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![Adarsh Anand, Jasmine Kaur, Anu A. Gokhale, and Mangey Ram
1 Impact of available resources on software
patch management
Abstract: Software security has been an area of immense research as most of the
things surrounding us are technology based. Much has been talked about vulner-
abilities, their categories and types. Some studies elaborated and extended the
available discovery models but few have considered the correction process in the
same work. In this study, an approach to deal with software vulnerability through
the release of patch/updates has been presented. The methodical work pre-
sented here discusses a mathematical model for optimal allocation of resources
to remove vulnerabilities through an update.
Keywords: severity, software patch, software security, software updates, vulnerability,
vulnerability correction model
1.1 Introduction
Software security is a matter of grave concern, and the need for secure software has
been stressed upon enough. The first half of the year 2019 had already seen 3,800
cases of publicly disclosed software breaches and 4.1 billion records exposed [1]. With
the hacking tools getting more and more advanced, it is a tough fight to keep the sys-
tem safe from the intruders. Even minor loopholes or oversights leave the software
highly vulnerable. Often, the exploited loopholes have a fix available, but due to lack
of comprehension of the situation’s gravity, they are never plugged. Such faults or
glitches in the system architecture, design, code or implementation that compromises
the software’s security are termed as software vulnerabilities. The most common vul-
nerabilities are caused by memory safety violations, input validation error, privilege
confusion bugs, privilege escalation, race conditions, side channel attack, and user in-
terface failure. The most common types of vulnerabilities are SQL injection, command
injection, buffer overflow, uncontrolled format string, integer overflow, cross-site
scripting, and so on. The software vulnerabilities are also categorized on the basis
of the extent of damage their presence or exploitability causes. The Common
Vulnerabilities and Exposures (CVE) database provides a Common Vulnerability
Scoring System (CVSS) score to the reported vulnerabilities known as the severity
Adarsh Anand, Jasmine Kaur, University of Delhi, Delhi, India
Anu A. Gokhale, Illinois State University, USA
Mangey Ram, Graphic Era Deemed to be University Dehradun, Uttarakhand, India
https://doi.org/10.1515/9783110619058-001](https://image.slidesharecdn.com/25169236-250521204009-66eaa99c/85/Systems-Performance-Modeling-Adarsh-Anand-Editor-Mangey-Ram-Editor-19-320.jpg)
![index on an ascending scale of 1 to 10 [2]. On the basis of severity score, vulner-
abilities are categorized as low, medium, high, and critical. The vulnerability dis-
covery process is modeled through Vulnerability Discovery Models (VDMs), which
help quantify the vulnerabilities discovered and understand their detection behavior
with time. The foremost software VDM was the Anderson’s thermodynamic model [3].
Rescorla [4] presented a linear and exponential trend in the vulnerability detection
process. The Alhazmi-Malaiya model, an S-shaped, logistic VDM defined the three
phases in the vulnerability discovery process as linear, learning, and saturation [5].
An effort-based model was proposed by Alhazmi and Malaiya [6] to model the effort
consumed in terms of resources and budget in finding the vulnerabilities. Arora et al.
[7] had discussed the optimal policy for vulnerability disclosure. Kapur et al. [8] pro-
posed a logistic rate in the vulnerability detection model. The model by Anand and
Bhatt [9] proposed a hump-shaped vulnerability detection rate. Bhatt et al. [10] dis-
cussed a VDM that categorizes the discovered vulnerabilities as leading vulnerabil-
ities and additional vulnerabilities. Vulnerability discovery process over multiple
versions of the software has been modeled by Anand et al. [11].
The software firms tend to test the software for vulnerabilities and release a re-
medial patch, or a bunch of patches simultaneously known as updates, depending
on the number of vulnerabilities to be catered. Software patches are sets of correc-
tive code meant to replace the defective, fault-causing code and thus prevent ex-
ploitability. Beattie et al. [12] presented a mathematical model to determine the best
time to apply a security patch for software vulnerability. The utility of patches in
improving the software was first mathematically discussed in a Software Reliability
Growth Model (SRGM) by Jiang and Sarkar [13], Arora et al. [14] had discussed the
impact of patching on the software quality. Das et al. and Deepika et al. [15, 16] had
explored the role of the tester and the user in software reliability growth via the
patch service. Anand et al. [17] highlighted the importance of providing patching
service in the software and proposed a scheduling policy for the optimal release of
software. Anand et al. [18] considered faults and vulnerabilities simultaneously and
presented optimal patch release policy. Recently, Kaur et al. [19] presented the first
vulnerability correction model (VCM) and discussed the mathematical frame for the
time gap between the correction of leading and dependent vulnerabilities.
Precautions need to be taken during the software development process to mini-
mize the possibility of vulnerabilities. Better coding practices, better organizational
practices, exhaustive testing, and so on, can help reduce the number of vulnerabil-
ities in the software. The presence of vulnerability itself in the software is not the
main concern but rather their exploitability is. It is not possible to ensure vulnera-
bility free software but their number can be minimized so as to avoid damage
through exploitability. After the release of the software the only way to ensure
software security is continuous and exhaustive testing of the software. The devel-
opmental resources in the form of manpower, budget, time, and so on, available
throughout the project are in a limited supply. The available resources are allocated
2 Adarsh Anand et al.](https://image.slidesharecdn.com/25169236-250521204009-66eaa99c/85/Systems-Performance-Modeling-Adarsh-Anand-Editor-Mangey-Ram-Editor-20-320.jpg)
![to each phase of the Software Development Life Cycle (SDLC) and a major portion of
it goes in software testing (both before and after software release). We know that test-
ing the software in-house is cheaper as compared to field testing, thus release of
patches and updates as part of maintenance activities is expensive. During the vul-
nerability removal process, usually preference is given to vulnerabilities with higher
severity as they are likely to cause bigger damage. But the less severe vulnerabilities
cannot be ignored as they too are dangerous and can cause critical damage upon ex-
ploitation. The number of vulnerabilities that can be dealt in an update depends on
many factors such as the number of vulnerabilities in the software, the resources
available to patch them, and the nature/severity of the vulnerability. Hence, an opti-
mal allocation of resources is very essential for the operational phase. A trade-off
needs to be understood to plan an update so that the maximum number of vulner-
abilities can be catered with the proper utilization of the limited resources at hand.
