=Paper= {{Paper |id=None |storemode=property |title=Human Behaviours Simulation in Ubiquitous Computing Environments |pdfUrl=https://ceur-ws.org/Vol-627/mass_6.pdf |volume=Vol-627 |dblpUrl=https://dblp.org/rec/conf/mallow/Garcia-ValverdeCSB10 }} ==Human Behaviours Simulation in Ubiquitous Computing Environments== https://ceur-ws.org/Vol-627/mass_6.pdf

Human behaviours simulation in ubiquitous
computing environments
Teresa Garcia-Valverde, Francisco Campuzano, Emilio Serrano and Juan A. Botia
University of Murcia, Spain. E-mails: {mtgarcia,fjcampuzano,emilioserra,juanbot}@um.es

Abstract—Ambient Assisted Living (AAL) systems’ main goal stage prior to deployment is presented. The main idea behind
is to augment live quality of elderly people, by using ICT based this is that the user is modelled with a computational model
systems. In this paper, we are concerned with the artificial and integrated into an ABSS model which incorporates as a
reproduction of a physical environment (i.e. a house) and an
elder (i.e. the attended) living in such environment. An agent simulated artifact, the environment, the hardware (i.e. mainly
based social simulation system is used for such purpose. Such sensors and interfaces with the user) and integrates the real
simulator will allow the integration of ubiquitous computing software (i.e. services and applications). The real software is
appliances, services and applications in such environment. A precisely the SUT here.
realistic reproduction of human behaviour in the simulator helps, The proposal is articulated by means of a methodological
in this context, in the validation of silent monitorisation, diagnosis
and action based applications. Proofs are given in the paper work. Such a methodology is a set of procedures which
which demonstrate the level of reality reached by comparing the guides the developer in the definition, creation, testing and
artificial behaviour with real ones. validation of the AmI system. It is based on a methodology
Index Terms—Ubiquitous computing, Ambient Assisted Living, previously described by Gilbert et al. [1]. It comprises the
behaviour simulation, user modelling. creation of the necessary ABSS models and how they should
be employed to find errors in AmI services. The application
I. I NTRODUCTION of the methodology is exemplified in a real domain. The
The main thesis presented in this paper is the following: application domain is AAL (Ambient Assisted Living). An
agent based social simulation (ABSS) [1] may help in the AAL system is an ICT based solution which is devoted to
engineering of Ambient Intelligence systems. ABSS is a augment quality of live for elderly people. In this case, the
simulation paradigm in which the focus is put on the definition interest is focused on a system called Necesity [4]. It is
of the separate components of the simulation in an isolated based on a sensor network deployed through the house and
manner. In such simulation runs, the emergence of behaviours a central processing unit. Sensors include presence, pressure
is the main subject under study. And the metaphor of agent is and open-door. The system is designed to work on single
used for specification of single components and interactions person environments (e.g. an elderly who lives alone and
among them. An ambient intelligence [2] system is a set of independently in his house). It is in charge of monitoring
appliances, services and applications which silently surrounds activity regime of the elderly 24x7 in a manner that when
and interact with the user in an intelligent manner. In such his activity pattern is anomalous, an emergency response is
kind of systems, the user is the central entity of the model. started. The rest of the paper will demonstrate that an artificial
Starting from the user, services and applications are built. reproduction of a house, sensors and the attended, together
A main difficulty one may find in the development process integrated with the real software, helps in the fine tuning of
of an AmI system is that of testing and validation. Testing is the activity pattern management software.
the process of executing a program with the intent of finding The rest of the paper is structured as follows. Section II
errors in the code [3]. Such errors must be debugged [3]. Some introduces the methodology used for the engineering of AmI
of the errors may be found by using a Unit approach with the services. Section III introduces the computational models em-
system under test (SUT). Common errors which are found ployed to artificially reproduce the behaviour of the attended.
in this stage are related to common programming mistakes Such behaviour is based on a probabilistic and hierarchical
(e.g. values of variables out of range, shoddy checking of automata which governs the activity and location of the
return values from methods and so on). Thus, robustness of modeled elderly in each instant of time. In section IV, the
the program is a must here. But a more elaborated test set may validation approach is presented. It is based on the statistical
be defined in order to assess the functionality of the system contrast of artificial data traces obtained by simulating the
(i.e. it behaves as expected). But, if the main issue in AmI automata just mentioned with similar traces coming from real
systems is a smooth interaction with the user, an Unit based users in similar context.
