Gap Processes for Analysing Buyers’ Burstiness in E-Business Process

Andreas Ahrens and Jelena Zaš

cerinska

Hochschule Wismar, University of Technology, Business and Design

Philipp-Müller-Straße 14, 23966 Wismar, Germany

Keywords:

E-Business Process, Buyers’ B urstiness, Gap P r ocesses, Binary Customer Behaviour.

Abstract:

Success of e-business process requires analysis of buyers’ burstiness. The research question is as follows: H ow

to describe buyers’ burstiness in e-business by a mathematical model? The aim of the research is to provide

a mathematical model for evaluation of buyers’ burstiness in e-business process. In this work the buyers’

burstiness in e-business process is described by a mathematical concept based on gap processes. Therefore,

the meaning of the key concepts of buyers’ burstiness, binary customer behavior and gap processes is studied.

Moreover, the analysis demonstrates how the key concepts are related to the idea of e-business process and

shows a potential model for development, indicating how the steps of the process are related following a

logical chain: conceptual framework → model development → empirical study → conclusions. The results

of the present research show the model for evaluation of buyers’ burstiness in e-business process. The model

itself is based on the assumption that the gaps between two buyers are statistically independent from each

other. The novel contribution of t he paper is revealed in the newl y created mathematical model for evaluation

of buyers’ burstiness in e-business process via gap processes.

1 INTRODUCTION

The phenomenon of burstiness attracts more and mo re

research efforts as it inﬂuences the ﬂow of a number

of processes including e-business. It should be noted

that th e ﬂow of e-business process is permanently op -

timized in order to increase the proﬁt (Ahrens et al.,

2015a ). Optimization of e-business process implies

choices about quantity of goods to be delivered, num-

ber of the staff to be employed as highlighted in

(Ahrens et a l., 2015a ), goods’ pricing, goods dis-

counts, computer software to be installed, network-

ing between a business company and its customers

to be established, etc. Additionally, such a result of

business process as purchase and/or sale of a good or

service indicates the output of this process. By phe-

nomenon’s burstiness, intervals of high-activity al-

ternating with long low-activity periods are meant.

Tab. 1 demonstrates the pheno menon of burstiness in

a range of scientiﬁc ﬁelds.

Beginning in 1960 Gilbert presented the ﬁrst

model in telec ommun ications 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 evaluate the perfor-

mance or, in other words, e-business process in the

present research, as well as a basic set of parameters

or, in other words, criteria, are still relevant today.

In business including e-business, burstiness of

workload is traditionally analyzed (Heinrich, 2014).

However, the paradigm has changed from an input

based business process or, in other words, burstiness

of workload to an outcome based process o r, in other

words, burstiness of buyers (Ahrens et al., 2015a).

The shift from analysis of burstiness of workload

to evaluation of burstiness of buyers allows increas-

ing the efﬁciency of e-business process and, conse-

quently, e-business proﬁt. It should be noted that the

concept burstiness of buyers is developed by the inter-

national group of researchers such as Ahrens, Purvi-

nis, Zaš

cerinska, Andre eva ( A hrens et al., 2015a).

The previous work in the ﬁeld of burstiness of buy-

ers includes elaboration of a concep tual framework on

criteria for qualitative decisions in business (Ahr ens

et al., 2015b), mathematical analysis of gap pr ocesses

underpinning elabor ation of a simulation model of b i-

nary customer behaviour within business related pro -

cesses (Ahrens et al. , 2015a), d esign of a simulatio n

model of binary customer behaviour in a bursty busi-

ness process b a sed on gap processes (Ahren s et al.,

2016).

The research question is as follows: How to de-

scribe buyers’ burstiness in e-business by a mathemat-

ical model?

Ahrens, A. and Zascerinska, J.

Gap Processes for Analysing Buyers’ Burstiness in E-Business Process.