Since the number of vulnerabilities in software is usually large, not all vulnerabilities
can be handled in a single update. For a singular issue or for dealing with a handful
of vulnerabilities, patches are released. But when a large number of vulnerabilities
need to be dealt with, the patches are clubbed together and released to the user as an
update. For a particular version of the software, multiple singular patches or updates
can be released depending on the need of the software.
In literature, the resource allocation problem has been extensively explored in the
context of software reliability growth models [20–30]. A lot has been discussed and
presented in past in the context of SRGMs but there is limited work done when VDM is
talked about from resource allocation point of view. A recent work by Bhatt et al. [31] is
the first to discuss an optimal resource allocation model for the vulnerability discovery
process.
The optimization problem to maximize a quantity (vulnerability correction)
while trying to minimize the use of the other (resource utilization), has been taken
up in the current work. An effort has been made to allocate an optimal amount of
resources for software vulnerability correction process. The allocation of the resour-
ces will lead to increased security, improved reliability, and quality of the software.
The flow of the model can be understood through Figure 1.1.
Patch 1
0 Patch 2 Patch 3 Patch 4 Nth Patch T
Figure 1.1: Flow of the model.
1 Impact of available resources on software patch management 3](https://image.slidesharecdn.com/25169236-250521204009-66eaa99c/85/Systems-Performance-Modeling-Adarsh-Anand-Editor-Mangey-Ram-Editor-21-320.jpg)
![The chapter has been bifurcated as follows: Section 1.2 discusses the notations and
model development, Section 1.3 presents a numerical example to validate the pro-
posed model, and Section 1.4 concludes the chapter and is followed by a list of the
references used.
1.2 Model development
1.2.1 Notations
The notations used in the model development are:
M : Number of severity level groups pertaining to software vulnerability
i : Variable representing the severity level group, i = 1, 2, . . ., M
NRi : Expected number of vulnerabilities of ith severity group
rRi : Vulnerability removal rate
yiðtÞ: Resource utilization at time t for ith severity group and
Yi t
ð Þ =
Ðt
0 yi w
ð Þdw for ith severity group
Y*
i : Optimal value of Yi, i = 1, 2, . . ., M
Z : Total resources available
ΩRiðtÞ : Number of vulnerabilities removed in ð0, t of the ith severity group,
that is, mean value function of the Non Homogeneous Poisson Process
(NHPP)
ΩRiðYiðtÞÞ: Cumulative number of vulnerabilities removed using resources YiðtÞ in
time ð0, t
T : Total time available for the vulnerability removal process
1.2.2 Resource allocation problem
The work in vulnerability modeling extensively deals with either the vulnerability de-
tection process or the vulnerability exploitation process. The vulnerability correction
process has not obtained much attention even though it is a very important aspect of
the vulnerability life cycle. The VCM presented by Kaur et al. [19] describes the vulnera-
bility removal/fixation phenomenon for the detected vulnerabilities. They had further
categorized the removed vulnerabilities as leading and dependent. In this section, we
shall extend upon their work and present another VCM that will then be used to allo-
cate resources for releasing updates. The work of Rescorla [4] along with the proposals
of Alhazmi and Malaiya [6] has been considered to design our present mathematical
structure.
4 Adarsh Anand et al.](https://image.slidesharecdn.com/25169236-250521204009-66eaa99c/85/Systems-Performance-Modeling-Adarsh-Anand-Editor-Mangey-Ram-Editor-22-320.jpg)
![Recently, Bhatt et al. [31] had presented a model to dynamically allocate resour-
ces to discover vulnerabilities of varying severity levels. The following differential
equation defines the relation between the effort consumed in detecting vulnerabil-
ities of ith severity level and the number of vulnerabilities discovered:
dΩi t
ð Þ
dt
xi t
ð Þ = ri Ni − Ωi t
ð Þ
ð Þ, i = 1, 2, ..., n, (1:1)
where Ωi t
ð Þdenotes the number of vulnerabilities of ith severity detected till time t;
Ni is the number of vulnerabilities detected of ith severity and ri represents their detec-
tion rate, while xi t
ð Þ represents the resources or effort spent in vulnerability detection.
Solution of the eq. (1.1) gives
Ωi t
ð Þ = Ni 1 − e− ri.Xi t
ð Þ
, i = 1, 2, ..., n, (1:2)
Using the above-mentioned analogy, the effort consumption in the vulnerability re-
moval phenomena can be defined on the lines of effort-based vulnerability detec-
tion phenomena. According to the work of Kaur et al. [19], the VCM is an NHPP and
effort-based VDM is NHPP; hence, the effort-based VCM would also follow NHPP.
