The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution
The simulation model of IT-product or service development by a "start-up" company growing inside an academic institution's "business center" is reviewed. The purpose of the model is to estimate final dates of reaching project goals of the "start-up" company. The us...
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Інститут проблем математичних машин і систем НАН України
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irk-123456789-1136632017-02-12T03:03:35Z The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution Lytvynov, V.V. Saveliev, M.V. Моделювання і управління The simulation model of IT-product or service development by a "start-up" company growing inside an academic institution's "business center" is reviewed. The purpose of the model is to estimate final dates of reaching project goals of the "start-up" company. The use of Petri nets for design of such model is shown. An example of model implementation by means of agent simulation is given. Розглядається імітаційна модель розробки IT-продукту або послуги, призначена для оцінки термінів досягнення проектних цілей "start-up" компанією, яка опікається з боку "бізнес-центру" при академічній установі. Відображено застосування мереж Петрі для проектування такої моделі. Наведено приклад реалізації моделі засобами агентного моделювання. Рассматривается имитационная модель разработки IT-продукта или услуги, предназначенная для оценки сроков достижения проектных целей "start-up" компанией, опекаемой со стороны "бизнес-центра" при академическом учреждении. Показано применение сетей Петри для проектирования такой модели. Приведен пример реализации модели средствами агентного моделирования. 2015 Article The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution / V.V. Lytvynov, M.V. Saveliev // Математичні машини і системи. — 2015. — № 4. — С. 92-99. — Бібліогр.: 9 назв. — англ. 1028-9763 http://dspace.nbuv.gov.ua/handle/123456789/113663 004.94: 378.147.88 en Математичні машини і системи Інститут проблем математичних машин і систем НАН України |
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Моделювання і управління Моделювання і управління |
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Моделювання і управління Моделювання і управління Lytvynov, V.V. Saveliev, M.V. The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution Математичні машини і системи |
| description |
The simulation model of IT-product or service development by a "start-up" company growing inside an academic institution's "business center" is reviewed. The purpose of the model is to estimate final dates of reaching project goals of the "start-up" company. The use of Petri nets for design of such model is shown. An example of model implementation by means of agent simulation is given. |
| format |
Article |
| author |
Lytvynov, V.V. Saveliev, M.V. |
| author_facet |
Lytvynov, V.V. Saveliev, M.V. |
| author_sort |
Lytvynov, V.V. |
| title |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution |
| title_short |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution |
| title_full |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution |
| title_fullStr |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution |
| title_full_unstemmed |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution |
| title_sort |
simulation model of it-product (service) development by a "start-up" company growing inside an academic institution |
| publisher |
Інститут проблем математичних машин і систем НАН України |
| publishDate |
2015 |
| topic_facet |
Моделювання і управління |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/113663 |
| citation_txt |
The simulation model of IT-product (service) development by a "start-up" company growing inside an academic institution / V.V. Lytvynov, M.V. Saveliev // Математичні машини і системи. — 2015. — № 4. — С. 92-99. — Бібліогр.: 9 назв. — англ. |
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Математичні машини і системи |
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92 © Lytvynov V.V., Saveliev M.V., 2015
ISSN 1028-9763. Математичні машини і системи, 2015, № 4
UDC 004.94: 378.147.88
V.V. LYTVYNOV
*
, M.V. SAVELIEV
**
THE SIMULATION MODEL OF IT-PRODUCT (SERVICE) DEVELOPMENT
BY A "START-UP" COMPANY GROWING INSIDE AN ACADEMIC INSTITUTION
*
Chernihiv National University of Technology University, Chernihiv, Ukraine
**
The Institute of Mathematical Machines and Systems Problems of the NAS of Ukraine, Kyiv, Ukraine
Анотація. Розглядається імітаційна модель розробки IT-продукту або послуги, призначена для
оцінки термінів досягнення проектних цілей "start-up" компанією, яка опікається з боку "бізнес-
центру" при академічній установі. Відображено застосування мереж Петрі для проектування
такої моделі. Наведено приклад реалізації моделі засобами агентного моделювання.