DOI: 10.5220/0005957900780085

In Proceedings of the 13th International Joint Conference on e-Business and Telecommunications (ICETE 2016) - Volume 2: ICE-B, pages 78-85

ISBN: 978-989-758-196-0

Table 1: Burstiness in different scientiﬁc ﬁelds

Scientiﬁc ﬁeld Phenomenon of burstiness

Telecommunications Burstiness of bit-e rrors in data transmission

Economics Burstiness of crises

Natural sciences Burstiness of disasters or earthquakes

Logistics Burstiness of trafﬁc

Social media Burstiness of hot topic, keyword or event

Business Burstiness of workload

E-Business Burstiness of buyers

The aim of the research is to provide a mathemat-

ical model fo r evaluation of buyers’ burstiness in e-

business process. The novel contribution of the paper

is revealed in the newly created mathematical model

for evaluation of buyers’ burstiness in e-business pro-

cess via gap processes. For the model elabora tion, the

meaning of the key concepts of buyers’ burstiness, bi-

nary customer behavior and gap processes is studied.

Moreover, the analysis demonstrates how the key con-

cepts are related to the idea of e-business process and

shows a potential model for development, indicating

how the steps of th e process are related following a

logical chain: conceptual framework → model devel-

opment → empirical study → con clusions.

The present contribution employs interdisci-

plinary research as it assists in synthe sizing, c onnect-

ing and blending ideas, data and information, meth-

ods, tools, concepts, and/or theories from two or more

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

For the design of a mathematical model fo r evalua-

tion of buyers’ burstiness in e-business process, the

synergy between e-business and telecommunications

is promoted as the phenome non of customer s in the

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

mission appear to be of a similar nature, namely, th e

bursty nature. Such mathematical models that con-

sider the bursty nature of bit-errors in data transmis-

sion have been successfully implemented in telecom-

munications for optimizing data communication pro-

tocols and will be adopted in this work to the buyers’

burstiness in e-business process. It should b e noted

that the present research is not limited to only two

scientiﬁc discip lines, na mely e-business and telecom-

munication, but is based on a number of scientiﬁc dis-

ciplines such as business, social media, logistics, lit-

erature, etc.

The remaining part of this paper is organized as

follows: Section 2 introduces buyers’ burstiness in e-

business process. A mathematical model for evalu-

ation of buyers’ burstiness in e-business process via

gap processes is presented in Section 3. The associ-

ated results of an empirical study will be discussed

in Section 4. Finally, some concluding remarks are

provided in Section 5.

2 BUYERS’ BURSTINESS IN

E-BUSINESS PROCESS

By e -business process, the process o f buying

and/or selling of goods and/or service s through In-

formation and Communication Techno logies ( ICT)

is mean t. In the present work, e-business process

is built within the paradigm of binary customer be-

haviour. For deﬁning binary customer behaviour,

such an everyday e-business situation is con sid ered

as potential custo mers have to solve an issue for-

mulated alr e ady in 1603 by William Shakespeare in

his play Ha mlet such as to be, or not to be (Shake-

speare, 1825). Regard ing a modern interpretation of

potential customers’ contem porary problems, Shake-

speare’s words ma y sound as to buy, or not to buy. It

should be noted that to buy, or not to buy is consid-

ered as binary customer behavior depicted in Fig. 1.

Fig. 2 shows a typical scenario in which a buyer who

To buy

Not to buy

Binary customer behavior

Figure 1: Elements of customers’ binary option

made a purchase as the output of e-business process

is highlighted (represented by "x") within a sequenc e

of people (represented by "-") who visited an e-shop.

It should be noted tha t by e-shop visitor any customer

who seeks and examines a product without buying it

is understood. E-business process which ends without

a purchase or sale cr eates a ga p between two buyers

(Ahrens et al., 2015a). These gaps are assumed to

be statistically independent from e ach other (Ahrens

et al., 2015a).

Gap Processes for Analysing Buyers’ Burstiness in E-Business Process

- - - - - - - - - - - - - - - - x - - - - - - x - - - - x

- - - x - - - - x - - - - - - - - - - - x x - - - - - - -

- - - - - - - - x - - - - x - - - - - - - - x - - - - - -

- - - - - - - - - x x - - - - - - - - - - - - - - - x - -

- - - - - - - - - - - - - - - - - x - - - - - - - - - - -

- - - - x - - - - - - - - - - - x - - - - - - - - - - - -

- - - - - - - - - - x - - - - - - x - - - - - - - - - - -

- - - - - - x - - - - - x - - x - - - - - - - - - - - - -

- - - - - - - - x - - - - - - x - - - - - - - - - - - - x

- - - x - - - - - - - - - - - - - - - - - x x x x x - - -

x - - - - - - x - - - - - - - - - - x - - - x - - - - - -

- - - - x - - - - - - - - - - - - - - x - - - - - - - - -

- x - - - x - - - - - - - - - - - x - x - - - - - - - - -

- - - - - - - - x - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - x - - - - - - - - - - - -

