Gap Structure and Characteristic Properties for Analysing Buyers’

Burstiness in e-Business Process

Andreas Ahrens

, Jeļena Zaščerinska

and Ojaras Purvinis

Hochschule Wismar, University of Applied Sciences - Technology, Business and Design,

Philipp-Müller-Straße 14, 23966 Wismar, Germany

Centre for Education and Innovation Research, Dammes iela 33, Riga LV-1069, Latvia

Kaunas University of Technology, K. Donelaičio g. 73, LT-44249 Kaunas, Lithuania

Keywords: e-Business Process, Buyers’ Burstiness, Gap Structure, Gap Characteristic Properties, Binary Customer

Behaviour.

Abstract: Optimization of e-business process allows increasing earning profits in e-business. Models based on gap

processes for the analysis of buyers’ burstiness in e-business process have attracted an increased research

interest in order to succeed in the optimization of e-business process. The research aim is to find model

approaches for creating gap structures and the description of their characteristic properties with a required

accuracy underpinning elaboration of a new research question. Interdisciplinary research was carried out

within the present investigation. The results of the present research show gap structures and gap

characteristic properties. In e-business, gap structure means a range of shop visitors who do not buy any

product. The gap characteristic properties are defined as gap density and gap distribution function. The

empirical study involved eight experts from different countries to validate the model and to project the

research. The findings of the study allow drawing the conclusions on the experts‘ positive evaluation of the

mathematical model for analysis of buyers’ burstiness in e-business process. The novel contribution of the

paper is revealed by the comparison of model approaches for creating gap structures and the description of

their characteristic properties with a required accuracy. Directions of further research are proposed.

1 INTRODUCTION

Economy is at the heart of the well-being of modern

society. However, economy depends on success of

companies and/or enterprises including e-companies

to organise their business and/or e-business

processes in an efficient way. Optimization of e-

business process allows increasing earning profits in

e-business. Optimization of business process implies

(Ahrens et al., 2015; Ahrens et al., 2018) such

choices as

 quantity of goods to be delivered and

 number of the staff to be employed,

 goods’ pricing,

 goods discounts,

 computer software to be installed,

 networking between a business company and its

customers to be established,

 queue management, etc.

Additionally, such a result of business process as

purchase and/or sale of a good or service indicates

the output of this process.

Efficient use of company’s scarce resources to

create, using knowledge, commodities and distribute

them among people (Khumalo, 2012, p. 606)

requires good or right decisions as delivered in

Figure 1 (Ahrens et al., 2015).



Decision

Badorwrong

Goodor

right

Figure 1: Decision differentiation.

Good or right decisions are expected to ensure

fast and harmonious ways to the well-being of

society in general, company including e-company

Ahrens, A., Zaš

cerinska, J. and Purvinis, O.

Gap Structure and Characteristic Properties for Analysing Buyers’ Burstiness in e-Business Process.

DOI: 10.5220/0006870800230034

In Proceedings of the 8th International Joint Conference on Pervasive and Embedded Computing and Communication Systems (PECCS 2018), pages 23-34

ISBN: 978-989-758-322-3

and/or individual in particular as illustrated in Figure

2 (Ahrens et al., 2015).



Goodorrightdecisions

Harmonious

waystothe

well‐being

ofsociety,

company

and/or

individual

Fastwayto

thewell‐being

ofsociety,

company

and/or

individual

Figure 2: Elements of good or right decisions.

In contrast, bad or wrong decisions serve as a

source of conflict or stress for society in total and/or

individual in particular as shown Figure 3 (Ahrens et

al., 2015).



Badorwrongdecisions

Stress

Conflict

Figure 3: Elements of bad or wrong decisions.

Good or right decisions are expected to ensure

fast and harmonious ways to the well-being of

society, company and/or individual. Therefore,

decision-making support systems are of great

research interest. Predictive capacity is one of the

forms of support to the decision making (Cronqvist

et al., 2015). For example, the most recurrent

techniques to predict and analyse market behaviour

are Technical and Graphic Analysis (Biglieri and

Almeida, 2018). As the research on forecasting and

prediction in many life domains remains of high

interest, certain research efforts have been devoted

to a newly emerged research area on such a

phenomenon as burstiness. It should be noted that

beginning in 1960 Gilbert presented the first model

in telecommunications which emphasized that bit

errors occurred in bundles or, in other words, bursts

(Gilbert, 1960; Elliott, 1963). Since then, the issues

of a general procedure to analyse the performance

or, in other words, business process in the present

research, are still relevant today. Figure 4

demonstrates the phenomenon of burstiness in a

range of scientific fields (Ahrens et al., 2016).