approach is no more valid here. It is clear that the user, or
at least a model of the user, should be incorporated in the II. AVA, AN AGENT BASED METHODOLOGY FOR THE
development process in order to measure to what extent, the VALIDATION OF A M I SYSTEMS
SUT is behaving as expected when interacting with him. In This section explains an agent based methodology for the
this paper, an approach to test and validate AmI systems in a validation of AmI systems called AVA. This methodology
paper discusses the performance of these steps for an AAL
system for elderly people
The development of an AmI system model is performed
in step 5. The model design associates the real system with
a representation of this system (the model) [6]. Here, the
AmI application must be modelled but also the users and
the environment. These models are necessary to validate the
AmI application because they interact with it. Moreover, a
realistic validation of the application needs realistic models
for users and environment. Therefore, models must describe
reality before being as simple as possible [7]. Section III
explains the construction of a user model for an specific AmI
application.
Step 6 deals with the implementation of the AmI system in
a simulation language. The implementation from the concepts
of the model is not a trivial task [6]. A general programming
language or a specific one of the available frameworks for
the development of ABSS can be used for the construction of
the simulation. The second option is much more convenient
Fig. 1. AVA, An Agent based methodology for the Validation of AmI systems because several of the typical tasks in the construction of
expressed as a flowchart
ABSS have been included in this kind of software packages
[1]. Examples of these tasks are scheduling agents’ actions
or building basic environments. The web of the Open Agent
proposes the development of ABSS in order to validate AmI Based Modeling Consortium2 nowadays lists 22 of these
applications. AVA is an extension of the methodology pro- frameworks. Section III shows the use of a specific software
mulgated by Gilbert et al. [1] for the development and use of package for the implementation of a realistic environment
general ABSS. The two main innovations with regarding the model: 3D Sweethome.
classical methodology by Giltber et al. are: (1) the existence
After building the simulation, this must be executed (step
of a step to generate simpler simulations and (2) the con-
7). Quick, cheap and numerous experiments can be performed
sideration of including real elements in the simulation to get
thanks to the ABSS. These executions produce large amounts
more realistic results. This section will show the advantages
of data regarding the behaviour of users, environment and
of these innovations for the specific purpose of validating
application models. Forensic analysis, step 8, is an offline
AmI applications. The AVA methodology is expressed as a
analysis to be conducted on the data stored from the pre-
flowchart in figure 11 .
vious step. The analysis should consider whether the AmI
Gilbert et al. [1] defines the target of a social simulation as application functionality is correct. Furthermore, this step must
some “real world” phenomenon which the researcher is inter- validate that the behaviour of users and environment models
ested in. The AVA methodology is proposed to validate an AmI is consistent with the observed reality (steps 2 and 3). Without
application including their interactions with the environment this validation, the theories generated from simulations have
and users. Thus, AVA starts considering an AmI target (step 1) no relation to reality (as they are based on non-descriptive
which includes an environment, users and an AmI application models). Therefore, the functionality of the AmI application
which may be finished or at an advanced stage of development. model is linked to the users and environment models. Section
Typically, the use of ABSS to generate knowledge involves a IV deals with the validation of the users model for an AAL
necessary familiarization with the domain in the first step. This system
is required to generate models of the target in the following One of the innovative points in the AVA methodology is the
steps of the methodology [1]. The main elements to be studied use of simple simulations as a means to validate descriptive
in an AmI system are: the environment (step 2), users (step simulations. Step 9 checks if any elements of the simulation
3) and the AmI application (step 4). Note that while the are too complex. In this case, complexity means that it is
environment and the user are inputs, the application system is difficult to assess whether the behaviour of an element is the
a process. In principle, the environment and users are external expected one. For example, some behaviours of users can be
and do not support changes. On the other hand, the AmI so complex that they need to be evaluated in isolation. An
application can be modified. This application will be refined example of this type of behaviour would be the resolution of
along the iterations of AVA to get a realistic validation. This collisions on the motion of a large number of agents. This
1 The flowchart uses standard elements of classic flowcharts [5] as flow
behaviour is a problem to be studied itself and its validation
of control (represented as arrows), processes (represented as rectangles),
would be much more complicated with additional elements in
decisions (rhombus), input/output (parallelograms), start and end symbols
(ovals) and predefined processes (rectangles with vertical lines at the sides). 2 OpenABM Consortium website: http://www.openabm.org/
the simulation (more users’ behaviours, a realistic environment
model, a realistic model of an AmI application, etc). In these
cases, the methodology proposes to consider these complex
elements as an object of study itself (step 10) and repeat the
AVA methodology for them (step 11). The reuse of models
and code in this new iteration will be direct because a more
descriptive simulation is available as result of the previous
steps. Once the complex element is validated in a simpler
simulation, which is the final result of the methodology, the
next step for the overall simulation (step 12) can be performed.