- - - - - - - - x x - - - - - - - - - - - - - - x - - - -

- - - - - - - - - - - - - - - - - - x - - - - - - - - - -

- x - - - - - - - - - - - - - x - - x - - - - - - - - - -

- - - x - - - - - - - - - - - - - - - - - - - x - - - - -

- - - - - - - - - - - x - - - - - - - - - - - x - - - - -

- - - - - - - - x - - - - - - - - - - - - - x - - - - - -

- x - - - - - - - - - - - - - - - x - - - - - - - - - - -

- - - - - - - - x x - - - - - - - - - - - - x - - - - - -

Figure 2: A buyer (represented by "x") within a sequence

of e-shop visitors (represented by "-")

x x - x x x - - x x x x x x - x x - - - - - - - - - - - -

- - - - - - - x x x x - x - - x x - - x x - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - x x x x

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - x x - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - x x x x - - - - - x - - x x -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - x x x - - - - x x x - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - x x x - - - - - - - - - - - - - - - x x - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

x x x x x - - - - - - - - - - - x x - - x x x x x x - x -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - x x x x x x - - - - - - - - - - - - - - - - - - - -

Figure 3: Buyers’ burstiness (represented by "x") within a

sequence of e-shop visitors (represented by "-")

It should be noted that the terms "ga p", "ga p pro-

cess" and "gap distribution function" are used synony-

mously in th e present c ontribution. Gaps are rooted in

the Hidden Markov Models (HMM) (Gilbert, 1960;

Elliott, 1963). What has however intere sted commu-

nication 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 pro c edure. These p robabilities are

typically difﬁcult to present analytically. Some so-

lutions were presented by Wilhelm in 1976 resulting

in gap models such as the L-model or the A-model

(Wilhelm, 1976; Ahrens, 200 0). With these models

the bursty nature of tr a nsmission errors in ICT cou ld

be simulated. This approach based on gap processes

is now considered as a possible solution of evaluation

of buyers’ burstiness in e-business process. Fig. 4 il-

lustrates the e-business proc ess between two buyers

described by gaps. However, the buyers can be more

block interval n

buyer

sequence of people

visitor

Figure 4: Buyer’s gap for describing binary customer be-

havior

indepen dently distributed over e. g. a day or they can

appear really concentrated a s highlighted in Fig. 3.

In situations where binary decisions in e-business

processes such as selling or buying are made, not

only purchases and sales are of any interest but also

how concentrated goods are sold or bought. That is

why mo dels which focus only on the purchases and

sales with a given probability are not exact enough to

describe e-business process. In general, the buyers’

probability can serve as a clear in dicator of how of-

ten people decide to buy e. g. a pro duct. However,

the buyers’ probability does n ot de liver any infor-

mation about how concentrated the purchases and/or

sales are. Thus, buyers’ burstiness is a criterion in

e-business process. The criterion of buyers’ bursti-

ness includes suc h indicators as buyers’ probability

and buyers’ concentration (Ahrens et al., 201 5a) as

summarized in Tab. 2.

Table 2: Criterion and indicators of burstiness in e-business

process

Criterion Indicator

Buyers’ burstiness Buyers’ probability and

Buyers’ conc e ntration

For comparison p urposes of the present interdis-

ciplinary research, Tab. 3 demonstrates the criterion

and indicator of evaluation of burstiness of hot topic,

keyword, event, etc . in a sequence of batched geo-

referenc e d documents in social media. This model is

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 infor-

mation (Kotozaki et al., 2015).

Table 3: Criterion and indicator of burstiness in social me-

dia

Criterion Indicator

Burstiness of hot topic or

keyword in a sequence of Locality

batched geore ferenced documents

ICE-B 2016 - International Conference on e-Business

This group of Japan e se researchers built their

model of evaluation of burstiness of hot topic, key-

word, etc in a sequence of batched geo referenced

docume nts on Kleinberg’s burst detection algorithm,

which is based on a queuing theory fo r dete c ting

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., 20 15).