The VCM can thus be defined as
dΩRi t
ð Þ
dt
yi t
ð Þ = rRi NRi − ΩRi t
ð Þ
ð Þ, i = 1, 2, ..., M. (1:3)
Solving the differential equation with initial conditions t = 0, Yi t
ð Þ = 0 and ΩRi t
ð Þ = 0,
we obtain the relation as
ΩRi t
ð Þ = NRi 1 − e− rRi.Yi t
ð Þ
, i = 1, 2, ..., M. (1:4)
Using the exponential distribution to define the behavior of the effort function as
described by Bhatt et al. [31], we obtain
dYi t
ð Þ
dt
= gi λi − Yi t
ð Þ
ð Þ, i = 1, 2, ..., M, (1:5)
where gi represents the rate at which the available resources are consumed in the
vulnerability removal of the ith severity level group and λi denotes the total resour-
ces that are available to remove vulnerabilities of a given severity level group. The
solution of the above-mentioned differential equation gives us
Yi t
ð Þ = λi 1 − e− gi.t
, i = 1, 2, ..., M. (1:6)
1 Impact of available resources on software patch management 5](https://image.slidesharecdn.com/25169236-250521204009-66eaa99c/85/Systems-Performance-Modeling-Adarsh-Anand-Editor-Mangey-Ram-Editor-23-320.jpg)
Systems Performance Modeling Adarsh Anand Editor Mangey Ram Editor
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- 5. Adarsh Anand andMangey Ram (Eds.) Systems Performance Modeling
- 6. De Gruyter Serieson the Applications of Mathematics in Engineering and Information Sciences Edited by Mangey Ram Volume 4
- 7. Systems Performance Modeling Edited by Adarsh Anandand Mangey Ram
- 8. Editors Adarsh Anand Faculty ofMathematical Sciences University of Delhi 110007 Delhi, India adarsh.anand86@gmail.com Mangey Ram Department of Computer Science and Engineering Graphic Era Deemed to be University 566/6 Bell Road 248002 Clement Town, Dehradun, Uttarakhand, India drmrswami@yahoo.com ISBN 978-3-11-060450-4 e-ISBN (PDF) 978-3-11-061905-8 e-ISBN (EPUB) 978-3-11-060763-5 ISSN 2626-5427 Library of Congress Control Number: 2020948102 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2021 Walter de Gruyter GmbH, Berlin/Boston Cover image: MF3d/E+/Getty Images Typesetting: Integra Software Services Pvt. Ltd. Printing and binding: CPI books GmbH, Leck www.degruyter.com
- 9. Acknowledgment The editors acknowledgeWalter de Gruyter and the editorial team for their ade- quate and professional support during the preparation of this book. They thank all authors who have contributed to this editorial work. Reviewers, who have helped through their comments and suggestions in improving the quality of the chapters, deserve significant praise for their assistance. Finally and most importantly, editors dedicate this editorial book to their family and friends. Adarsh Anand University of Delhi, India Mangey Ram Graphic Era Deemed to be University, India https://doi.org/10.1515/9783110619058-202
- 11. Preface Virtually all countriesnow depend on complex computer-based systems. Infrastructure and utilities rely on the computer-based systems, and almost everything that surrounds us includes a computer and controlling software. Information and communication technologies have been at the heart of economic changes for more than a decade, nota- bly in all areas of businesses. In line with this, this edited issue of System Performance Modeling includes invited papers that deal with the modeling and analysis of software systems with the aid of computers. Emphasis is on concepts, theories, and techniques developed in the infocom discipline. The topics covered are organized as follows: Chapter 1 discusses software vulnerability patch management, which is one of the newer areas of research. Chapter 2 discusses the debugging process for modeling quality and reliability aspects of the software project management. In Chapter 3, an analysis pertaining to vehicular cloud computing has been presented. Chapter 4 presents a comparative study dealing with the agile methodology in- culcating increasing failure rate software reliability models. In today’s time, everyone is talking and dealing with the three Vs, which we know by the name of big data. Chapter 5 presents a mathematical framework to model the fault big data analysis based on effort estimation and artificial intelli- gence for Open Source Software Project. Every system, be it hardware or software, requires data. The more accurate the data, the more are the chances that the results will be error-free. Chapter 6 presents a modeling framework that deals with the meaning of data streams and its impact on the system performance. Chapter 7 discusses assessing the reliability of public switched telephone net- work, which is the most useful telecommunication network in general. No software is complete unless some articulation is talked about for hard- ware, as both go hand in hand when talked about a complex system. Chapter 8 contains a description of the utility of Weibull failure laws for reliability measures of a series–parallel system. Adarsh Anand University of Delhi, India Mangey Ram Graphic Era Deemed to be University, India https://doi.org/10.1515/9783110619058-203
- 13. About the editors AdarshAnand did his doctorate in the area of Software Reliability Assessment and Innovation Diffusion Modeling in Marketing. Presently, he works as an assistant professor in the Department of Operational Research, University of Delhi (INDIA). He has been conferred with Young Promising Researcher in the field of Technology Management and Software Reliability by Society for Reliability Engineering, Quality and Operations Management (SREQOM) in 2012. He is a lifetime member of the Society for Reliability Engineering, Quality and Operations Management (SREQOM). He is also on the editorial board of International Journal of System Assurance and Engineering Management (Springer). He has guest edited several special issues for journals of international re- pute. He has publications in journals of national and international repute. His research interest includes software reliability growth modeling, modeling innovation adoption and successive gen- erations in marketing, and social network analysis. He has worked with CRC Press for two editorial projects; “System Reliability Management: Solutions and Technologies” and “Recent Advancements in Software Reliability Assurance.” He has also authored one textbook with CRC group “Market Assessment with OR Applications.” Dr. Mangey Ram received the Ph.D. degree major in mathematics and minor in computer science from G. B. Pant University of Agriculture and Technology, Pantnagar, India. He has been a faculty member for around 12 years and has taught several core courses in pure and applied mathematics at undergraduate, postgraduate, and doctorate levels. He is currently a professor at Graphic Era (Deemed to be University), Dehradun, India. Before joining the Graphic Era, he was a deputy man- ager (probationary officer) with Syndicate Bank for a short period. He is the editor in chief of International Journal of Mathematical, Engineering and Management Sciences, and the guest editor and member of the editorial board of various journals. He is a regular reviewer for international journals, including IEEE, Elsevier, Springer, Emerald, John Wiley, Taylor & Francis, and many other publishers. He has published 