Step 12 checks if the developer has found errors in func-
tionality. If that is the case, the AmI application of step 4 must
be modified in order to correct these errors and the process
repeated. Besides the primary objective (validating the AmI Fig. 2. A plane model in Ubik’s editor and its 3D representation
application), is typical to find bugs of previous steps at this
point in the form of implementation failures or unrealistic
models. A. Environment Modelling
The final decision, step 13, checks if actual elements of For Multi-Agent Based Simulation (MABS), it is available
the AmI system can be connected to the simulator. The AVA Ubiksim4 , a simulator developed by University of Murcia
methodology proposes to inject or connect real elements in that works over MASON5 . It has integrated an environment
the simulation progressively in order to make more realistic modeling tool based on SweetHome3D6 , an application con-
validations3 . This process is called “reality injection” and the veniently adapted for modelling attended people and their
basic idea is that real elements can coexist with simulated environment. It is possible to create houses over a 2D plane,
elements. After connecting real elements, the methodology also it offers a 3D navigable view (figure 2). This view is used
must be repeated from step 4 to improve the application and for simulation’s visualization at real time.
the models. The result is an exhaustive validation which is In the physical environment generated by using the Ubik
as realistic as possible. The obvious question is why models editor, a simple house (see figure 2) with a kitchen, a bath-
and simulations are necessary if real elements (as real users) room, a bedroom and a living room is modelled. Presence
can be injected. The answer is that a model, by definition, sensors are included in every room of the house. And a sensor
is somewhat easier to study than the modelled reality. The for open door (it is necessary for knowing when the elder
purpose of including real elements in simulations is to improve leaves the home) is also included in the outdoor. When a
the realism of the models. Then, in subsequent iterations, the simulation is run, the person moves in the house and stimulates
real elements will not be included because the pure simulations sensors when he is detected by them. Such sensors, through
allow faster and cheaper tests. the ubiquitous computing software, generate events. And these
Finally, if models are descriptive enough, the bugs found in events generate log entries. Such simulated log entries are used
the functionality of the AmI application model will correspond afterwards to check if the virtual elder behaves in a realistic
to failures of functionality in the real AmI application. These manner (see section IV).
failures should have been corrected in each iteration of the Notice that log entries (both in the simulator and the
AVA methodology. Therefore, the result of the methodology real setting) are generated by the same monitoring service
(step 14) is that the AmI target is exhaustively validated. which continuously checks if the elder may be suffering some
problem, by using a pattern recognition approach (more details
III. R EALISTIC BEHAVIOUR MODELLING on this may be found in [4]) on the events coming from
In this section, the particular models used, in the application sensors. In the first case, the person is virtual, in the second
of the AVA methodology in the AAL domain, are introduced. it is real. But the monitoring service is the same.
In section III.A, it is presented how the physical environment
(i.e. the house and furniture) and sensors were defined. Section B. Behaviour Modelling
III.B refers to the production of realistic computational models The target of the modelling activity is a typical aged person,
for elders living in such environment and making sensors to who lives independently and alone in his own house. As
react on their presence. Having such models (i.e. the house, he lives alone, the following situation may occur: he may
sensors and persons) within a simulation, and its integration suffer some health problem and stay immobilised in the
with the ubiquitous computing software, such software can be floor for too much time before anybody comes and notices
tested.