A comparison of the model of evaluation of bursti-

ness of hot topic, keyword, etc. in social media shown

by the group of Jap anese researcher s (Kotozaki et al.,

2015) with the model for evaluation of buyers’ bursti-

ness in e-business process is reﬂected in Tab. 4. The

compara tive analysis of Tab. 4 reveals that Klein-

berg’s burst detection algorithm, which is based on a

queuing theory, is built on a sequ ence of phenomena

while gap distribution function is featured by sequen-

tial indep endence of g aps between two buyers.

The comparative analysis assists in concluding

that e-business process is char acterized by sequential

indepen dence of gaps between two buyers. Conse-

quently, the methodological background fo r evalua-

tion of buyers’ burstiness in e-business process should

take it into account while developing a m athemati-

cal model for evaluation of buyers’ burstiness in e-

business process.

3 MODEL FOR EVALUATION OF

BUYERS’ BURSTINESS IN

E-BUSINESS PROCESS

The term "model" is of gre at re search interest. In

pedagogy, by mode l a pa ttern is meant. In mathemat-

ics, a mode l is an interpretation of a theory. In e ngi-

neering, business and comp uter sciences, a model de-

scribes a system. Interdisciplina ry (pedagogy, ma the-

matics, engineering, business and comp uter sciences)

analysis of the term mode l leads to such a newly de-

ﬁned notion of the term model a s a pattern of individ-

ual’s or individuals’ interpretation of a phenomenon.

Models can b e presented in a variety of forms such as

verbal, graphic, computer, e tc .

For model creation, we can deﬁne a block interval

n (identiﬁed as the probability p

(n) where at least

one buyer ap pears. The parameter n refer s e.g. to the

number of people en te ring a shop in a given time e. g.

a day. Choosing the para meter n = 1 the probability

(n) equals the buyers probability p

The block buyer probability p

(n) can be de -

scribed as a function of the buyers’ probability p

and

the block interval leng th n as investigated by real data

0 0.5 1 1.5 2 2.5 3

−2

−1.5

−1

−0.5

log

(n)) →

log

(n) →

Survey 1

Survey 2

Survey 3

Figure 5: Measured block buyer’s probabilities p

(n) as a

function of the interval l ength n

analysis (see Fig. 5). Here, the following approx ima-

tion is used

(n) =



· n

1 ≤ n ≤ n

1 n > n

(1)

Re-writing (1) yields

log

(n)) = α log

(n) + log

) . (2)

Therein, the value α denotes the linear dependence

between log

(n)) and log

(n) and is a mea-

sure for the buyers’ concentration (also referred to

the conc e ntration of buying). The value of n

in-

dicates the maximum interval length to which the

linear-dependence can be maintained (see also Fig. 6).

0 1 2 3 4

−2

−1.5

−1

−0.5

log

(n)) →

log

(n) →

(1 − α) = 0.0

(1 − α) = 0.2

(1 − α) = 0.5

Figure 6: Approximated block buyer’s probability p

(n) as

a function of the interval length n for different parameters

of the (1 − α) at a buyer’s probability of p

= 10

−2

The analysis of c oncentration parameters (1 − α)

(referred to the concentratio n of buying) has shown

that parameters in the range of 0.0 until 0.5 describe

Gap Processes for Analysing Buyers’ Burstiness in E-Business Process

Table 4: Comparison of models for evaluation of burstiness in social media and e-business process

Model’s Element Social Media E-Business Process

Sequence of batched Sequential independence

Feature georefe renced of gaps

docume nts between two buyers

Kleinberg’s burst

Methodological detection algorithm Gap distribution

backgr ound based on queuing function

theory

realistic scenarios. Thereby, a parame te r (1 − α) = 0

describes the situation where the potential buyers ap-

pear independently distributed from each other. With

increasing parameter (1 − α) the buyers appear more

and more concentrated and the probability p

(n) de-

creased for a given n.