Ключові слова: імітаційне моделювання, життєвий цикл розробки програмного забезпечення, ме-
режі Петрі, агентне моделювання, NetLogo.
Аннотация. Рассматривается имитационная модель разработки IT-продукта или услуги, предна-
значенная для оценки сроков достижения проектных целей "start-up" компанией, опекаемой со
стороны "бизнес-центра" при академическом учреждении. Показано применение сетей Петри для
проектирования такой модели. Приведен пример реализации модели средствами агентного моде-
лирования.
Ключевые слова: имитационное моделирование, жизненный цикл разработки программного обес-
печения, сети Петри, агентное моделирование, NetLogo.
Abstract. The simulation model of IT-product or service development by a "start-up" company growing
inside an academic institution's "business center" is reviewed. The purpose of the model is to estimate fi-
nal dates of reaching project goals of the "start-up" company. The use of Petri nets for design of such
model is shown. An example of model implementation by means of agent simulation is given.
Keywords: simulation modeling, software life circle, Petri nets, agent simulation, NetLogo.
1. Introduction
Nowadays in developed countries devolved from industrial society to information-oriented socie-
ty there is a tendency for arranging business centers and incubators inside Universities to support
and guide young companies which create new technologies, products and services. First of all
these are the companies associated with various information technologies – software, computer
hardware, computer aided design, Internet and mobile applications [1].
Being guided by a business center, such companies are going through several stages, i.e.
from an informal group of like-minded people to a start-up and a spin-off company, and then they
become an independent business already with no participation of the business center. At all these
stages, the supervisory board of the business center faces a task to make decisions as to support
formation of such companies, transfer them from a start-up state to a spin-off, as well as close
them down. These solutions are quite complex and require both methodologies and tools to eva-
luate quality of the companies supported by the business center, for example, based on SW CMM
maturity model [2].
This publication considers modeling of an IT-project carried out on the basis of the most
popular among small businesses life cycles: an evolutionary model of rapid prototyping [3]. Con-
ceptual modeling will be performed using Petri networks, while the model itself will be imple-
mented by means of NetLogo agent simulation [4].
ISSN 1028-9763. Математичні машини і системи, 2015, № 4 93
2. Work statement
Activity of a start-up/spin-off company growing inside the business center under the University
can be seen as a time-limited project. And from the point of view of the business center this will
be a project on floating a successful independent company, but from the standpoint of the compa-
ny, this will be a project on launching a newly created product (service) or project on the compa-
ny mastering specific skills required for its business. Obviously, success or failure of the project
undertaken by the start-up/spin-off company being guided will be the same result of this project
from the view point of the business center under University.
In project management the classical strategy for a project modeling is the method of
PERT (Program (Project) Evaluation and Review Technique – an assessment and analysis pro-
grams (projects) technology), where such modeling is performed using graphs of relationship of
activities (arrows) and events (nodes). And the management of such projects is carried out by the
critical path method, where the graph mathematical analysis result reveals a set of such activities
that a change of duration of any of them leads to a change in the entire project implementation
time.
At the same time, assessing certain activity duration is not a trivial task for the IT projects,
since such assessments are very subjective and depend on the performers’ background, especially
for immature organizations, which are the start-up/spin-off companies. In addition, the models
developed by the classical method tend to a cascade form of the life cycle, which does not reflect
the iterative nature of the information technology development. Thus, the task is to build an ade-
quate model of the project feasibility assessment.
Purpose of the suggested simulation model is to assess the feasibility of production goals
supported by the company (product release, development of a new service, acquisition of specific
competencies, improving the efficiency of labor, etc.). Such model should include:
• The life cycle of the project implementation through achieving the company's goals,
such as creation of the product (service).
• Sets of typical activities which make up the above-mentioned life cycle phases.