175 plus research publications in IEEE, Taylor & Francis, Springer, Elsevier, Emerald, World Scientific, and many other national and international journals of repute and also presented his works at national and international conferences. His fields of research are reliability theory and applied mathematics. Dr. Ram is a senior member of the IEEE, life member of Operational Research Society of India, Society for Reliability Engineering, Quality and Operations Management in India, Indian Society of Industrial and Applied Mathematics, member of International Association of Engineers in Hong Kong, and Emerald Literati Network in the UK. He has been a mem- ber of the organizing committee of a number of international and national conferences, seminars, and workshops. He has been conferred with the Young Scientist Award by the Uttarakhand State Council for Science and Technology, Dehradun, in 2009. He has been awarded the Best Faculty Award in 2011; Research Excellence Award in 2015; and recently, Outstanding Researcher Award in 2018 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India. https://doi.org/10.1515/9783110619058-204
- 15. Contents Acknowledgment V Preface VII Aboutthe editors IX List of contributing authors XIII Adarsh Anand, Jasmine Kaur, Anu A. Gokhale, and Mangey Ram 1 Impact of available resources on software patch management 1 Shinji Inoue and Shigeru Yamada 2 Debugging process modeling for quality/reliability assessment of software system 13 Shivani Gupta and Vandana Gupta 3 Availability analysis of vehicular cloud computing 21 Gabriel Ricardo Pena and Nestor Ruben Barraza 4 Increasing failure rate software reliability models for agile projects: a comparative study 45 Yoshinobu Tamura and Shigeru Yamada 5 Fault big data analysis based on effort prediction models and AI for open-source project 67 Mario Diván and María Laura Sánchez-Reynoso 6 Modeling the meaning of data streams and its impact on the system performance 79 Kuldeep Nagiya and Mangey Ram 7 Performance evaluation of switched telephone exchange network 123 S. C. Malik and S. K. Chauhan 8 On use of Weibull failure laws for reliability measures of a series–parallel system 141 Index 177
- 17. List of contributingauthors Adarsh Anand Department of Operational Research University of Delhi Delhi, India adarsh.anand86@gmail.com Nestor Ruben Barraza Universidad Nacional de Tres de Febrero Buenos Aires, Argentina nbarraza@untref.edu.ar S. K. Chauhan Shaheed Rajguru College of Applied Sciences for Women University of Delhi New Delhi, India statskumar1@gmail.com Mario Diván National University of La Pampa La Pampa, Argentina mjdivan@eco.unlpam.edu.ar Anu A. Gokhale Illinois State University Normal, Illinois, USA aagokhale@ilstu.edu Shivani Gupta University of Delhi Delhi, India shivani222gupta@gmail.com Vandana Gupta University of Delhi Delhi, India khaitan.vandana@gmail.com Shinji Inoue Kansai University Osaka, Japan ino@kansai-u.ac.jp Jasmine Kaur University of Delhi Delhi, India jasminekaur.du.aor@gmail.com S. C. Malik Maharshi Dayanand University Rohtak, India sc_malik@rediffmail.com Kuldeep Nagiya Graphic Era Deemed to be University Dehradun, Uttarakhand, India kuldeepnagiya@gmail.com Gabriel Ricardo Pena Universidad Nacional de Tres de Febrero Buenos Aires, Argentina gpena@untref.edu.ar Mangey Ram Department of Mathematics, Computer Science and Engineering Graphic Era Deemed to be University Dehradun, Uttarakhand, India drmrswami@yahoo.com María Laura Sánchez Reynoso National University of La Pampa La Pampa, Argentina mlsanchezreynoso@eco.unlpam.edu.ar Yoshinobu Tamura Tokyo City University Tokyo, Japan tamuray@tcu.ac.jp Shigeru Yamada Tottori University Tottori, Japan yamada@tottori-u.ac.jp https://doi.org/10.1515/9783110619058-206
- 19. Adarsh Anand, JasmineKaur, Anu A. Gokhale, and Mangey Ram 1 Impact of available resources on software patch management Abstract: Software security has been an area of immense research as most of the things surrounding us are technology based. Much has been talked about vulner- abilities, their categories and types. Some studies elaborated and extended the available discovery models but few have considered the correction process in the same work. In this study, an approach to deal with software vulnerability through the release of patch/updates has been presented. The methodical work pre- sented here discusses a mathematical model for optimal allocation of resources to remove vulnerabilities through an update. Keywords: severity, software patch, software security, software updates, vulnerability, vulnerability correction model 1.1 Introduction Software security is a matter of grave concern, and the need for secure software has been stressed upon enough. The first half of the year 2019 had already seen 3,800 cases of publicly disclosed software breaches and 4.1 billion records exposed [1]. With the hacking tools getting more and more advanced, it is a tough fight to keep the sys- tem safe from the intruders. Even minor loopholes or oversights leave the software highly vulnerable. Often, the exploited loopholes have a fix available, but due to lack of comprehension of the situation’s gravity, they are never plugged. Such faults or glitches in the system architecture, design, code or implementation that compromises the software’s security are termed as software vulnerabilities. The most common vul- nerabilities are caused by memory safety violations, input validation error, privilege confusion bugs, privilege escalation, race conditions, side channel attack, and user in- terface failure. The most common types of vulnerabilities are SQL injection, command injection, buffer overflow, uncontrolled format string, integer overflow, cross-site scripting, and so on. The software vulnerabilities are also categorized on the basis of the extent of damage their presence or exploitability causes. The Common Vulnerabilities and Exposures (CVE) database provides a Common Vulnerability Scoring System (CVSS) score to the reported vulnerabilities known as the severity Adarsh Anand, Jasmine Kaur, University of Delhi, Delhi, India Anu A. Gokhale, Illinois State University, USA Mangey Ram, Graphic Era Deemed to be University Dehradun, Uttarakhand, India https://doi.org/10.1515/9783110619058-001