Figure 4: Burstiness in different scientific fields.

Burstiness is used to support decision making

through designation of a tendency in a field of

scientific investigation (Pierrehumbert, 2012) as

pointed in Figure 5.



Decisionmakingsupport

system

Phenomenon’s

burstiness

Figure 5: The inter-connections between decision making

support system and phenomenon’s burstiness.

Analysis of burstiness as a predictor of

performance was carried out in

 the management science (Riedl and Woolley,

2017) as well as

 e-business (Ahrens and Zaščerinska, 2017b),

 entrepreneurship education (Ahrens et al., 2018).

Further on, modern decision making support systems

are closely connected with data analytics and

management. The proliferation, ubiquity and

increasing power of computer technology has

dramatically increased data collection, storage, and

manipulation ability (Dermino and Fortingo, 2015).

As data sets have grown in size and complexity,

direct "hands-on" data analysis has increasingly been

augmented with indirect, automated data processing

(Dermino and Fortingo, 2015). Automated detection

has been already aided by other discoveries in

computer science (Dermino and Fortingo, 2015),

such as

 neural networks, cluster analysis, genetic

algorithms (1950s),

 decision trees and decision rules (1960s), and

 support vector machines (1990s).

However, effective methods and approaches for

automated detection are still an open research area

that is constantly being developed.

Burst detection method as a method for

automated detection has recently attracted a lot of

PEC 2018 - International Conference on Pervasive and Embedded Computing

research interests (Fei et al., 2013; Kalogeratos et

al., 2016). Intense research activities on burst

patterns were carried out (Subašic ́ and Berendt,

2010). However, a lack of common procedures

today makes it impossible to compare methods in a

principled way (Subašic ́ and Berendt, 2010). The

burst detection method exploits the burstiness nature

of a phenomenon (Fei et al., 2013). Burst means

sudden concentration, for example buyers’

concentration, in time periods (Fei et al., 2013).

For the optimization of e-business process, a

mathematical model based on gap processes for

analyzing buyers’ burstiness has been presented

(Ahrens and Zaščerinska, 2017a). The previous

research focused on

 determination of criteria for qualitative decisions

(Ahrens et al., 2015),

 identification of criteria of burstiness (Ahrens et

al., 2016),

 analysis of buyers’ burstiness as a predictor of

performance (Ahrens and Zaščerinska, 2017b) as

well as

 the model’s parameter estimation and practical

application (Ahrens and Zaščerinska, 2017a),

 mathematical analysis of gap processes (Ahrens

et al., 2018).

The research question is as follows: What are gap

structure and gap characteristic properties?

The aim of the research is to find model

approaches for creating gap structures and the

description of their characteristic properties with a

required accuracy underpinning elaboration of a new

research question.

The present contribution employs

interdisciplinary research as interdisciplinary

research assists in synthesizing, connecting and

blending ideas, data and information, methods, tools,

concepts, and/or theories from two or more

disciplines in order “to make whole” (Repko, 2012).

For the purposes of the present research, the

synergy between e-business and telecommunications

is promoted as the phenomenon of customers in the

e-business process as well as bit-errors in data

transmission appear to be of a similar nature,

namely, the bursty nature. Such methodologies that

consider the bursty nature of bit-errors in data

transmission have been successfully implemented in

telecommunications for optimizing data

communication protocols and will be adopted in this

work to the buyers’ burstiness in e-business process.

It should be noted that the present research is not

limited to only two scientific disciplines, namely, e-

business and telecommunication, but is based on a

number of scientific disciplines such as business,

social media, logistics, literature, etc.

The process of interdisciplinary research is

organized in three phases (Ahrens and Zaščerinska,

2016):

 In Phase 1 of the interdisciplinary research, an

issue is separately explored by two or more

scientific disciplines.

 In Phase 2, the same issue is examined by the

synergetic point of view of these two or more

scientific disciplines.

 In Phase 3, results of the analysis are interpreted.

The remaining part of this paper is organized as

follows: Section 2 introduces methodological

foundation of burstiness. Buyers’ burstiness in e-

business is presented in Section 3. The associated

results of an empirical study will be presented in

Section 4. Finally, some concluding remarks are

provided in Section 5 followed by a short outlook on

interesting topics for further work.