• Lists of competencies required for activity and standardized duration of these activities,
if implemented by a competent person.
The input data of this model will be as follows: a real set of experts available at the com-
pany; the planned network model of the project implementation; the company's strategy to allo-
cate work among specific specialists; probability estimate of work performance and other infor-
mation specific to a particular project.
As a result of the run, the model shall answer the following questions:
• What are the project implementation terms considering the project realization strategy
chosen by the company?
• Whether the allocated resources are sufficient for the project implementation?
3. Conceptual framework
According to [5], development of the conceptual model is the next step to create a simulation
model after defining the problem and the general task setting. As a rule at the beginning such
conceptual model is being described using the natural language in terms of the subject area, and
only then the model is described using the simulation languages. Further on one can proceed ei-
ther with the software implementation, or with the mathematical model and its formal solution.
We will give here such description of our conceptual model.
The project life cycle (product creation) determines the generalized phases, in which the
project exists from its beginning until the end. Typically, these are the phases of planning, design-
ing, developing, testing and implementing. Such phases are not necessarily linear, but they may
be repeated and held simultaneously. Each phase is characterized by the objectives to be achieved
94 ISSN 1028-9763. Математичні машини і системи, 2015, № 4
Project
Plan
R
ap
id
an
al
ys
is
D
atabase
In
te
rfa
ce
System
function
Prototyping
U
ser’s approval
«P
ro
je
ct
»
D
ev
el
op
m
en
t
C
ustom
ization
O
pe
ra
tio
n
an
d
m
ai
nt
en
an
ce
Fig. 1. Structural evolution model of rapid
prototyping
at this stage, consists of a set of activities; and considered completed upon their successful im-
plementation. Development of a set of design and technical documentation, test cycle, and im-
plementation of a solution at an Employer’s site may serve as an example of such objectives.
As noted above, each phase consists of activities that result in the creation of project arti-
facts – usually separate documents, its chapters and parts, as well as software and technical mod-
ules, as well as their integration. Activities are interconnected by a priority relation, for example,
certain activity cannot be started before the previous one is completed, and together they form a
network model being described by the transition graph from one activity to another.
A performer is connected to each activity – this is usually a specific company’s represent-
ative who has a relevant competence to do this activity. A set of areas of knowledge from SWE-
BoK [6] can be considered as such competencies for an IT-project. At the same time, people are a
limited resource of the company both in quantitative and qualitative terms. For modeling purpos-
es, we can range [0..1] an estimate of competences per each performer. Then some standardized
activity will be done by a specific performer in a time inversely proportional to this assessment.
Standardized conditional time of work execution will be a modeling step for this model.
In other words, in the framework of the model one activity is carried out in one unit of time, if the
performer of this activity is competent to do it with a value of 1. The activities, an objective dura-
tion of which takes more time, shall be divided into several smaller activities. The model can in-
clude some specific activities – “training” which changes the competence level of the performer
who “performs” it, thus the model can simulate the cost of specialists training.
The model input data will be the IT-project implementation life cycle chosen by the com-
pany, a list of planned activities, competency of the company's specialists and the strategy for
their allocation per activities. Time required for the simulated IT-project implementation will be a
result of modeling.
4. Model of the IT-project life cycle-prototyping
It is believed that the idea of prototyping when creating software was offered by Frederick
Brooks in the famous work “The Mythical Man-
Month”, although F. Brooks himself thought that this
idea was antedated by Vinton Royce, creator of the
cascade model [7]. In this article, a description of the
structural evolution model of rapid prototyping will
be given here in accordance to R. Futrell et al [3].
Below is its graphical representation.