Describing the buying process b y gaps, the block

buyer probability p

(n) can be deﬁned by the gap -

distribution function u(k) = P(X ≥ k), which de-

scribes the probability of a gap larger than k, as high-

lighted in Fig. 7. With the assumption that the dis-

tances (gaps k) between neighboring buyers are sta-

tistically independent from eac h other, the buyers’

characteristic, namely the occurrence of bursty buy-

ers, is deﬁned by the buyers’ gap-distribution function

u(k) = P(X ≥ k) completely. The approach

(n) =







n−1

∑

k=0

u(k) 1 ≤ n ≤ n

1 n > n

(3)

can be used to develop the buyer’s gap distribution

function u(k) for the buyers’ gaps step by step. Com-

paring (1) an d (3), one gets:

n−1

∑

k=0

u(k) = n

1 ≤ n ≤ n

(4)

and for the searc hed error-gap distribution u(k) we

yield step by step:

n = 1 : u(0) = 1

n = 2 : u(0) + u(1) = 2

n = 3 : u(0) + u(1) + u(2) = 3

··· : ··· = ···

n ≤ n

: u(0) + u(1 ) + ···+ u(n − 1) = n

The buyer’s-gap distribution function u(k) results ﬁ-

nally in

u(k) =



(k + 1)

− k

0 ≤ k < n

0 k ≥ n

(5)

Re-writing of u(k) leads to the buyers-gap density

function v(k) = P(X = k), which de scribes the prob-

ability of a gap X equal to k:

u(k) = v(k) + v(k + 1) + v(k + 2) + ···

u(k + 1) = v(k + 1) + v(k + 2) + · · ·

and by calculating the d ifference between u(k) and

u(k + 1) the buyers-g ap density function v(k) =

P(X = k) ca n be obtained

v(k) = u(k) − u(k + 1) . (6)

Assuming that the buyers are independently dis-

tributed, i.e. (1 − α) = 0, and using equation (5) and

(6) one gets the following re sult for the buyers-gap

density function v(k):

v(k) =



1 k = (n

− 1)

0 k 6= (n

− 1)

(7)

With this result, the disadvantage of the model setup

becomes evident. The model setup deﬁned in (1)

leads to a deterministic buyers-gap process. In sit-

uations, wh e re the buyers appear concentrated, i.e.

(1 − α) > 0, one can a lso ﬁnd an enlarged value at

v(n

− 1). This error leads to engraving inaccuracies

in the simulation process. The reason is the disconti-

nuity at n = n

in equation (1). A modiﬁcation of this

model setup is necessary.

The following so lution can be assumed: The lin-

ear increases of log

(n)) can only be accepted

for sma ll parameters of n. The value of log

(n))

has to change steadily into the value lo g

(n)) = 0

for larger n. To the minimization of the model inac -

curacy at v(n

− 1) equation (5) has to be multiplied

by the value e

−β k

. The m odiﬁcation of the model

approa c h is highlighted in Fig. 8 with respect to the

block buyer’s probability p

(n).

For the buyers-g a p distribution function u(k) the

following expression arises:

u(k) = ((k + 1)

− k

) · e

−β·k

0 ≤ k ≤ ∞ (8)

with

lim

k→∞

−β·k

= 0 β > 0 (9)

ICE-B 2016 - International Conference on e-Business

block interval

n = 3

P(1 buyer on position 1)

p u(0)

P(1 buyer on position 2)

p u(1)

P(1 buyer on position 3)

p u(2)

buyer

with p

Figure 7: Calculating the block-error probability p

(n) using the error-gap distribution function u(k)

0 1 2 3 4

−2

−1.5

−1

−0.5

log

(n)) →

log

(n) →

Eq.(1)

Proposed setup

Figure 8: Approximated r el ationship between the probabil-

ity p

(n) and the block interval n for different parameters

of the (1 − α)

and

β ≈ p

1/α

. (10)

Fig. 9 illustrates the buyers-gap distribution func-

tion u(k) for different parameters (1 − α) assum-

ing a buyer’s probability of p

= 10

−2

. The resul-

tant buyers-g a p density function v(k) is depicted in

Fig. 10. With these modiﬁcations, the buyers char-

acteristic can be modeled by two parameters (the

buyer’s probab ility p

and the buyer’s concentration

value (1 − α)).