2 METHODOLOGICAL

FOUNDATION OF

BURSTINESS

Queuing theory serves as the methodological

foundation of burstiness.

Queuing theory is the mathematical study of

waiting lines, or queues (Möller, 2014). Queuing

theory (or "queueing theory") examines every

component of waiting in line to be served, including

the arrival process, service process, number of

servers, number of system places and the number of

"customers" (which might be people, data packets,

cars, etc.) (Shanmugasundaram and Banumathi,

2017). The arrival process is closely connected with

burstiness as phenomenon’s arrival is of bursty

nature (Froehlich and Kent, 1998). Burstiness effects

the queue as a higher level of burstiness increases

delay (Kumar, 1994) in a waiting line. Figure 6

demonstrates the relationship between the queuing

theory and its elements, namely the arrival process

and burstiness.

There is a number of approaches to burstiness

analysis. Table 1 (adapted from Ahrens et al., 2016)

presents three approaches to burstiness analysis. The

approach entitled Gap Processes for Analysing

Burstiness (Ahrens and Zaščerinska, 2016) has been

recently developed. Gap processes have emerged

due to the constantly growing meaning of the

Internet as an open global communication system

that leads to a huge number of different

communication applications and services for the

Gap Structure and Characteristic Properties for Analysing Buyers’ Burstiness in e-Business Process

giant community of Internet users. Users may access

several communication services per time whereas

every service requires certain communication

parameters like bandwidth, delay, error-rates or jitter

to work with adequate quality of transmission. A

service provider who likes to offer network quality

depending on communication services such as real

time audio or video transmission requires

appropriate tools for access network design,

monitoring and enhancement.

QueuingTheory

Arrivalprocess

Burstiness

Figure 6: The relationship between queueing theory,

arrival process and burstiness.

Table 1: Three approaches to burstiness analysis (adapted

from Ahrens et al., 2016)

Approach’s

element

Hidden

Markov

Model

(HMM)

Kleinberg’s

burst

detection

algorithm

(2002)

Gap

Processes for

Analysing

Burstiness

(Ahrens and

Zaščerinska,

2016)

Methodological

background

A sequence

model or

sequence

classifier is a

model whose

job is to assign

a label or class

to each unit in

a sequence,

thus mapping a

sequence of

observations to

a sequence of

labels

(Jurafsky and

Martin, 2016).

The algorithm

for detecting

bursty

network

traffic that

yields a

nested

representation

of the set of

bursts and

imposes a

hierarchical

structure on

the overall

stream.

Gap

distribution

function

within a

sequence of

the disturbed

and

interrupted

transmission

intervals

Feature

Markov chain

is only useful

for assigning

probabilities to

unambiguous

sequences

(Jurafsky and

Martin, 2016)

as system state

is partially

observable.

Sequence of

batched

georeferenced

documents

Sequential

independence

of gaps

etween two

researchers

sequentially

independent

gaps of

length k

between the

individual

phenomenon

Important characteristics of radio channels, such

as interrelationships between bit-errors, are included

in digital models, which are used for several

optimization tasks. Multipath propagation is a

typical effect in radio channels such as the short

wave channel since the emitted electromagnetic

waves are subject to diffraction, refraction and

reflection. Therefore, they reach the receiving site at

different angles and with different attenuation and

phase. Thus, the channel output shows dependencies

between adjacent symbols (Wilhelm, 1976; Ahrens,

2000). For instance, for the development of channel

coding algorithms these effects have to be

considered, and the optimization requires a

corresponding digital channel model. The simple

model of a memoryless channel cannot be applied.

Figure 7 illustrates the differences between a

memoryless channel and a channel with memory

(“x” denotes a bit error and “-” a correct bit).

Figure 7: Error structures with and without memory in

Information and Communication Technology (ICT).

From digital channel modeling it is known that

the bit-error rate is not sufficient to describe a lot of

digital channels (e. g. Wireless channels) since the

bit errors do not appear independently from each

other. Often channels with memory arise, and the

bit-errors appear concentrated. Similar dependencies

can be found in data networks regarding the

characteristics of the traffic (e.g. the temporal

intervals between consecutive data packets) (Kessler

et al., 2003). Such processes can be identified as gap

processes, i.e., the temporal intervals between data

packets as well as the bit-errors in

telecommunication systems (Ahrens et al., 2018).

Frequently used and well-suited practical

approximations are provided, if the model is based

on the independence of the gap intervals (Wilhelm,

PEC 2018 - International Conference on Pervasive and Embedded Computing

1976). These models are completely described by

the gap density or the gap distribution, respectively.