The first stage of this model life cycle is the
creation of a project plan based on the preliminary
requirements. Then, the rapid analysis is done, the
database, user interface, and system functions are
designed. In this case, one is intentionally restricted
by creation of a high-level partial model at the do-
cumentation level. Next, one proceeds with the de-
velopment of a system prototype that is shown to an
Employer; after that comments and suggestions are
determined and the cycle of already improved proto-
type occurs again. The process stops when the Employer officially approves a working model of
the system. After that the design and technical documentation is being updated upon performed
system and the working model is adjusted up to the level of work use. The life cycle is completed
when the system is transferred to the operation and maintenance stage.
According to the teaching experience of the authors in the universities one can note that
this model is very popular among students because from their point of view it allows you quickly
ISSN 1028-9763. Математичні машини і системи, 2015, № 4 95
The project has been
started
Carry out the
project
The project has been
completed
Fig. 2. Initial Petri net which modules the
IT-product
creation project
Goals have been
defined
Resources have been
allocated
Time has been set
Start the
project
Project is being
carried out
Complete the
project Goals were achieved
Resources were
not depleted
Deadlines were not
missed
Fig. 3. Petri net which modules the IT-product creation project
starting the system implementation and does not burden the "paperwork". Based on the above,
this very model of the software life cycle will form the basis of our simulation model.
5. Modeling of Petri net
At present, the systems modeling using Petri nets is very popular in the academic environment,
owing to its clearness and developed mathematical tools. A Petri net is a bipartite-oriented multi-
graph consisting of vertices of two types – positions and transitions, interconnected by the arcs
[8].
For modeling purposes, we will use the method of gradual detailing of Petri nets states
and transitions, which in fact is a well-known method of information systems designing by the
top-down method.
5.1. Petri net of the top-level for a typical
project
An initial Petri net for the project model
can be presented in the form of two succes-
sive states “Project has been started” and
“Project has been completed”, as well as
one of transition “Start the project”, see
Fig. 2. It is obvious that such a network is
finite.
Let’s detail the initial network states
and transition. Thus the transition “Carry
out the Project” can be expanded to state “Project is being carried out”, preceded by transition
“Start the Project” and with the subsequent transition to “Complete the project”. At the same
time, state “Project has been started” can be detailed in the following states: “Goals<of the
project> have been defined”, “Re-
sources<for the project>have been
allocated” and “Time<of the
Project>has been set”. Similar ac-
tions can be performed for the state
“Project has been completed”, see
Fig. 2. Note that transition “Start
the project” can fire only if all three
previous states have network to-
kens. And firing of the “Complete
the Project” transition makes its
subsequent states “true”.
The Petri net presented in
Fig. 3 can be a base for any model
of the IT-products life cycle, where
the state "Project is being carried out" is detailed in accordance with its model.
5.2. Detailing the state of "Project is being carried out" on the model of the “rapid proto-
typing” life cycle
Fig. 4 presents the Petri net, detailing the state of “Project is being carried out” for the model of
the “rapid prototyping” life cycle. In contrast to the above generalized model where prototyping
cycle does not include a need to revise the project schedule, repeat the system analysis, review
96 ISSN 1028-9763. Математичні машини і системи, 2015, № 4
the database, system functions, and human-machine interface (HMI), the proposed network con-
siders this need, which makes it closer to real practical IT-projects.
Complete the
project
Project
schedule is not
ready
Perform planning
Project
schedule is
ready
Analysis is not
relevant
Perform an
analysis
Analysis has
been done
Data base
structure is not
relevant
Design a database
Data base
structure has
been detined
HMI was not
defined
Define HMI
HMI has been
defined
Functions are
unknown
Define
functions
Functions are
defined
The code is not
ready
Write a code
Code is ready
Design a system
Employer’s
review
Design
documents
customization
Implement the
system
Documentation is
not ready
Documentation is
ready
System has been
implemented
System has
been reviewed
Decline the
system
Approve the
system
Start the
Project
Fig. 4. Petri net for state “Project is being carried out” of the “rapid prototyping” life cycle model
As can be seen from Fig. 4 transition “Start the Project” initializes the state of “Project
schedule is not ready” and “Analysis is not relevant”. Transition “Run Analysis” takes into ac-
count the fact that the project analysis cannot be started without having the project schedule
available, i.e. time and resources to perform such analysis, as well as subsequent activities are not
taken into account. Transition “Design the system” allows actions to develop HMI, database, sys-
tem functions, and code that in real projects are usually carried out in parallel. State “System has
been considered” allows either of the two transitions “Decline ...” and “Approve the system”.