4 EMPIRICAL ANALYSIS

The present part of the co ntribution demonstrates

the design, results and ﬁn dings of the e mpirical study.

0 20 40 60 80 100

0.2

0.4

0.6

0.8

u(k) →

n →

(1 − α) = 0.0

(1 − α) = 0.2

(1 − α) = 0.5

Figure 9: Buyers-gap distribution function u(k) for different

parameters of the (1 − α) at a buyer’s probability of p

−2

The design of the study comprises the purpose and

question, materials and m ethodology.

The emp irical study was aimed at evaluating the

buyers’ burstine ss in a e-business process. It should

be noted that for the empirical study’s purposes, by

e-business process, the process of buying a scientiﬁc

paper is determined. The empirical study’s question

was as follows: Is the e-business process, name ly the

online process of selling and buying a scientiﬁc paper,

characterized by buyers’ burstiness? The present em-

pirical study was c a rried out in January 2016. A naly-

sis of statistical documents of e-shop which sells sci-

entiﬁc papers was carried out.

Interpr e tive research paradigm was used in the

present empirical study. The in te rpretive paradigm

aims to understand other cultures, from the inside

Gap Processes for Analysing Buyers’ Burstiness in E-Business Process

0 2 4 6 8 10

−2

−1

v(k) →

n →

(1 − α) = 0.0

(1 − α) = 0.2

(1 − α) = 0.5

Figure 10: Buyers-gap density function v(k) for different

parameters of the (1 − α) at a buyer’s probability of p

−2

through the use of ethnographic methods such as in-

formal interviewing, participan t observation and es-

tablishment of ethically sound relationships (Taylor

and Medina, 2013).

Explora tory research aimed at generating new

questions and hypothesis was employed in the empir-

ical study (Phillips, 2006). The exploratory method-

ology proceeds from exploration in Phase 1 through

analysis in Phase 2 to hypothesis development in

Phase 3.

The qualitatively oriented empirical study allows

the construction of only few cases (Mayring, 2004).

The cases themselves are not of interest, only the con-

clusions and transfers we c an draw from these doc-

uments (Flyvbjerg, 20 06). Selecting the cases fo r

the case study comprises use of information-oriented

docume nts, as opposed to random documents (Flyvb-

jerg, 2006). This is b ecause an average case is often

not the richest in information. I n addition, it is often

more important to clarify the deeper causes behind a

given problem and its consequences than to describe

the symptoms of the pro blem and how frequently they

occur (Flyvbjerg, 2006).

Analysis of statistical documents of e-shop which

sells scientiﬁc papers revealed that one author’s

website was visited 1161 times in 2015. From

around 100 scientiﬁc papers of this particular au-

thor, one scientiﬁc paper was bought 109 times in

2015. Fig. 11 demonstrates the monthly distribu-

tion of the purchases of this particular scientiﬁc pa-

per. Summarizing content analysis (Ma yring, 2004)

of the data reveals the buyers’ burstiness in buying an

e-product.

1 2 3 4 5 6 7 8 9 10 11 12

sales →

month →

Figure 11: Monthly distribution of the purchases of this par-

ticular scientiﬁc paper.

5 CONCLUSIONS

The theoretical analysis of the binary customer

behaviour assists in outlining gap processes in e-

business process. The theoretical ﬁndings on the

inter-relationship between e-busine ss process, binary

customer behaviour, the buyers’ burstines and gap

processes allow determining the model for evalu-

ation of buyers’ burstiness in e-business p rocess.

The model for evaluation of buyers’ burstiness in e-

business process is based on the chosen g ap distribu-

tion function. The proposed model could be used for

both, namely simulation and detection of burstiness

of buyers. The presented mathematical model could

be used when making business decisions about the re-

sources neede d to pr ovide a serv ic e.

The empirical ﬁndings of the research allow draw-

ing the conclusion s on the buyers’ burstiness in e-

business process. The following new research qu es-

tion has been formulated: How to optimize e-business

process based on gap processes?