The assumption that successive gaps are statistically

independent is regarded as a good practical

approximation. The analysis of error structures of

real wireless channel connections in Central Europe

leads to the gap distribution such as exponential,

Weibull or gap-distribution functions defined by

Wilhelm (Wilhelm, 1976; Ahrens, 2000; Wilhelm,

2018). It should be noted that the terms “gap”, “gap

process” and “gap distribution function” are used

synonymously in the present contribution. Gaps are

rooted in the Hidden Markov Models (HMM)

(Ahrens, 2000).

As regard to the historical development of this

approach, Gilbert’s work (Gilbert, 1960) has been

extended by Wilhelm who introduced some closed

form solutions for describing the bit-error

distributions in wireless communication channels

such as the short-wave transmission channel

(Wilhelm, 1976) by outlining regenerative model

approaches. These investigations were encouraged

by practical measurement campaigns in the sixties

and seventies. Wilhelm elaborated already at that

time simulation models such as the L-model or the

A-model which took the effect of burstiness into

consideration. He recognized that the bit-error

probability (also sometimes referred as bit-error

rate) is not sufficient to describe the effect of

burstiness in wireless communication. Instead he

defined solutions which take burstiness into account

by defining models with two input parameters such

as the bit error rate and the error concentration

value. Wilhelm (Wilhelm, 1976) mapped the process

of bit-errors in telecommunication systems onto

processes defined by gaps between two consecutive

bit errors. Since the gap-length undergoes some

variations, the statistical description requires

appropriate probability distribution functions. By

defining a gap-distribution function (defined as the

probability that a gap between two bits in larger than

k bits) or a gap-density function (defined as the

probability that a gap between two bits equals k bits)

he could find closed form solutions. The model

characteristic has later been extended by Ahrens

(2000). Supported by practical measurements, these

models make use of the assumption that the block

error rate (i.e. a block with at least one bit-error) can

be described as a function of the bit-error probability

and the block length. In the double-logarithmic scale

the linearity between the block error rate and the

block length is used to define the simulation model

characteristic as well as is used to define the inherent

concentration between consecutive bit-errors. The

model characteristic is proved by many

measurements campaigns (Ahrens, 2000).

Digital simulation models such as the beforehand

mentioned models for describing burstiness in

wireless transmission systems are an important

prerequisite for optimizing the underlying

components for data transmission such as

transmitting or receiving algorithms. Such

simulation models have been heavily used for

optimizing of coding schemes. So was the

probability of undetected errors for shortened

Hamming codes investigated by Lange and Ahrens

(Lange and Ahrens, 2001) on bursty channels.

Another example showing the importance of such

simulation models is the modelling of connection

arrivals in Ethernet-based data networks (Kessler et

al., 2003), where the intervals between consecutive

data packets in a data network were analysed. What

has however interested communication protocol

developers and coding theorists, are the probabilities

of error structures in any finite time interval such as

the block length or the cycle length of a transmission

procedure (Wilhelm, 2018). These probabilities are

typically difficult to present analytically (Wilhelm,

2018).

Many studies have found that the block error

probability (

) dependent on the block length

(n) in the initial part is linear when presented

double-logarithmically (Wilhelm, 2018). With this

approach, in the seventies Wilhelm (2018)

developed the L-model (Gap Model) and A-model

(Gap Model) with complete sets of formulae

concerning the probabilities of error structures

occurring in bursts, and in blocks. These gaps are

assumed to be statistically independent from each

other. With these models, the bursty nature of

transmission errors in ICT could be simulated.

For comparison purposes, Table 2 demonstrates

the model of analysis of burstiness of hot topic,

keyword, event in a sequence of batched

georeferenced documents in social media developed

by a group of Japanese researchers as geo-annotated

user-generated data on social media sites is

becoming one of the most influential sources of

information (Kotozaki et al., 2015). This group of

Japanese researchers built their model of analysis of

burstiness of hot topic, keyword in a sequence of

batched georeferenced documents on Kleinberg’s

burst detection algorithm (2002), which is based on

the queuing theory for detecting bursty network

traffic (Kotozaki et al., 2015). It should be noted that

Kleinebrg’s solution does not provide clear

distinction between within-burst and out-of-burst

records (Mai et al., 2015).

Gap Structure and Characteristic Properties for Analysing Buyers’ Burstiness in e-Business Process

Table 2: Criterion and indicator of burstiness in social

media.

