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Today, a firm’s major concern is to know the way in which an innovation is adopted in the marketplace. The purpose of this paper is to focus on the two-stage nature of diffusion process in which the time lag between people being informed and their act of making final purchase is considered.

The paper discusses an approach based on the time lag for modeling awareness and adoption process as two separate and yet connected processes. Varying forms of time lag (constant, deterministic or random) have been considered while modeling the required framework. Furthermore, an equivalence approach has been shown between the present framework and the two well-known and established approaches of infinite queuing theory and hazard rate function.

The results are verified on sales data of two different consumer durables and it show good prediction capability of proposed models in capturing the real-life scenario. Further, the equivalence approach helps us to quantify such scenarios which were difficult to be modeled with any one particular approach. Further, the possibility of capturing different market scenarios by studying various distribution functions has been identified.

The proposed methodology is based on a two-stage adoption process. The same can be extended to a multi-stage adoption process as in today’s competitive environment. “Motivation” is one such factor that is highly important which can be considered in some later studies. In future, the authors wish to study the multi-stage adoption process considering the different forms of time lag function.

The equivalence approach discussed in the paper can help to cater the possibility of capturing different market scenarios by studying various distribution functions.

The proposed approach helps to cater the time lag between awareness and adoption process and develop different mean value functions to account for the manner in which sales are happening under different circumstances. The proposed methodical approach can also help decision makers in managing their available resources in a prudent manner.

In the current market scenario, software upgrades and updates have proved to be very handy in improving the reliability of the software in its operational phase. Software upgrades help in reinventing working software through major changes, like functionality addition, feature enhancement, structural changes, etc. In software updates, minor changes are undertaken which help in improving software performance by fixing bugs and security issues in the current version of the software. Through the current proposal, the authors wish to highlight the economic benefits of the combined use of upgrade and update service. A cost analysis model has been proposed for the same.

The article discusses a cost analysis model highlighting the distinction between launch time and time to end the testing process. The number of bugs which have to be catered in each release has been determined which also consists of the count of latent bugs of previous version. Convolution theory has been utilized to incorporate the joint role of tester and user in bug detection into the model. The cost incurred in debugging process was determined. An optimization model was designed which considers the reliability and budget constraints while minimizing the total debugging cost. This optimization was used to determine the release time and testing stop time.

The proposal is backed by real-life software bug dataset consisting of four releases. The model was able to successfully determine the ideal software release time and the testing stop time. An increased profit is generated by releasing the software earlier and continues testing long after its release.

The work contributes positively to the field by providing an effective optimization model, which was able to determine the economic benefit of the combined use of upgrade and update service. The model can be used by management to determine their timelines and cost that will be incurred depending on their product and available resources.

The purpose of the present work is to mathematically model the reliability growth of a multi-version software system that is affected by infected patches.

The work presents a mathematical model that studies the reliability change due to the insertion of an infected patch in multi-version software. Various distribution functions have been considered to highlight the varied aspects of the model. Furthermore, weighted criteria approach has been discussed to facilitate the choice of the model.

The model presented here is able to quantify the effect of an infected patch on multi-version software. The model captures the hike in bug content due to an infected patch.

Multi-version systems have been studied widely, but the role of an infected patch has not been yet explored. The effect of an infected patch has been quantified by modeling the extra bugs generated in the system. This bug count would prove helpful in further studies for optimal resource allocation and testing effort allocation.

The purpose of this paper is to provide a mathematical framework to optimally allocate resources required for the discovery of vulnerabilities pertaining to different severity risk levels.

Different sets of optimization problems have been formulated and using the concept of dynamic programming approach, sequence of recursive functions has been constructed for the optimal allocation of resources used for discovering vulnerabilities of different severity scores. Mozilla Thunderbird web browser data set has been considered for giving the empirical evaluation by working with vulnerabilities of different severities.

As per the impact associated with a vulnerability, critical and high severity level are required to be patched promptly, and hence, a larger amount of funds have to be allocated for vulnerability discovery. Nevertheless, a low or medium risk vulnerability might also get exploited and thereby their discovery is also crucial for higher severity vulnerabilities. The current framework provides a diversified allocation of funds as per the requirement of a software manager and also aims at improving the discovery of vulnerability significantly.

The finding of this research may enable software managers to adequately assign resources in managing the discovery of vulnerabilities. It may also help in acknowledging the funds required for various bug bounty programs to cater security reporters based on the potential number of vulnerabilities present in software.