- 20. index on anascending scale of 1 to 10 [2]. On the basis of severity score, vulner- abilities are categorized as low, medium, high, and critical. The vulnerability dis- covery process is modeled through Vulnerability Discovery Models (VDMs), which help quantify the vulnerabilities discovered and understand their detection behavior with time. The foremost software VDM was the Anderson’s thermodynamic model [3]. Rescorla [4] presented a linear and exponential trend in the vulnerability detection process. The Alhazmi-Malaiya model, an S-shaped, logistic VDM defined the three phases in the vulnerability discovery process as linear, learning, and saturation [5]. An effort-based model was proposed by Alhazmi and Malaiya [6] to model the effort consumed in terms of resources and budget in finding the vulnerabilities. Arora et al. [7] had discussed the optimal policy for vulnerability disclosure. Kapur et al. [8] pro- posed a logistic rate in the vulnerability detection model. The model by Anand and Bhatt [9] proposed a hump-shaped vulnerability detection rate. Bhatt et al. [10] dis- cussed a VDM that categorizes the discovered vulnerabilities as leading vulnerabil- ities and additional vulnerabilities. Vulnerability discovery process over multiple versions of the software has been modeled by Anand et al. [11]. The software firms tend to test the software for vulnerabilities and release a re- medial patch, or a bunch of patches simultaneously known as updates, depending on the number of vulnerabilities to be catered. Software patches are sets of correc- tive code meant to replace the defective, fault-causing code and thus prevent ex- ploitability. Beattie et al. [12] presented a mathematical model to determine the best time to apply a security patch for software vulnerability. The utility of patches in improving the software was first mathematically discussed in a Software Reliability Growth Model (SRGM) by Jiang and Sarkar [13], Arora et al. [14] had discussed the impact of patching on the software quality. Das et al. and Deepika et al. [15, 16] had explored the role of the tester and the user in software reliability growth via the patch service. Anand et al. [17] highlighted the importance of providing patching service in the software and proposed a scheduling policy for the optimal release of software. Anand et al. [18] considered faults and vulnerabilities simultaneously and presented optimal patch release policy. Recently, Kaur et al. [19] presented the first vulnerability correction model (VCM) and discussed the mathematical frame for the time gap between the correction of leading and dependent vulnerabilities. Precautions need to be taken during the software development process to mini- mize the possibility of vulnerabilities. Better coding practices, better organizational practices, exhaustive testing, and so on, can help reduce the number of vulnerabil- ities in the software. The presence of vulnerability itself in the software is not the main concern but rather their exploitability is. It is not possible to ensure vulnera- bility free software but their number can be minimized so as to avoid damage through exploitability. After the release of the software the only way to ensure software security is continuous and exhaustive testing of the software. The devel- opmental resources in the form of manpower, budget, time, and so on, available throughout the project are in a limited supply. The available resources are allocated 2 Adarsh Anand et al.
- 21. to each phaseof the Software Development Life Cycle (SDLC) and a major portion of it goes in software testing (both before and after software release). We know that test- ing the software in-house is cheaper as compared to field testing, thus release of patches and updates as part of maintenance activities is expensive. During the vul- nerability removal process, usually preference is given to vulnerabilities with higher severity as they are likely to cause bigger damage. But the less severe vulnerabilities cannot be ignored as they too are dangerous and can cause critical damage upon ex- ploitation. The number of vulnerabilities that can be dealt in an update depends on many factors such as the number of vulnerabilities in the software, the resources available to patch them, and the nature/severity of the vulnerability. Hence, an opti- mal allocation of resources is very essential for the operational phase. A trade-off needs to be understood to plan an update so that the maximum number of vulner- abilities can be catered with the proper utilization of the limited resources at hand. Since the number of vulnerabilities in software is usually large, not all vulnerabilities can be handled in a single update. For a singular issue or for dealing with a handful of vulnerabilities, patches are released. But when a large number of vulnerabilities need to be dealt with, the patches are clubbed together and released to the user as an update. For a particular version of the software, multiple singular patches or updates can be released depending on the need of the software. In literature, the resource allocation problem has been extensively explored in the context of software reliability growth models [20–30]. A lot has been discussed and presented in past in the context of SRGMs but there is limited work done when VDM is talked about from resource allocation point of view. A recent work by Bhatt et al. [31] is the first to discuss an optimal resource allocation model for the vulnerability discovery process. The optimization problem to maximize a quantity (vulnerability correction) while trying to minimize the use of the other (resource utilization), has been taken up in the current work. An effort has been made to allocate an optimal amount of resources for software vulnerability correction process. The allocation of the resour- ces will lead to increased security, improved reliability, and quality of the software. The flow of the model can be understood through Figure 1.1. Patch 1 0 Patch 2 Patch 3 Patch 4 Nth Patch T Figure 1.1: Flow of the model. 1 Impact of available resources on software patch management 3
- 22. The chapter hasbeen bifurcated as follows: Section 1.2 discusses the notations and model development, Section 1.3 presents a numerical example to validate the pro- posed model, and Section 1.4 concludes the chapter and is followed by a list of the references used. 1.2 Model development 1.2.1 Notations The notations used in the model development are: M : Number of severity level groups pertaining to software vulnerability i : Variable representing the severity level group, i = 1, 2, . . ., M NRi : Expected number of vulnerabilities of ith severity group rRi : Vulnerability removal rate yiðtÞ: Resource utilization at time t for ith severity group and Yi t ð Þ = Ðt 0 yi w ð Þdw for ith severity group Y* i : Optimal value of Yi, i = 1, 2, . . ., M Z : Total resources available ΩRiðtÞ : Number of vulnerabilities removed in ð0, t of the ith severity group, that is, mean value function of the Non Homogeneous Poisson Process (NHPP) ΩRiðYiðtÞÞ: Cumulative number of vulnerabilities removed using resources YiðtÞ in time ð0, t T : Total time available for the vulnerability removal process 1.2.2 Resource allocation problem The work in vulnerability modeling extensively deals with either the vulnerability de- tection process or the vulnerability exploitation process. The vulnerability correction process has not obtained much attention even though it is a very important aspect of the vulnerability life cycle. The VCM presented by Kaur et al. [19] describes the vulnera- bility removal/fixation phenomenon for the detected vulnerabilities. They had further categorized the removed vulnerabilities as leading and dependent. In this section, we shall extend upon their work and present another VCM that will then be used to allo- cate resources for releasing updates. The work of Rescorla [4] along with the proposals of Alhazmi and Malaiya [6] has been considered to design our present mathematical structure. 4 Adarsh Anand et al.