Approval of the system leads to the subsequent transition to complete the project, while the dev-
iation of the system repeats the cycle of project planning and system analysis (in this case for the
upcoming changes).
In the present form, Petri net does not yet take into account a need for resources and time,
and thus cannot be used for the stated purposes of simulation modeling.
5.3. A Petri net which models activity work on the project tasks
As noted above in the description of conceptual model, the project is characterized by a variety of
works, planned completion due dates and a set of performers, at that all three of these varieties
are finite. In Petri nets this can be simulated by a set of tokens in the states and inputs/outputs on
transitions, see [9]. Let us consider the following Petri net, see Fig. 5.
ISSN 1028-9763. Математичні машини і системи, 2015, № 4 97
N
Activity
quantity
Choose an
activity
Activity has
been
selected
Add an activity
N
Quantity of
available
time
N
Quantity of
available
specialists
Choose a leader
Choose an
intern
Choose a linear
Worker has
been
selected
Assign the
activity
Activity has
been
assigned ?
Success
Failure
Perform P1
Return the
specialist
Replan
New
activity
Specialist is
available
Perform P2
Fig. 5. Petri net, which simulates activity of the project group on the tasks
Initial Petri net marking is defined by arrangement of tokens as follows:
• Number of the project tasks is set by a number of tokens in the “Number of activities”
state;
• Duration of the project (in terms of conditional time planning) is set by a number of to-
kens in the “Availability of time” state;
• Number of available specialists is set by a number of tokens in the “Number of available
experts” state;
• All other states remain “empty”.
Transitions “Select ... a leader, a linear, and an intern” define “cost” of work performance
by a specialist with diverse degree of training in unit time. In this example, the lead specialist re-
duces time available to complete the project per 1 unit, the linear – per 2 units and the intern by 3
conditional units of the project time.
Transition “Assign activity” connects the single work with a specific performer. Transi-
tions “Run” are stochastic and fire with a certain probability of success (P2) or failure (P1) when
performing work. After the work is completed the expert returns to the pool of available special-
ists. “Failed” work recurs in a variety of outstanding works for a new run.
Network stops when the available time or activities are exhausted. Herewith a number of
tokens in the “Success” state will show a number of successfully completed activities, in the
“Number of activities” state – a number of outstanding activities, and in the “Availability of
time” state – remaining time in case of exhaustion of all outstanding work or zero, when the
available time is exhausted.
5.4. Petri net simulating work on a specific task
The Petri net models considered above simulates execution of a project task through a direct link
between a specialist’s qualification and time needed for him to do the work. That may be enough
for the initial planning tasks and the project life assessments. However, another model may be
98 ISSN 1028-9763. Математичні машини і системи, 2015, № 4
required to obtain more accurate estimates of time spent for work. An example of such model is
shown in Fig. 6.
1
The work
has begun
N
Time has been
defined
Success
Failure
Work is being
carried out
Commence
work
Perform P1
Complete P2
Complete P3
Fig. 6. Stochastic Petri net modeling the time spent at work on a specific task
The initial marking of this Petri net is defined by tokens arrangement as follows:
• Token in "Work has been started" defines a possibility to start work.
• Terms of work performance (in units of conditional planning time) are set by the number
of tokens in the “time has been defined” state.
• All other states remain “empty”.
Transition “Start the work” fires provided that time is available ( 0N in the “Time has
been defined”) and the token in the “Work has been started” state.
Transitions with marks P1, P2, P3 are stochastic and fire with a certain probability. In this
case, 1P n is the probability of further work, 2P n – of successful completion of work, and
P3(n) – of a failure of work performance on the nth time step.