4 UbikSim: http://ubiksim.sourceforge.net, last access: 20 May 2010
3 Notice that this not involves necessarily a Participatory Multiagent Simula- 5 MASON Toolkit: http://cs.gmu.edu/∼eclab/projects/mason/, last access: 20

tion. The real elements do not have to be humans playing the role of simulation May 2010
components. These elements can be software applications, hardware or even 6 Sweet Home 3D: http://www.sweethome3d.eu/es/index.jsp, last access: 20
parts of the environment. May 2010
that something is wrong. But it is possible to develop an
ubiquitous computing system which detects it and generates
some emergency response process [4]. By following the AVA
methodology, we may use a simulated elder within a simulated
environment to test such system before it is deployed in a real
environment for pilot testing. Such simulated elder should be
necessarily simulated along the 24 hours of the day, repeatedly
for a determined number of weeks. For this, it is assumed
that the day is divided into time slots (i.e. morning, noon,
afternoon and night). In each time slot, it is also assumed that Q = {a0 = N ormalT ime, a1 = M edicationT ime,
the simulated person behaves specifically for such slot. a2 = M ealT ime, a3 = SleepT ime, a4 = Anomalous}
The behaviour of simulated people are modelled proba- (a)
bilistically. In this approach, behaviours are defined as sit-
uations the agent should play in each moment. Transitions
between behaviours are probabilistic. The underlying model
is a hierarchical automaton (i.e. in a higher level there is a
number of complex behaviours that the agent may play and
once it is in a concrete state, within the state there is another
automaton with more simple behaviours). So, the modelling
of each behaviour is treated separately and the modeller is
abstracted of unnecessary details. So, in the lowest level (basic
actions), each state is atomic. An agent never conducts two
behaviours of the same level simultaneously.
The behaviours used for modelling elders are of three types:
• Monotonous behaviours: the kind of behaviour the elder
manifest always approximately in the same time slot, and
on a daily basis (e.g. sleeping, having meal, medication
and so on). Q = {a00 = SpareT ime, a10 = M edicationT ime,
• Non monotonous behaviours: the kind of behaviour the a20 = M ealT ime, a30 = SleepT ime, ax1 = T oiletT ime,
elder usually manifest, not bounded to a concrete time a02 = ShowerT ime, a03 = CleanT ime}

slot, and repeated within a non constant period (e.g. going (b)
to the toilet, having a shower, cleaning the house and so
on).
Q = {a200 = GoingT oF ridge, a201 = GoingT oCooker,
• Any time behaviours: such behaviours will sometimes
a202 = Cooking, a203 = GoingT oT able, a204 = Eating}
interrupt others the elder is already doing, and will be (c)
generated regardless they were already generated in a
temporal proximity (e.g. in his spare time). Fig. 3. (a) Level 0 automaton, (b) Level 1 automata, (c) Level 2 automaton
for state a20
A probabilistic automaton [8] is defined as the quintuple
(Q, V, P (0), F, M ) where Q is a finite set of states, V is a
finite set of input symbols, P (0) is an initial state vector,
F is a set of final states and M is a matrix that represents of the exponential family [9], [10]. Section IV defines all
probabilities of transition for every state. In this definition, distribution functions used.
transition’s probabilities depend on time. According to differ- Notice that monotonous behaviours must be activated at
ent daily time slots, the agent’s behaviour acts on a different specific time hours or within specific time intervals. For
pattern. There are time slots for eating, sleeping and taking example, in the case of MedicationTime, a new necessity of
medication (Monotonous behaviours). changing to such state will be generated exactly at the time to
Notice that, when the elder is at any state, the necessity take medicines. In the case of MealTime and SleepTime, the
of changing to another state may arise. But this is not done necessity is generated within a time interval. The distribution
immediately. Moreover, a number of different changes (i.e. that models these transitions is bounded in this time slot. It
transitions) may be pending simultaneously. Thus, a list of must be assured that agent eats and sleeps every day, because
pending tasks (i.e. or events) is maintained. Such tasks are of that, if not transition is generated into the time slot, a
ordered by a static priority (e.g. going to the toilet goes before transition is generated at the end time.