Criterion Indicator

Burstiness of hot topic, keyword, etc in a

sequence of batched georeferenced documents

Locality

A comparative analysis of the model of analysis

of burstiness of hot topic, keyword in social media

shown by the group of Japanese researchers

(Kotozaki et al., 2015) and the model for evaluation

of researchers’ burstiness in research process

(Ahrens et al., 2016) is reflected in Table 3.

Table 3: Comparison of models for analysis of burstiness

in social media and research.

Model’s element Social media Research process

Criteria

Burstiness of hot topic,

keyword, etc in a

sequence of batched

georeferenced

documents

Researchers’

burstiness

Indicators Locality

Researchers’

probability

Researchers’

concentration

Feature

Sequence of batched

georeferenced

documents

Sequential

independence of

gaps between two

researchers

sequentially

independent gaps

of length k

between the

individual

researchers

Methodological

background

Kleinberg’s burst

detection algorithm

(2002), based on a

queuing theory for

detecting bursty

network traffic and

yields a nested

representation of the set

of bursts that imposes a

hierarchical structure

on the overall stream.

Gap distribution

function within a

sequence of the

disturbed and

interrupted

transmission

intervals

The comparative analysis of Table 3 reveals that

Kleinberg’s burst detection algorithm, which is

based on the queuing theory, is applicable to a

sequence of phenomena while gap distribution

function is featured by sequential independence of

gaps between two researchers (Ahrens et al., 2016).

The comparative analysis assists in drawing such a

conclusion as a process including business process is

characterized by independence of gaps between two

researchers or, in other words, research subject or

object.

Therefore, mathematical models that consider the

bursty nature of bit-errors in data transmission have

been successfully implemented in

telecommunications for optimizing data

communication protocols and will be adopted in this

work to the optimization of bursty business

processes. The approach based on gap processes is

now considered as a possible solution of analysis of

buyers’ burstiness in business process.

3 BUYERS’ BURSTINESS IN

E-BUSINESS PROCESS

Phenomenon’s burstiness is revealed as

phenomenon’s frequency at an unusual high rate

(Kalogeratos et al., 2016). Interval of high-activity

alternating with long low-activity periods can be

found in many areas of our daily life. A classical

example is e-business process. By e-business

process, the process of buying and/or selling of

goods and/or services through ICT is meant (Ahrens

et al., 2015). Bursty e-business process is the process

in which high-activity of buying and/or selling of

goods and/or services through ICT alternates with

low-activity intervals.

e-Business process which ends without a

purchase or sale means a gap (Ahrens et al., 2015) in

the present work. The gap process can be understood

as a sequence of intervals. The gaps between two

buyers are assumed to be statistically independent

from each other (Ahrens et al., 2015). Figure 8

demonstrates gap structures. In Figure 8, buyers are

represented by "x" within a sequence of shop visitors

indicated by "-". In e-business, gap structure means a

range of shop visitors who do not buy any product.

In graphs of gap structure, the gap generally refers to

the difference between shop visitors indicated by “-”

and buyers represented by “x”.

Figure 8: Gap structures.

PEC 2018 - International Conference on Pervasive and Embedded Computing

In bursty situations, not only purchases and sales

are of any research interest but also how

concentrated goods are sold or bought. That is why

models which focus only on purchases and sales

with a given probability are not exact enough to

describe e-business process. It should be noted that

phenomenon is described through criteria, indicators

and constructs. According to the theoretical findings

of Lasmanis (2003, p. 9) and Špona and Čehlova

(2004, p. 88), criteria serve to structure, assess and

evaluate while indicators determine developmental

dynamics. Criteria can be determined by analysis of

(Špona and Čehlova, 2004, p. 88) definition of the

research object, structure of the research object and

factors. Analysis of source of criteria determines the

use of terminology on criteria, indicators and

construct as following:

 term criterion is defined as the key element to

structure object of the research,

 term indicator is identified as the component to

determine developmental dynamics of the object

and

 term construct is specified as the sub-component

of the research object.

Comparative analysis of the terms “criteria”,

“indicator” and “construct” with “parameter”,

“characteristic” and “property” leads to

understanding that the following terms are used

synonymously:

 criteria and parameter,

 indicator and characteristic, and

 construct and property.