Much of the attention has been focused on the vulnerability discovery modeling and the risk associated with the security flaws. But, as far as the authors’ knowledge is concern, there is no such study that incorporates optimal allocation of resources with respect to the vulnerabilities of different severity scores. Hence, the building block of this paper contributes to future research.

The “quality” of any product or service defines the agility of the product and its life cycle in dynamic environment. The demand of high “quality” becomes an imperative concern, when “software” is acting as a product or a service. Since the nature of the software is intangible and more complex, therefore the assurance of providing accurate results is anxiety for companies. The overall quality of the software is based upon many individual factors (or attributes) that makes software reliable, inclined and a long-lasting product in the marketplace. But how these factors can influence each other is significant to identify. Therefore, the purpose of this paper is to study the quality aspect of the software and analyse the interrelationship of impactful attributes.

The analysis has been done through responses sought from software development teams/clients in India. The questionnaire related to the software quality was administered to the sample population. Interconnection among impactful characteristics has been analysed by using a qualitative technique called interpretive structural modelling (ISM). The driving and dependency of the attributes under consideration has been classified using cross-impact matrix multiplication applied to classification (MICMAC) analysis. The procedure of applying ISM method has been automated and provided it as package “ISM” using R software.

In general, it is very complex job to determine the most impactful attribute of software quality. By applying ISM and MICMAC analysis on the set of attributes under consideration, it has been found that “reliability” along with “usability” and “performance” is the most influential attribute of software quality and preferred most.

Though ISM provides an organized modelling framework yet its results are considered less statistically significant. Therefore, it would be interesting to concatenate the present findings with the findings of any analytical methodology; which gives statistically significant results.

The present proposal deals with the interpretation of the software quality attributes and their contextual relationship but with more effective and efficient manner. It can help management to understand the complexity of relationship amongst attributes (which are quality attributes here) more accurately and precisely. Since today is an era of automation, the manual part is being substituted so as to reduce the labour cost, improve safety, security and product quality to increase production. This study is, therefore, an effort and a helping hand in making the hassle free calculations for obtaining intermediate matrices and doing eventual calculations.

n numbers of parameters can be selected to analyse the interrelationship of any project/study. Eradication human errors in applying transitivity law or applying any other operation in solving problem. The package created here can save precious time of users. Provides well-formatted and readable excel output files that make interpretation easier.

Software is one such product/service which plays a significant role in this high-technological world, where each and every firm try their best to be on the top of the list of consumers’ preference. For this purpose, companies reduce manual efforts by converting it into qualitative software that provides deliverables in a systematic manner. Therefore, it becomes imperative to study various interrelated quality attributes of the software. On the similar platform, ISM is a widely used technique and just to provide a helping hand in quantification of the qualitative attributes this paper facilitates the readers with algorithm developed using R software.

The ideology of this article is to study the performance concerns of SDN Controllers, with the help of developed SRGM and thereby obtain its optimal testing duration. The effect of undetected uncertainty in the parameter values have also been catered in the proposal.

These uncertainties in the parameter values are studied as the risk of not meeting desired set of requirements, whose removal causes additional cost. Considering these two constructs as attributes of MAUT, the controller's optimal testing duration is obtained.

The article focuses towards obtaining the optimal duration for which the SDN Controllers must be tested. It was observed that the inculcation of risk-attribute has provided the higher utility value as compared to any other existing scenarios.

Plenty of SRGM have been proposed in the literature which talks about the testing stop time determination problems. But, none of them have considered the impact of risk of not meeting the requirements (reliability) along with cost to obtain its testing stop time. Further, validation of the proposed model in presented with the help of two releases versions of SDN controller platform, ONOS, entitled as “Kingfisher” and “Loon” and has acquired promising results.

The purpose of this study/paper is to propose a mathematical model that is able to predict the future popularity based on the view count of a particular YouTube video. Since the emergence of video-sharing sites from early 2005, YouTube has been pioneering in its performance and holds the largest share of internet traffic. YouTube plays a significant role in popularizing information on social network. For all social media sites, viewership is an important and vital component to measure diffusion on a video-sharing site, which is defined in terms of the number of view counts. In the era of social media marketing, companies demand an efficient system that can predict the popularity of video in advance. Diffusion prediction of video can help marketing firms and brand companies to inflate traffic and help the firms in generating revenue.