“Success” or “Failure” states show status upon completion. Herewith the network will
stop in one of these two states when the available time is exhausted, since the transition “Perform
P1” can no longer be made and one of the transitions P2 or P3 will fire.
6. Software implementation
The model is implemented in the NetLogo modeling environment, developed in 1999 by Uri Wi-
lensky in the Center for Connected Learning and Computer-Based Modeling, United States [6].
This tool which is not an environment for Petri nets modeling was chosen in order to check the
hypothesis of commensurability of a programmer’s efforts to transfer into a program code of
models made in the Petri nets form and those models made in the UML diagrams form. Another
hypothesis under check was a possibility of an agent-based simulation modeling, where the
agent’s behavior sets the Petri net, similar to the example shown in Figure 6. It is worth noting
that both hypotheses were practically proved out. Working example of the software implementa-
tion is shown in Fig. 7.
The result model allows evaluating:
• timing of the project having a given configuration of staff: a number of performers, their
qualitative composition (graduate students, masters, bachelors, students);
• amount of work performed by a single performer.
Having this information one can estimate an adequacy of allocated resources to imple-
ment project within a given period of time.
ISSN 1028-9763. Математичні машини і системи, 2015, № 4 99
Fig. 7. An example of the simulation process
7. Conclusions and suggestions.
As a result of conducted investigation the simulation model of implementation process per the
life cycle model of IT-project structural prototyping by a small company or a university team was
developed, which allows us to estimate time required to implement such project depending on the
strategy of the human resources allocation for the activities being performed.
Using Petri nets to formalize the conceptual model enables rapid transition to a software
implementation, and does not yield to UML means which are traditionally used to build models
before writing a code. Petri nets have shown their clearness when describing an agent’s behavior
in an agent-based simulation.
REFERENCES
1. Литвинов В.В. Опыт взаимодействия Университетов и промышленности в сфере трансфера ИТ-
технологий в Западной Европе / В.В. Литвинов, В.С. Харченко // Математичні машини і системи. –
2015. – № 1. – С. 111 – 123.
2. Інструментальні засоби оцінки зрілості іт-компаній, які підтримуються бізнес-центрами при
університетах / В.В. Литвинов, М.В. Савельєв, І.С. Скітер [та ін.] // Вісник Чернігівського держав-
ного технологічного університету. – 2015 (у друці).
3. Фатрелл Р.Т. Управление программными проектами: достижение оптимального качества при
минимуме затрат / Фатрелл Р.Т., Шафер Д.Ф., Шафер Л.И.; пер. с англ. – М.: Издательский дом
"Вильямс", 2003. – 1136 с.
4. Wilensky U. NetLogo itself [Електронний ресурс] / U. Wilensky. – NetLogo, Center for Connected
Learning and Computer-Based Modeling, Northwestern University, 1999. – Evanston IL. – Режим дос-
тупу: http: //ccl.northwestern.edu/netlogo.
5. Томашевський В.М. Моделювання систем / Томашевський В.М. – К.: Видавнича група ВНУ,
2005. – 352 с.
6. Software Engineering Body of Knowledge [Електронний ресурс]. – SWEBOK V3, IEEE computer
society. – Режим доступу: http://www.computer.org/web/swebok/v3.
7. Брукс Ф. Мифический человеко-месяц или как создаются программные системы / Брукс Ф.; пер.
с англ. – СПб.: Символ – Плюс, 2001. – 394 с.
8. Murata T. Petri Nets: Properties, Analysis and Applications / T. Murata // Proceedings of the IEEE. –
1989. – Vol. 77, N 4. – P. 541 – 558.
9. Башкин В.А. Некоторые методы ресурсного анализа сетей Петри: дис. … доктора физ.-мат. наук:
05.13.17 / Башкин Владимир Анатольевич. – Ярославль, 2014. – 268 с.
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