The inter-connections between the terms “criteria,

indicators and constructs”, on the one side, and

“parameter, characteristics and characteristic

properties”, on the other side, can be illustrated by

the definition of the term “parameter”: a parameter

means definable, measurable, and constant or

variable characteristic, dimension, property, or

value, selected from a set of data (or population) to

understanding a situation (or in solving a problem)

(Business Dictionary, 2015).

In general, the buyers’ probability can serve as a

clear indicator of how often people decide to buy

e.g. a product. However, the buyers’ probability

does not deliver any information about how

concentrated the purchases and/or sales are. Thus,

gap characteristic properties include buyers’

probability and buyers’ concentration (Ahrens et al.,

2015) as summarized in Table 4.

Table 4: Criterion and indicators of burstiness in e-

business process.

Criterion Indicators

Buyers’ burstiness

Buyers’ probability

Buyers’ concentration

From the modelling of peoples’ buying

behaviour, it is known that the whole process of

buying cannot be described by the buyer’s

probability since often buyers do not appear

independently from each other. Therefore, in many

cases the analogy with channels with memory arises.

A proper solution can be found when describing the

temporal intervals between buyers by gaps. The

modelling of such processes requires statistical

parameters of a gap process such as the gap density

v(k) = P(X = k) and the gap distribution u(k) = P(X

 k). Here it is worth noting that the discrete variable

k is given through the time resolution of the

underlying (measurement) system. Frequently used

and well-suited practical approximations are

provided if the model is based on the independence

of the gap intervals. Figure 9 gives an overview of

different gap distribution function used to model

burstiness in the process of buying as well as

burstiness of bit-errors in telecommunication

systems.

Figure 9: Several distribution functions.

The focus of this contribution is the

approximation of the measured gap interval

distribution by a suitable distribution function. As

quality parameter for the approximation between the

measured gap interval distribution and a given

distribution function the mean square error is used

and minimized.

Figure 10: Gap interval distribution of measured data and

approximated distribution functions.

Gap Structure and Characteristic Properties for Analysing Buyers’ Burstiness in e-Business Process

Figure 10 visualizes exemplarily the measured

gap distribution compared to the approximating

distribution functions.

The parameter of approximated distribution

function are presented in Table 5. Besides the

Weibull distribution, the Wilhelm distribution

approximates best the measured gap distributions in

the sense of minimizing the mean square error E

min

Table 5: Optimum parameters of distribution functions for

measurement interval.



It can be stated from Figure 10, that the statistical

properties of the buying process are well

approximated by distribution functions with two

parameters (Weibull, Wilhelm), whereas distribution

functions with only one single parameter

(Exponential) provide not such a good result. Thus,

the mean time between of two consecutive buyers

i.e. the buyer probability, is not sufficient to describe

the buying process.

4 EMPIRICAL ANALYSIS

The present part of the contribution demonstrates the

design of the empirical study, results of the

empirical study and findings of the study.

The design of the empirical study comprises the

purpose and question, sample and methodology of

the present empirical study.

The guiding study question is as follows: What

is experts‘ evaluation of the model for analysis of

buyers’ burstiness in e-business process?

The purpose of the empirical study is to analyze

experts’ evaluation of the model for analysis of

buyers’ burstiness in e-business process.

The present empirical study is justified by the

use of the expert method that is considered to be one

of the most appropriate for collecting, analyzing and

evaluating of information, as well as for forecasting,

when it is necessary to take responsible decisions in

relation to innovations (Iriste and Katane, 2018) in a

variety of processes including the e-business

process. The method by means of which obtained

results are based on the opinions and assessments of

competent experts is called an expertise, an expert’s

opinion or the method of expert assessment (Iriste

and Katane, 2018).

The present empirical study involved three

experts from different countries in September 2017,

one expert in January 2018 and four experts in May

2018. All the respondents have been awarded PhD

Degree in different sciences. As the respondents

with different cultural backgrounds and diverse

educational approaches were chosen, the sample was

multicultural. Thus, the group (age, field of study

and work, mother tongue, etc.) is heterogeneous.

The sample of eight experts consisted of

 three researchers who acted as reviewers at the

13th International Joint Conference on e-

Business and Telecommunications (ICETE

2017),

 one expert from IGI Global, International

Publisher of Information Science and

Technology Research as well as

 four researchers who acted as reviewers at the 3

International Conference on Pervasive and

Embedded Computing (PEC 2018)

In order to save the information of the study

confidential, the respondents’ names and surnames

were coded as E1 (Expert 1), E2 (Expert 2), E3

(Expert 3), E4 (Expert 4), E5 (Expert 5), E6 (Expert

6), E7 (Expert 7), and E8 (Expert 8).

