the arrows” as it happens in an FSM. This model shows the probabilities 
of a visit to an event after a previous event. Using a straightforward heuristic 
(Rabiner (1989) and Menascé and Almeida (2000)), the following shows the 
transitions between the various events in the life-cycle of a Gift: 
 
 
 
Observe how the outgoing state transition probabilities sum up to 1 
for each event. The average number of visits to an event i, denoted by vi is 
again equal to the sum of the number of visits to all states multiplied by the 
transition  probability  bji    from  each  of  the  other  states  to  state  i.  In  this 
situation, the first event a is the entry event which has trivially one visit, and 
the terminating event e has no next state. So the set of equations to be solved 
is: 
 
  1 1 = v    
-
=
´ =
1
1
n
j
ji j i b v v   i = 2,…,n-1 
 
if n denotes the total number of events. In this case this leads to the following 
average number of visits: 
 
  [ ] 1 333 . 3 1 333 . 3 1 = v  
 
Some elements are interesting and significant to notify: 
The average number of visits to the certify (c) event is equal to 1, 
which is actually as to be expected, because every Gift can only be certified 
once.  
The number of visits (per Gift) to the allocate (b) event is equal to the 
number of visits to the ArchiveAllocation (d) event. This is again very logical 
since every Allocation that is created once must also be archived once.  
There  are  on  average  3.333  allocations  of  (portions)  of  Gifts  to 
Projects.  Of  course  this  is  only  an  “average”,  but  still  an  interesting 
observation. 
  A most interesting measure is the “average length”, which gives the 
total number of visits to the events in the object lifecycle. In this case for a 
Gift it is equal to 
 
  666 . 9 = =
i
i v L  
 
So, on average, almost 10 events happen in the lifecycle of a Gift 
Business object.  
  In other cases it can be interesting, for example, to get the buy-to-visit 
ratio’s (assuming the life-cycle contains a “buy”-event) on the basis of the 
number of event visits. 
 
 
C.  Resource usage models 
 
Once the event visit models have been analyzed, interesting capacity planning 
models  can  be  developed.  The  events  in  the  previous  models  are  –  by 
definition  –  Business  events:  they  happen  in  the  Business  reality.  In  an 
activity-based approach to (service-oriented) capacity planning (Dedene et al 
(2004)), Business events should be translated into standard services. Suppose 
two standard services have been defined: 
 
·  Web Server (WS) : a Web Application Server. 
·  Database Server (DS) : a separate Database Server 
 Every  Business  event  can  be  characterized  by  its  Services  Interaction 
Diagram (SID), which indicates the visit scenario’s to the various standard 
services. Suppose the Allocation of a (portion) of a Gift has the following 
SID: 
 
 
 
In this diagram C denotes the “client”. In this case the Web Server 
rejects  (on  average)  10%  of  the  Allocation  request  (purely  for  Internet 
rechnology reasons, other Business related scenario’s must be modeled in the 
Business object lifecycle). The Database Server is activated on average 0.9 
times, namely in the sequence C – WS – DS – WS – C . The Web Server is 
activated twice in the same sequence (with a probability 0.9) and one time in 
the  other  sequence,  so  the  average  number  of  times  the  Web  Server  is 
activated during an allocation = 2 x 0.9 + 1 x 0.1 = 1.9 times. 
  As a result there are for every Gift on average 1.9 x 3.33 = 6,33 
activations of the Web Server. If it is know, for example, that typically 10,000 
Gifts  are  created  per  month,  the  allocations  alone  will  generate  63,300 
activations of the Web Server (but maybe not necessarily during the same 
month). If the same analysis is performed for the other Business events, the 
total  impact  on  the  Web  Server  and  Database  Server  services  can  be 
determined and translated into Service Demands on CPU and IO-devices. 
 
 
IV.  STATIC OPERATIONAL MEASURES 
 
Another type of analysis may focus more on the objects themselves instead of 
the events. This can be seen as a more static operational view.  
 