- 23. Recently, Bhatt etal. [31] had presented a model to dynamically allocate resour- ces to discover vulnerabilities of varying severity levels. The following differential equation defines the relation between the effort consumed in detecting vulnerabil- ities of ith severity level and the number of vulnerabilities discovered: dΩi t ð Þ dt xi t ð Þ = ri Ni − Ωi t ð Þ ð Þ, i = 1, 2, ..., n, (1:1) where Ωi t ð Þdenotes the number of vulnerabilities of ith severity detected till time t; Ni is the number of vulnerabilities detected of ith severity and ri represents their detec- tion rate, while xi t ð Þ represents the resources or effort spent in vulnerability detection. Solution of the eq. (1.1) gives Ωi t ð Þ = Ni 1 − e− ri.Xi t ð Þ , i = 1, 2, ..., n, (1:2) Using the above-mentioned analogy, the effort consumption in the vulnerability re- moval phenomena can be defined on the lines of effort-based vulnerability detec- tion phenomena. According to the work of Kaur et al. [19], the VCM is an NHPP and effort-based VDM is NHPP; hence, the effort-based VCM would also follow NHPP. The VCM can thus be defined as dΩRi t ð Þ dt yi t ð Þ = rRi NRi − ΩRi t ð Þ ð Þ, i = 1, 2, ..., M. (1:3) Solving the differential equation with initial conditions t = 0, Yi t ð Þ = 0 and ΩRi t ð Þ = 0, we obtain the relation as ΩRi t ð Þ = NRi 1 − e− rRi.Yi t ð Þ , i = 1, 2, ..., M. (1:4) Using the exponential distribution to define the behavior of the effort function as described by Bhatt et al. [31], we obtain dYi t ð Þ dt = gi λi − Yi t ð Þ ð Þ, i = 1, 2, ..., M, (1:5) where gi represents the rate at which the available resources are consumed in the vulnerability removal of the ith severity level group and λi denotes the total resour- ces that are available to remove vulnerabilities of a given severity level group. The solution of the above-mentioned differential equation gives us Yi t ð Þ = λi 1 − e− gi.t , i = 1, 2, ..., M. (1:6) 1 Impact of available resources on software patch management 5
- 24. The purpose ofour optimization problem is to remove the maximum number of vul- nerabilities of varying severity levels in a given update keeping in mind the limited resources available. Hence, an optimization problem can be formulated as: Maximize X M i = 1 ΩRiðYiÞ = X M i = 1 NRið1 − e− rRiYi Þ subject to X M i = 1 Yi ≤ Z, Yi ≥ 0, where i = 1, ..., M. (1:7) The solution of the optimization problem allocates resources in a particular up- date, that is, it helps the debugging team allocate its limited resources based on the number and nature and of the vulnerability. The leftover vulnerabilities will be ca- tered to in the next update via a software patch. A run-through of the model has been shown via a numerical illustration in the following section. 1.3 Numerical illustration For the purpose of model validation a simulated dataset has been considered, which contains the vulnerability removal data. The dataset contains 636 vulnerabil- ities that are further categorized on the basis of their severity levels. Six severity level groups have been designed as shown in the first column of Table 1.1. It has been assumed that we have a fixed supply of resources of 3,100 units. But we have not allocated all our resources in a single go and wish to divide it proportionately between the multiples updates as discussed earlier. For the first update, we have limited ourselves to 1,000 units of resources. We have used the above-discussed VCM (eqs. (1.4) and (1.6)) to estimate the value of rR and allocate these 1,000 units of resources for the different severity groups. Software packages SPSS and LINGO have been utilized for parameter estimation and for solving the optimization prob- lem respectively. Table 1.1 represents the dynamically allocated resources (Y) for each severity group, number of vulnerabilities removed (ΩR) on the basis of the al- located resources. As given in Table 1.1, approximately 72% of the initial 636 vulnerabilities have been removed in the first update itself. This amount contains a propionate re- moval from each severity group based on their initial content. This high percentage of removal has been achieved due to various factors such as rigorous debugging (both due to in-house and field testing) and user participation. It is important to re- move the major portion of the vulnerabilities in the first update itself so that the reli- ability can be maximized as soon as possible. 6 Adarsh Anand et al.