Interpretive research paradigm (Taylor and

Medina, 2013) that corresponds to the nature of

humanistic pedagogy (Luka, 2008) was used in the

present empirical study. Interpretive paradigm is

characterized by the researchers’ practical interest

in the research question (Cohen, Manion and

Morrison, 2007). Researcher is the interpreter.

Exploratory research was employed in the

empirical study (Phillips, 2006). Exploratory

research is aimed at generating new questions and

hypothesis (Phillips, 2006). The exploratory

methodology proceeds from exploration in Phase 1

through analysis in Phase 2 to hypothesis

development in Phase.

The qualitatively oriented empirical study

allows the construction of only few cases

(Mayring, 2004). Experts should be selected

according to the aim of the research (Iriste and

Katane, 2018). The choice of experts was based on

two criteria (Flyvbjerg, 2006) such as recognized

knowledge in the research topic and absence of

conflict of interests. The number of experts

depends on the heterogeneity of the expert group:

the greater the heterogeneity of the group, the

fewer the number of experts (Okoli and Pawlovski,

2004). Thus, eight is an appropriate number of

PEC 2018 - International Conference on Pervasive and Embedded Computing

experts to make a decision in relation to the

innovation, namely gap structures and

characteristic properties for analysis of buyers’

burstiness in e-business process, as well as to

forecast and project the present research (Iriste and

Katane, 2018). Therein, the non-structured

interviews comprised eight experts who were

researchers from different countries. It should be

noted that all the researchers were connected with

research in such scientific fields as e-business,

computing and telecommunications. All the eight

researchers have an extended research experience

and they have decisively contributed to their fields

of expertise.

In order to analyse the model for analysis of

buyers’ burstiness in e-business process, non-

structured inteviews were caried out. Non-structured

interviews with experts were conducted in order to

search for the main categories of the research field

(Kroplijs and Rascevska, 2004).

Expert 1 emphasized that the mathematical

model for characterizing e-business process is

interesting. He found the idea to be interesting and

the model – fair. The expert suggested to implement

and show the related empirical work.

Expert 2 underlined that the authors argued that

burstiness is a feature that appears in many different

fields. The expert acknowledged that the authors

proposed a model for buyers’ burstiness in e-

business processes based on gap processes. The

expert pointed out that the authors deal with the

interesting problem, the contribution is well-written

and structured. Further on, the expert stressed that

the proposed model makes sense. The expert was

interested in hints about how this model could be

used to improve the performance of e-business

processes.

Expert 3 highlighted that the problem of buyers’

burstiness in e-business processes had been

examined, and the authors proposed a new model.

The problem is relevant and interesting. The expert

wished to clarify the benefits and use of the

proposed model.

Expert 4 pointed that the submitted paper

proposes to obtain a mathematical model of the

burstiness of e-business with gap process. The

author found that digital channel models such as

Wilhelm distribution are well suited for describing

the statistical properties.

Expert 5 admitted that the submitted paper

addresses an interesting problem. Expert 5 suggested

 a more detailed experimental evaluation to be

reported,

 more clear comparisons with the literature on the

gap analysis should be discussed, and

 the advantages of adopting the proposed analysis

should be presented more in detail.

Expert 6 identified that the paper aims to model the

burstiness that occurs during the buying process of

e-business transactions by defining the gap

structures and characteristics which occurs during

the bursts. The paper states the methodological

foundation of burstiness using queuing theory and

presents three approaches used to analyze such

burstiness. The paper defines burstiness in the

context of E-business processes. The paper defines

gap as an E-business process that ends without a

purchase and uses it to model the burstiness in the

buying behaviors of E-business users.

Expert 7 disclosed that by applying queuing

theory to the E-business phenomenon, the authors

design a novel analytical model by combining two

different disciplines. Expert 7 described that the

paper clearly defines what gap structure and gap

characteristic are and how they are applied to the E-

business processes.

Expert 8 revealed that the idea of relate bit-error

of traffic to business is interesting. The book gives a

very interesting point to relate the bursty property of

bit-error to business process. Queuing theory and

Hidden Markov Models (HMM) are highly related

to the main topic. The main strength of the

contribution is that it identifies the common property

between phenomenon of business process and bit-

errors in data transmission to be of a similar nature,

namely, the bursty nature. More analysis and

evaluation in this area will be very useful and

important.