The present research ha s such limitations: The

inter-connections betwee n e-business process, binary

customer behaviour, the buyers’ burstines and gap

processes have been set. Another limitation is the

empirical study based on one case only. Therein, the

results of the study cannot be representative for the

whole area . Nevertheless, the results of the research,

namely the elaborated mathematical model for evalu-

ation of buyers’ burstiness in e-business process that

is based on gap processes, m ay be used as a basis of

analysis of buyers’ burstiness in e-business process. If

the results of other cases had been available for anal-

ysis, different results could h ave been attained. There

is a po ssibility to continue the study.

Further research tends to facilitate the advance-

ment of intercon nections betwe en buyers’ burstiness

and e-business process. The search for relevant meth-

ods, tools an d techniques for evaluation of buyers’

burstiness in e-business process is proposed. Fu-

ture research tends to analyse the implementation

of the elaborated m athematical model based on gap

processes for evaluation of buyers’ burstiness in e-

ICE-B 2016 - International Conference on e-Business

business process. A comparative research of models

for evaluation of burstiness in other scientiﬁc ﬁelds

could be carried out, too.

REFERENCES

Ahrens, A. (2000). A new digital channel model suitable

for the simulation and evaluation of channel error ef-

fects. In Colloquium on Speech Coding Algorithms

for Radio Channels, London ( U K).

Ahrens, A., Purvinis, O., Zaš

cerinska, J., and Andreeva, N.

(2015a). Gap Processes for Modelling Binary C us-

tomer Behavior. In 8th International Conference on

Engineering and Business Education, pages 8–13, Os-

tfold University College, Fredrikstad (Norway).

Ahrens, A., Zaš

cerinska, J., Purvinis, O., and Andreeva,

N. (2015b). Criteria for Qualitative Decisions in

Business Logistics: Conceptual Framework. In 10th

International Conference Intelligent Technologies in

Logistics and Mechatronics Systems (ITELMS), pages

11–20, Panevezys (Lithuania).

Ahrens, A., Zaš

cerinska, J., Purvinis, O., and Andreeva, N.

(2016). A Model for Simulation of Binary Customer

Behaviour in a Bursty B usiness Process. In Interna-

tional Forum on Innovative Technologies and Man-

agement for Sustainability., Panevezys (Lit huania).

Elliott, E. O. (1963). Estimates of Error Rates for Codes on

Burst-Noise Channels. Bell System Technical Journal,

42(5):1977–1997.

Flyvbjerg, B. (2006). Five Misunderstandings About Case-

Study Research. Qualitative Inquiry, 12(2):219–245.

Gilbert, E. N. (1960). Capacity of a Burst-Noise Channel.

Bell System Technical Journal, 39:1253–1265.

Heinrich, R. (2014). Aligning Business Processes and In-

formation Systems: New Approaches to Continuous

Quality Engineering. Springer, New York, 1 edition.

Kotozaki, K., Tamura, K., and Kitakami, H. (2015). Identi-

fying Local Burstiness in a Sequence of Batched Geo-

referenced Documents. International Journal of Elec-

tronic Commerce Studies, 6(2):269–288.

Mai, T., Aj wani, D., and Sala, A. (2015). Proﬁling User

Activities with Minimal Trafﬁc Traces. In 15th In-

ternational Conference Engineering the Web in the

Big Data Era (ICWE)., pages 116–133, Rott erdam

(Netherlands).

Mayring, P. (2004). Qualitative Content Analysis. In A

Companion to Qualitative Research, pages 266–269.

SAGE, Glasgow (UK).

Phillips, D. (2006). Comparative education: method. Re-

search in Comparative and International Education,

1(4):304–319.

Repko, A. (2012). Interdisciplinary Research Process and

Theory. SAGE, New Jersey, 2 edition.

Shakespeare, W. (1825). The Tragicall Historie of Hamlet

Prince of Denmarke. As it hath beene diuerse times

acted by his Highnesse seruants in the Cittie of Lon-

don: as also in the two Vniuersities of Cambridge

and Oxford, and else-where [The "First Quarto"].

Nicholas Ling & J. Trundell, London.

Taylor, P. C. and Medina, M. N. D. (2013). Educational

research paradigms: From positivism to multiparadig-

matic. The Journal of Meaning-Centered Education.,

1(2).

Wi lhelm, H. (1976). Datenübertragung (in German). Mil-

itärverlag, Berlin.

Gap Processes for Analysing Buyers’ Burstiness in E-Business Process