cleaning). To provide more realism, an automata hierarchy is intro-
For generating transitions in real time, probability dis- duced representing each state by lower level automata which
tribution functions are used according to the type of the define more specialized behaviours.
behaviour and its features. These distributions are member As shown in figure 3(a), in level 0 the initial state
is a0 =NormalTime. For every one of the other states 1 Let pt be a list of pending tasks ordered by priority
{a1 =MedicationTime,a2 =MealTime,a3 =SleepTime} exist 2 Let states be a list with all posible automata’s states
3 Let times be a list of time instants when transitions
a list of times generated by a probability function. When a 4 are going to be generated
time counter arrives to one of these times, a transition to state 5 Distribution Functions to model the ocurrence
6 of monotonous behaviours:
owner of the list is added to pending tasks list. When the action 7 Let mb be the function to model monotonous behaviours
is finished, the automaton returns to initial state if there is not 8 Let nb be the function to model non monotonous behaviours
9 Let ab be the function to model anytime behaviours
another pending task. The final state is a4 =Anomalous, if it 10
is reached, the execution will be stopped. 11 //Instants of time initialization
12
In level 1 (figure 3(b)) non monotonous behaviours are 13 for all s in states do
represented. There is an initial state in every refinement where 14 if isAnytime(s) then
15 times(s)<-ab()
the person does the main task of the upper level (eating, 16 else if isMonotonous(s) then
sleeping or taking medication). The state ax1 =ToiletTime is 17 //Initial and final instants of bounded time slot
18 i <- ini(s)
considered in every refinement of level 0. However, the states 19 e <- end(s)
a02 =ShowerTime and a03 =CleanTime only may be activated 20 times(s)<-mb(i, e)
21 else if isNonMonotonous(s) then
in normal state of level 0. 22 times(s)<-nb()
In the lowest level (level 2), the new automata define some 23 endif
24 endfor
specialized actions refining every state of level 1. These new 25
states do not give relevant information, but the agent gains 26 actualTime <- 0
27 //actual state is defined by 3 numbers, one per level
more realistic behaviours. 28 level0 <- 0
With the sequence of actions in figure 3(c) the person cooks 29 level1 <- 0
30 level2 <- 0
before eating. It refines state a20 of level 1, the agent is not 31 actualState<-newState(level0,level1,level2)
going to be static in the kitchen, because it must be going to 32
33 //Once initialized the times, the automata begin to move
different places and spends some time in every state. 34
In figure 4 a base implementation for agent’s behaviour is 35 //If an anomalous state is reached, the execution stops
36 while(level0(actualState)<>4)
presented. First of all, all possible automata’s states are iterated 37 //If actual task ends, initial state is activated
for initializing lists which contain time instants (lines 13-24). 38 if timeLeft(actualState)=0 then
39 actualState <- newState(0,0,0)
These time instants are generated by a probability distribution 40 endif
function, and they represent when a transition to its associated 41 //If next state has higher priority than actual state,
42 //actual state becomes a pending task and it is stored
state is going to be launched. After of that, the automaton 43 //in pt
begins to run. At every time instant, if actual time is equal 44 if (size(pt))>0
45 nextState <- first(pt)
than first item of a time list, a transition is added to pending 46 if priority(nextState)>priority(actualState) then
tasks list (lines 57-60). When there is one state with higher 47 add(pt,actualState)
48 actualState<-nextState
priority than actual state in pending tasks list, a transition is 49 remove(pt,nextState)
also generated. Then, if actual state is unfinished, it is stored 50 endif
51 endif
as a pending task and a new state is reached (lines 46-50). 52 for all s in states do
When this new state is finished, leaved state may be resumed. 53 time <- first(times(s))
54 //If actual time matches first time instant in
The configuration parameters for the whole simulation in- 55 //times, the task associated with this time instant
volve: 56 //is added to pending tasks
57 if actualTime=time then
• Temporal limit in every room before entering in anoma- 58 remove(times(s),time)
59 add(pt,s,priority(s))
lous state (tmax ) 60 endif
• The probability distribution parameters according to the 61 endfor
62 actualTime <- actualTime + 1
kind of behaviour 63 //Decrement remaining time for finishing actual task
• Time slots of routinary temporal behaviours, like eating 64 time <- timeLeft(ActualState) - 1
65 setTimeLeft(actualState, time)
or sleeping (inis , ends , s ∈ M ealT ime, SleepT ime) 66 endwhile

IV. VALIDATION OF THE APPROACH
Fig. 4. Realistic behaviour implementation
From section II, it is clear that user modelling is a means for
testing AmI services and applications without a real environ-
ment. This task is performed in the third step of the AVA
methodology. Regarding to the validation, other important A. Data Preprocessing
steps within AVA are the steps from 5 to 8. Model validation Activity data from real users were obtained within a pilot
is needed in order to show that models are able to describe project devoted to the validation of the Necesity system.