Summarizing content analysis (Mayring, 2004)

of the data reveals that experts positively evaluated

the mathematical model based on gap processes for

studying buyers’ burstiness in e-business process.

5 CONCLUSIONS

The process of buying can be characterized by the

intervals between two consecutive buyers. Based on

measured gap interval distributions, suitable

distribution functions and their parameters are

determined. As a quality parameter, the minimum

mean square error was used. Beside the Weibull

distribution digital channel models like the Wilhelm

distribution are well suited for describing the

statistical properties. However, the applicability of

Gap Structure and Characteristic Properties for Analysing Buyers’ Burstiness in e-Business Process

this model concerning the simulation of buyers’

behaviour deserves further study.

This paper analyzed the burstiness of e-business

process aimed at obtaining a mathematical model

based on gap processes which was finally validated

by experts in the field. The empirical findings of the

research allow drawing the conclusions on experts’

positive evaluation of the model based on gap

processes for analysis of buyers’ burstiness in e-

business process.

The empirical findings assist in identifying

advantages of the presented research on the

proposed model based on gap processes for analysis

of buyers’ burstiness in e-business process. It should

be noted that advantages are identified as any trait,

feature or aspect that gives an individual, entity or

any other thing a more favorable opportunity for

success (Business Dictionary, 2016a). In contrast,

disadvantages are identified as any trait, feature or

aspect that does not give an individual, entity or any

other thing a more favorable opportunity for success

(Business Dictionary, 2016b). Such advantages of

the presented research on the proposed model based

on gap processes for analysis of buyers’ burstiness

in e-business process are outlined as

 the carried our research facilitates the

investigation of burstiness in a variety of

scientific fields,

 the presented research is of interdisciplinary

nature,

 a novel analytical model is designed by

combining two different disciplines, and

 the implemented research identifies the common

property between phenomenon of e-business

process and bit-errors in data transmission to be

of a similar nature, namely, the bursty nature.

Validity and reliability of the research results have

been provided by involving other researchers into

several stages of the conducted research. External

validity has been revealed by international co-

operation as following:

 the research preparation has included individual

interdisciplinary consultations given by other

researchers,

 the present contribution has been worked out in

co-operation with international colleagues and

assessed by international colleagues,

 the research has been partly presented at

international conferences.

Therein, the findings of the present research are

validated by other researchers.

The following research question has been put

forward: What are advantages of the model based on

gap processes for the analysis of buyers’ burstiness

in e-business process?

The present research has limitations. The inter-

connections between e-business process, the buyers’

burstiness and gap processes have been set.

Theoretical integration of gap processes into a

simulation model for the optimization of business

processes could be a limiting parameter as gap

processes are rooted in telecommunications.

Moreover, simulation models for optimization of

business and other processes are mostly based on the

queueing theory. It should be noted that gap

processes are an emerging phenomenon in the field

of the queueing theory. Another limitation is the

empirical study based on experts‘ evaluation only.

Therein, the results of the study cannot be

representative for the whole area. Nevertheless, the

results of the research, namely the elaborated model

based on gap processes for analysis of buyers’

burstiness in e-business process, may be used as a

basis for optimization of e-business process. If the

results of other empirical studies had been available

for analysis, different results could have been

attained. There is a possibility to continue the study.

The inter-relationships between the queueing

theory and gap processes are to be further analysed.

Comparative study of gap processes in

telecommunications and other scientific fields is to

be carried out within the future research. Integrating

the proposed simulation model based on gap

processes of bursty business process in a queuing

model would be the next step in order to benefit

from the simulation model presented in this work.

Parameter such as waiting time or queue length

should be studied and predicted. Further research

tends to facilitate the advancement of the theoretical

framework on burstiness in diverse and dynamic

environments. The search for relevant methods,

tools and techniques for burstiness detection,

regulation, monitoring, measurement, management,

simulation, evaluation in diverse and dynamic

environments is proposed. Further research

facilitates practical applications of the validated

simulation model based on gap processes for the

optimization of business process to evaluate buyers’

burstiness in business process as well as in a variety

of diverse and dynamic environments. A

comparative research of models for evaluation of

burstiness in diverse and dynamic environments

could be carried out, too. Further research would

tend to implement empirical studies with

participation of other groups of respondents.

PEC 2018 - International Conference on Pervasive and Embedded Computing

ACKNOWLEDGEMENTS

This work has been supported by Baltisch-Deutsches

HochschulKontor within the project “Advances in

Data Mining II: Interdisciplinary Studies”.

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