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- 27. T XIV THE JUNIOR MEMBER heoffices of Kenyon, Hood and Gallatin were in the Mills Building, and consisted of six rooms, one for each of the members of the firm, and three for the clerks, stenographers and library. They were plainly but comfortably furnished, and gave no token of extraordinary prosperity or the lack of it. In no sense did they resemble the magnificent suites which were maintained elsewhere in the building by more precocious firms which had discovered the efficacy of the game of “bluff,” and which used it in their business with successful consistency. And yet there was an air of solidity here which indicated a conservatism more to the liking of the class of people who found use for the services of Kenyon, Hood and Gallatin. John Kenyon, the senior member, belonged to that steadily decreasing class of lawyers who look upon their profession as a calling with traditions. He belonged to an older school of practitioners which still clung to the ethics of a bygone generation. The business of many big corporations went up in the elevator which passed before the door of John Kenyon’s private office to a floor above, where its emissaries could learn how to take the money that belonged to other people without being jailed, or, having been jailed, how they could most quickly be freed to obtain the use of their plunder. But Mr. Kenyon made no effort to divert this tide. He wanted no part of it in his office. The corporate interests which he represented were for the most part those which required his services to resist the depredations planned upstairs. John Kenyon would have been a great lawyer but for the lack of one important ingredient of greatness—imagination. His knowledge
- 28. of the lawwas extraordinary. His mind was crystal-clear, analytical but not inventive, judicial but not prophetic. He would have graced the robes of a Justice of the Supreme Bench; but as a potent force in modern affairs he was not far from mediocrity. He had begun his career in the office of Philip Gallatin’s grandfather, had been associated with Philip Gallatin’s father, but with the passing of the old firm he had opened offices of his own. The initiative which he lacked had been supplied by Gordon Hood, a brisk Bostonian of the omniscient type; and the accession of young Philip Gallatin four years ago had done still more to supply the ingredients which modern conditions seemed to require. It had meant much to John Kenyon to have Phil in the firm, for the perspective of Time had done little to dim the luster which hung about the name of Gallatin and the junior member had shown early signs that he, too, was possessed of much of the genius of his forebears. Kenyon had watched the development of the boy with mingled delight and apprehension and, with the memory of the failings of his ancestors fresh in his mind, had done what he could to avert impending evil. It was at his advice that young Gallatin had gone to the Canadian woods, and he had noted with interest and not a little curiosity his return to his desk two months ago sobered and invigorated. Phil had plunged into the work which awaited him with quiet intention, and the way he had taken hold of his problems and solved them, had filled the senior partner with new hopes for his future. He loved the boy as he could have loved a son, as he must love the son of Evelyn Westervelt, and it had taken much to destroy John Kenyon’s belief in Phil’s ultimate success. But this last failure had broken that faith. Through the efforts of Gordon Hood the firm had won the suit for which Phil Gallatin had prepared it, but it was an empty victory to John Kenyon, who had seen during the preparation of the case Phil Gallatin’s chance, his palingenesis—the restitution of all his rights, physical and moral. Fully aware of John Kenyon’s attitude toward him, for two weeks Philip Gallatin had remained uptown and, until his dinner at Mrs. Pennington’s, to which he had gone in response to especial pleading,
- 29. had hidden himselfeven from his intimates. He had sent word to John Kenyon that he was indisposed, but both men knew what his absence meant. John Kenyon had been the one rock to which Phil Gallatin had tied, the one man with whom he had been willing to talk of himself, the one man of all his friends from whom he would even take a reproach. It was on John Kenyon’s account, more even than on his own, that Gallatin so keenly suffered for his failure at the critical moment. The time had indeed come for a reckoning, and yesterday Gallatin had planned to retire from the firm and save his senior partner the pains of further responsibility on his account. He had been weighed in the balance, a generous balance with weights which favored him, and had been found wanting. But last night a miracle had happened and the visit of renunciation which he had even planned for this very morning had been turned into one of contrition and appeal. And difficult as he found the interview before him, he entered the office with a light step and a face aglow with the new resolution which had banished the somber shadow that for so long had hung about him. It was early, and the business of the day had just begun. At his appearance several of the stenographers looked up from their work and scrutinized him with interest, and the chief clerk rose and greeted him. “Good morning, Tooker,” he nodded cheerfully. “Is Mr. Kenyon in yet?” “No, sir. It’s hardly his time——” “Please tell him I’d like to see him if he can spare me a moment.” Then he entered a door which bore his name and closed it carefully behind him, opened his desk, glanced at his watch, made two or three turns up and down the room and then took up the telephone book, Logan—Lord—Lorimer, Loring. There it was. 7000 Plaza. He hesitated again and then rang up the number. It was some moments before the butler consented to get Miss Loring, and when he did she did not recognize his voice.
- 30. “Who is it?”she asked. “Can’t you guess?” “Oh, Phil! I didn’t know you at all. Where are you?” “At the office.” “Already! And I’m not out of bed!” “Did I wake you? I’m sorry——” “I’m glad. I didn’t mean to go to sleep, but I did sleep, somehow ——” “I haven’t been asleep. I couldn’t——” “Why not?” “It’s so much pleasanter to be awake.” “I think so, too, but then I dreamed, Phil.” “Pleasant dreams?” “Oh, beautiful ones, full of demigods and things.” “What things?” “Enchanted broughams. Oh, how did it happen, Phil?” “It had to happen.” “I can’t believe it yet.” He laughed. “If I were there I’d try to convince you.” “Yes, I think you could. I’m willing to admit that.” “Are you sorry?” “N-o. But I’m so used to being myself. I can’t understand. It’s strange—that’s all. And I’m glad you called me. I’ve had a terrifying feeling that you must be somebody else, too.” “I am somebody else.” “I mean somebody I don’t know very well.”
- 31. “There’s a remedyfor that.” “What?” “Doses of demigod. Repeat every hour.” “Oh——!” “Don’t you like the prescription?” “I—I think so.” “Then why not try it?” “I—I think I ought to, oughtn’t I?” “I’m sure of it. In a day or so the symptoms you speak of will entirely disappear.” “Are you sure?” “Positive.” “I—I think they’re less acute already. You really are you, aren’t you?” “If I wasn’t, you wouldn’t be you, don’t you see?” “Yes, and I’d be frightfully jealous if I had been somebody else.” She laughed. “Oh, Phil! What a conversation! I hope no one is listening.” “I’m sure they’re not. They couldn’t understand anyway.” “Not unless they’re quite mad—as we are. What are you doing? Working?” “Yes, drawing a deed for an acre in Paradise.” “Don’t be foolish. Who for?” “Me. And there’s a deed of trust.” “I’ll sign that.” “We’ll both sign it. It’s well secured, Jane. Don’t you believe me?” “Yes, I do,” slowly.