the users’ behaviours. The rest of the section shows how the Around 25 users, all elderly people living independently, were
model validation has been approached. But basically, activity used in such Pilot project. In this paper, data coming from
data from real users is compared (in statistical form) with the three users, under monitorisation during two months, were
same type of data produced by the artificial models. used. Data is in the form of a Necesity log. The logs offer the
possibility to represent where the user is, at any moment, at
the house (including also if he leaves the house or he is seated
or sleeping). Thus, three different data sets, with log entries
corresponding to sensor events are available. These data sets
need further processing.
Validating the artificial models is assuring that the right
probability distribution function is used to reproduce the
transition between the different states (i.e. behaviours). Thus,
data series are obtained from log data as they were a random
number series generated by the corresponding probability
distribution. Such series are used afterwards in a goodness of
fit test. For example, in case of the non monotonous behaviours (a)
and anytime behaviours, preprocessing the log data involves
the extraction of the time series of the moments in which each
event is produced. These time series only include values within
the typical awake period of the corresponding user. Obviously,
while the user are sleeping, his daytime routines change.
The data preprocessing for the monotonous behaviours is
slightly different. This kind of behaviour is usually produced
in a bounded time slots. For example, having dinner, having
lunch or sleeping are behaviour which occur during specific
time periods of the day. So, the preprocessing involves the
extraction of the behaviours events inside the time slots. The
time slots can be slightly different for each person, but it is
possible to define an approximation of them which will be (b)
valid for all (see in section III the configuration parameters).
Finally, in each slot time, the time intervals between each
ocurred event are measured. The extracted time series are
composed of these time intervals.
B. Model Diagnosis
Validation is one of the most important issues in a sim-
ulation system. Validation consists in the determination that
the simulated model is an acceptable representation of the
real system, for the particular objectives of the model [11].
There are many techniques for validating simulations [11],
[12], and specially, for validating agents based on simulated (c)
models [13].
The models which describe social processes, as the model
proposed here, are generally hard to validate. In this approach,
the behaviour is probabilistically modelled. However, some
statistic tests should be done to assume that a probabilistic
model is reasonable to explain the data. This process is called
model diagnosis. And this section is devoted to make the
diagnosis of the models presented above. The most serious
problem that one usually faces in this kind of validation is the
lack of real data [14]. However, in this work the data from the
Necesity project is available and can be used.
From these preprocessed data, some histograms for different
behaviours and people are shown in Fig. 5. The sample (d)
density is shown with a black line. The dashed line shows Fig. 5. (a) Minutes between 21:00 hours and the instant the attended C goes
the probability density function of the theoretical distribution to bed, (b) Time between dinners for attended B, (c) Time between uses of
the toilet for attended A, (d) Time between spare time for attended A
that models that behaviour.
Graphs 5 (a) and (b) show two monotonous behaviours,
sleeping and having dinner (having lunch is similar). In these
kinds of behaviours the event that raises the behaviour occurs
during a time interval. The interval is usually the same for a specific distribution. It is a form of hypothesis testing where
each attended person, i.e., a person usually goes to sleep or the null hypothesis says that sample data follows the stated
to have dinner at the same hours. Because of this, the curve distribution. The hypothesis regarding the distributional form
of the behaviour can be fitted to a gamma distribution. The is rejected if the test statistic, Dn , is greater than the critical
gamma distribution is usually employed as a probability model value obtained from a table, or, which is the same, if the p-
for waiting times, in this case, the waiting time until the next value is lower than the significance level. The significance
event of the behaviour. So, a gamma distribution is suitable level is fixed in this work at 0.05, which it is the value usually
for modelling monotonous behaviours. referred in statistical literature.