In the present work, viewership is studied as an important diffusion-affecting parameter pertaining to YouTube videos. Primarily, a mathematical diffusion model is proposed to predict YouTube video diffusion based on the varying situations of viewership. The proposal segregates the total number of viewers into two classes – neoterics viewers, i.e. viewers those viewing a video on a direct basis, and followers, i.e. viewers those watching under the influence.

The approach is supplemented with numerical illustration done on the real YouTube data set. Results prove that the proposed approach contributes significantly to predict viewership of video. The proposed model brings predicted viewership and its classification highly close to the true value.

Thereby, a behavioral rationale for the modeling and quantification is offered in terms of the two varied and yet connected classes of viewers – “neoterics” and “followers.”

The relationship between the various existing smell taxonomies and the smell impacting factors has been established. The ideology is to identify the most critical smell influencing factors in the vicinity of various software development environments.

To fulfill the said task, the utilization of the amalgamation of two multicriteria decision-making techniques, namely, Entropy method and CODAS method, is presented.

Through this article, the most critical smell impacting criteria with respect to the smell taxonomies is identified. Furthermore, the behaviour of 4 software development principles was then analysed, and their working state has been successfully assessed.

The ideology to study design-related smells in the software system has been studied by a lot of researchers. Some of them have worked upon their detection and the corresponding refactoration process with the help of several algorithms like machine learning and artificial intelligence. But how and to what extent these design-related smells impact the software development environment has remained out of the limelight till now. Through this article, this research gap has been identified, and an attempt to fill it has been made.

YouTube allows its users to upload and view videos on its platform. YouTube provides notification to the subscribers whenever a channel uploads a new video thereby making the channel subscribers the potential viewers of the video. And thus, they are the first to come to know about any new offering. But later on, the view count also increases due to virality, that is, mass sharing of the content by the users on different social media platforms similar to word-of-mouth in the field of marketing. Therefore, the purpose of this paper is to examine different diffusion patterns as they can help to inflate traffic and generate revenue.

YouTube's view count grows majorly through virality. The pattern of view count growth has generally been considered unimodal in most of the available research in the field of YouTube. In the present work, the growth process due to views through the subscribers and views due to word-of-mouth (virality) is presented. Considering that the impact of virality in view count growth comes later in the video life cycle; the viewing patterns of both the segments have been mathematically modeled; independently.

Different models have been proposed to capture the view count growth pattern and how the impact of virality changes the view count growth curve and thereby results in a multimodal curve structure. The proposed models have been verified on various view count data sets of YouTube videos using SPSS (Statistical Package for the Social Sciences), and their ranks have been determined using a weighted criteria–based approach. The results obtained clearly depict the presence of many modes in the life cycle of view counts.

Till now, the literature is evident of the video life cycle following a bell shape curve. This study claims that the initial thrust is by subscribers and then the contribution in the view count by people watching via word-of-mouth comes into picture and brings in another hump in the growth curve.

Mathematical modeling of innovation diffusion is a constantly evolving field within marketing science. The diffusion process explains the dispersion of an innovation among potential buyers. Prior research on innovation diffusion has been based on modeling varied aspects of real life situations in marketing. One such aspect is studying the adoption process depending on the awareness and motivation level among the customers. Awareness is having knowledge of an innovation, whereas motivation is about the perception of an individual. In line with these aspects, the purpose of this paper is to propose a unified modeling framework for the adoption process based on the awareness and motivation about the product.

When the market is well informed about the product, there are some people who are motivated and some, who have adopted the product earlier and shall now influence others in their buying behavior. It is very much similar to queuing system in which some units are waiting in a queue for the service, service for some units are being processed and some units have already been served. This analogous behavior between two approaches has motivated the use of infinite server queuing theory in modeling adoption of the product. Thereafter, the authors have proposed a unification scheme to model different market scenarios.

From analyzing the values of comparison criteria, it was not clear that which among them is performing best. Thus there was a need for an approach which can judiciously find the optimal model. For this very purpose the authors applied distance-based approach which was capable of computing the optimal model based on the distance of attribute value from the optimal. The analysis performed on two real life sales data sets depict that model in which awareness is following logistic pattern and motivation and adoption are following a constant pattern is ranked one.

The idea has been validated on product. It would be interesting to know how the methodology works on service.

The modeling framework discussed in this paper can be helpful to know from the available set of alternative, which among them is performing better in capturing the spread of the product in the market. The proposed framework offer some managerial guidance by highlighting the unusual aspects of diffusion process and also present an approach to judge the best among a set of different models.