 
A.  Average cardinalities 
 
The Class-Association diagram indicates a one-to-many relationship between 
Gifts  and  Allocations.  Many  database  resource  management  tools  require 
database administrators to determine the actual average cardinalities. In this 
case, they follow from the probabilities that have been analyzed before: for 
each Gift there are on average 3.33 Allocations, which is in this case at least 
an upper bound for the average cardinalities.   Indeed, another factor that plays a role is the speed at which archived 
objects are actually removed from the database. If the speed is the same for all 
objects, that 3.33 would indeed be the average cardinality. If however, for 
some reason, Gift are deleted slower than Allocations, the average cardinality 
is indeed lower. However, referential integrity will require that a Gift cannot 
be deleted as long as there are Allocations that are dependent on it, which 
implies  that  typically  Gifts  will  not  be  deleted  faster  than  Allocations,  in 
general. 
 
 
B.  Database residence times 
 
The  steady  state  probabilities  also  provide  usable  input  for  estimating  the 
average database residence time for objects. In the case of Gifts, the objects 
may reside under 3 states in the database: 
 
·  Gifts that are created, but not yet certified  
(on average with a probability 0.435) 
·  Gifts that are certified but not yet archived  
(also with a probability 0.435) 
·  Gifts that are archived but not yet removed from the database  
(with a probability 0.130). 
 
So the average probabilities under which we will find the objects in the 
database are known from this. 
  Another useful information is the average time between two relevant 
events. In this case, suppose it is known that 
 
·  The average time between creation of a Gift and its certification is 4 
months. 
·  The average time between certification of a Gift and its archiving is 
20 months. 
·  Suppose  archived  Gifts  are  kept  still  24  months  in  the  database 
before they are actually removed. 
 
In this case this implies that every Gift resides on average 48 months in 
the database, in one of the 3 states that were mentioned before. A reverse 
engineering of the actual states of the objects in the database may help to 
refine the probabilistic behavior models 
 
 
V.  DISCUSSION AND FURTHER RESEARCH 
 
This paper was only a first exploration of some extensions to current object-
oriented conceptual modeling techniques to incorporate probabilistic behavior in  the  models.  For  sure  this  type  of  extension  is  needed  to  build  realistic 
Business Agents, i.e. active objects for which probabilistic behavior is evident.  
 
Many topics proposed here require further research, such as: 
 
·  Simple  algorithms  for  the  translation  of  Probabilistic  FSMs  into 
Event Visit models, and the other way around.  
·  So far, only “correct” probabilistic behavior was included, leading – 
for example – to only one and exactly one “certify” event per Gift. In 
reality, errors can happens, and erroneous multiple certifications may 
happens  are  events,  although  they  must  be  intercepted  by  the 
Business model implementation. Including this aspects will further 
refine the SIDs for the events. 
·  Algorithms  for  the  extraction of the probabilities and/or the event 
visits from actual user behavior. 
·  The  time  series  aspects  of  the  models  need  a  detailed  further 
investigation. In particular bursting phenomena on some events may 
destroy completely the meaning of “average” results. 
·  The detailed translation into capacity planning models, elaborating 
more in detail some models of (Menascé et al (2000)). 
·  The application of the same results in a distributed Service-Oriented 
Architecture (Lemahieu et al (2005)) 
 
 
REFERENCES 
 
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Snoeck M., Dedene G., Verhelst M. Depuydt A., 1999, Object-Oriented Enterprise Modelling 
with MERODE, (Leuven University Press). 
Vandenbulcke J.A., Lemahieu W.O., 2005, Databasesystemen voor de praktijk, (ten Hagen & 
Stam Uitgevers).  
Rabiner L.R., 1989, A Tutorial on Hidden Markov Models and Selected Applications in Speech 
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and Capacity Planning, (Prentice Hall PTR Upper Saddle River, NJ). 
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Operational  Business  –  ICT  alignment,  Proceedings  of  the  11th  European  Conference  on 
Information Technology Evaluation, (Amsterdam, The Netherlands). 
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2005, Coordinating COTS Applications by Means of a Business Event Layer, IEEE Software 
22; 4. 

A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition,

Coordinating COTS Applications by Means of a Business Event Layer,

Databasesystemen voor de praktijk, (ten Hagen & Stam Uitgevers).

Existence Dependency: the Key to Semantic Integrity between Structural and Behavioral Aspects of Object Types,

Object-Oriented Enterprise Modelling with MERODE,

Scaling for E-Business: Technologies, Models, Performance and Capacity Planning, (Prentice Hall PTR Upper Saddle River,

From conceptual probabilistic behavior to operational measurements.

https://lirias.kuleuven.be/bitstream/123456789/122777/1/TEM_4_05_Dedene.pdf

From conceptual probabilistic behavior to operational measurements.

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Research Papers in Economics