A kind of non monotonous behaviour, i.e. going to the toilet, Table I shows the p-values obtained from the K-S test for
is shown in Fig. 5 (c). In this case, the behaviour is fitted with each validated behaviour with the adequate distribution. The
an exponential distribution. Non monotonous behaviours are null hypothesis is that the behaviour sample data come from
also waiting time models, but they are defined in wake periods. the stated distribution and it is rejected if p-value is lower than
This is a special case of the gamma distribution which can be the significance level.
modelled with an exponential distribution.
Finally, the group of anytime behaviours are behaviours Behaviour
Person Sleep Dinner Eat Toilet Spare time
which will be often interrupted for the other behaviours. A 0.404 0.311 0.361 0.111 0.086
Because of this, size of intervals in an anytime behaviour B 0.488 0.467 0.542 0.079 0.108
are small due the interruptions. This causes the characteristic C 0.337 0.489 0.575 0.137 0.103
curved heavy-tailed distribution, specifically, the Pareto II TABLE I
distribution, also known as Lomax distribution. P- VALUES
Gamma, exponential and Lomax distributions are members
of the exponential family of probability distributions. Actually,
they are special cases of the beta prime distribution (also From these results, none of the stated null hypothesis can
known as beta distribution of the second kind, Beta II). The be rejected. Therefore behaviour of the attended people could
Beta II distribution nests many important distributions as the be fitted by the specified distribution, as it is described above.
gamma, the exponential or the Lomax distribution. The gamma
V. R ELATED WORKS
and the Lomax distributions are special cases of Beta II. On the
other hand, the exponential distribution is a special case of the Various approaches have been proposed to create au-
gamma distribution Γ(α, β) when α = 1, and a special case tonomous characters. For example, in [21] every character is
of the Lomax distribution with some restrictions [15], [16]. provided with a small KBS (Knowledge-Based System). Such
So, the Beta II distribution can be used here as a generalized method is very flexible, but defining the knowledge base is a
distribution for all group of behaviours: monotonous, non complex and time-consuming task. A reasoning system is also
monotonous and anytime behaviours. Then, each behaviour used in [22].
can be specified according to its features in order to obtain a The approach to behavioural autonomy presented in section
better fitting. III is based in [23], in that approach the idea is to develop
Now, in the rest of the section, empirical evidences agents that act and choose in the way actual humans do. The
which support using gamma, exponential and Lomax for agents are represented using parametrized decision algorithms,
monotonous, non monotonous and anytime behaviours are and choose and calibrate these algorithms so that the agents’
given. behaviour matches real human behaviour observed in the same
Notice that it is possible to estimate the distance between decision context. For this purpose, they uses a parametrized
time series generated, as explained above, from real log learning automaton with a vector of actions associated that can
data and time series generated by simulation of theoretical be weighted to choose actions along the time the way humans
distributions. Such estimation is done by using some statistical would.
test, like the Kolmogorov-Smirnov (K-S) test [17]. The K-S The decision of representing the automaton’s transitions
test is a nonparametric and distribution-free goodness-of-fit with probabilities instead of using a vector of strengths is
test. This means that they do not rely on parameter estimation based in [24], where the behaviour sequences are modelled
or precise distributional assumptions [18]. The proposed model through probabilistic automata (Probabilistic Finite-State Ma-
in this work does not assume any concrete distribution and chine, PFSMs). Probabilistic personality influence implies that
does not require parameter estimation. This way, the K-S one cannot fully predict how a character will react to a
properties are suitable for the hypothesis test. stimulus.
The K-S test and the chi-square test are the most commonly In [25] and [26], the behavioural models described use
used and for large size sample both tests have the same power. a hierarchical structure of finite state automata similar as
However, the chi-square test requires a sufficient sample size model described in section III. Each behaviour of a behaviour
in order to obtain a valid chi-square approximation [19], [20]. sequence is called a behaviour cell. At the top of the structure
The K-S is a goodness-of-fit test to indicate whether it is there is a behaviour entity with a finite state automaton com-
reasonable or not to assume that a random sample comes from posed of at least one behaviour cell. An elementary behaviour
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