- 32. There was apause and then he asked, “When can I see you?” “Soon.” “This afternoon?” “I’ve a luncheon.” “And then——” “Tea at the——Oh, Phil, I’ll have to cut that. There’s a dance to- night, too, the Ledyards’.” “This is getting serious.” “What can I do? I’ve been frightfully rude already. Can’t you go?” “Not sufficiently urged.” “Then I shan’t either. I don’t want to go. I want—the acre of Paradise.” “Where will I meet you, Jane?” “Here—at four.” “I’ll be there.” “Until then, good-by, and, Phil——” “Yes.” “Please wear that flannel shirt, disreputable hat and——” “And the beard?” “No—not the beard. But I want to be convinced there’s no mistake.” “I’d rather convince you without them.” “Oh, I’ve no doubt you will,” she sighed. “There’s so much I’ve got to say to you, Phil. I won’t know where to begin——” “Just where you stopped.” “But I—I wasn’t saying anything—just then. I couldn’t. There— there were reasons.”
- 33. He laughed gayly. “I’vestill other reasons.” “Oh!” “Convincing ones.” “Phil, I won’t listen. Good-by!” “Good-by.” “Hadn’t we better go for a walk?” she asked. “No—please——” “Oh, very well,” with a tone of resignation. “There—you see, I’m submitting again. At four, then. Good-by.” She cut off and he hung up the receiver, sitting for a long while motionless, looking out of the window. He took out his watch and was examining it impatiently when the chief clerk came in. “Mr. Kenyon will see you now, Mr. Gallatin,” he said. John Kenyon paused in the reading of his mail and looked up over the half-moons in his glasses when Gallatin appeared at the door. “Come in, Phil,” he said quietly, offering his hand. He sat down at his desk again and formally indicated the chair nearest it. His manner was kindly and full of an old-fashioned dignity, indicating neither indifference nor encouragement, and this seemed to make Philip Gallatin’s position if anything more difficult and painful. Instead of sitting, Gallatin turned toward the window and stood there. “I’ve come back, Uncle John,” he muttered. Kenyon glanced up at him, the calm judicial glance of a man who, having no venal faults himself, tolerates them in others with difficulty. There was no family relationship between the men, and Gallatin’s use of the familiar term at this time meant much, and something in Phil Gallatin’s pose arrested Kenyon’s eye, the jaw that had worked forward and was now clamped tightly by its throbbing
- 34. muscles, the bulkof the squared shoulders and the decision with which one hand clasped the chair-back. “I’m glad of that, Phil,” he said. “I was on the point of thinking you had given me up.” “I had. I had given you up. I haven’t been down here because I knew it wasn’t necessary for me to come and because I thought you’d understand.” “I understood.” “I wrote you two or three letters, but I tore them up. I wanted to sever my connection with the firm. I wanted to save you the pain of thinking about me any longer. I knew I hadn’t any right here, that I haven’t had any right here for a long while—two or three years, that I had been taking my share of fees I had never earned, and that it was only through your friendship for me that I’ve been encouraged to stay as long as this. I wanted to save you the pain of talking to me again——” “I’ve never denied you my friendship, Phil. I don’t deny it now. I only thought that you might have——” Gallatin turned swiftly and raised his hand. “Don’t, Mr. Kenyon! For God’s sake, don’t reproach me,” he said ardently. “Reproaches won’t help me—only wound. They’ve already been ringing in my ears for days—since the last time——” he paused. “Never mind.” Gallatin strode the length of the room, struggling for the control of his voice, and when he came back it was to stand facing the senior partner quite composed. “There isn’t a man in the world who would do as much for one who merited so little. I’m not going over that. Words can’t mean much from me to you; but what I would like you to know is that I don’t want to go out of the firm, and that, if you’ll bear with me, I
- 35. want another chanceto prove myself. I’ve never promised anything. You’ve never asked me to. Thank God, that much of my self-respect at least is saved out of the ruins. I want to give my word now——” “Don’t do that,” said Kenyon hurriedly. “It isn’t necessary.” “Yes, I must. I’ve given it to myself, and I’ll keep it, never fear. That—was the last—the very last.” Kenyon twisted his thin body in his chair and looked up at the junior member keenly, but as he did so his eyes blurred and he saw, as thirty years ago he had seen the figure of this boy’s father standing as Phil Gallatin was standing enmeshed in the toils of Fate, gifted, handsome, lovable—and yet doomed to go, a mental and physical ruin, before his time. The resemblance of Philip Gallatin to his father was striking—the same high forehead, heavy brows and deep-set eyes, the same cleanly cut aquiline nose, and heavy chin. There were lines, too, in Phil Gallatin’s face, lines which had appeared in the last two years which made the resemblance even more assured. And yet to John Kenyon, there seemed to be a difference. There was something of Evelyn Westervelt in him, too, the clean straight line of the jawbone and the firmly modeled lips, thinner than the father’s and more decisive. “I’m glad of that, Phil,” he said slowly. “I’m not asking you to believe in me again. Broken faith can’t be repaired by phrases. I don’t want you to believe in me until I’ve made good. I want to come in here again on sufferance, as you took me in six years ago, without a share in the business of the firm that I don’t make myself or for which I don’t give my services. I want to begin at the bottom of the ladder again and climb it rung by rung.” “Oh, I can’t listen to that. Our partnership agreement——” “That agreement is canceled. I don’t want a partnership agreement. It’s got to be so. I’ve been thinking hard, Mr. Kenyon. It’s responsibility I need——”
- 36. “You’re talking nonsense,Phil. You did more work in the Marvin case than either Hood or myself.” “Perhaps, but I didn’t win it,” he said quickly. “The firm did.” “I can’t agree with you. I’ll come in this office on the conditions I suggest, or I must withdraw. My mind is made up on that. I don’t want to go, and it won’t be easier for me anywhere else. This is where I belong, and this is where I want to fight my battle, if I can do it in my own way without the moral or financial help of any one— of you, least of all.” Gallatin paused and walked, his head bent, the length of the room. John Kenyon followed him with his eyes, then turned to the window and for a long while remained motionless. Philip Gallatin returned to the vacant chair and sat leaning forward eagerly. The senior partner turned at last, his kind homely face alight with a smile. “You don’t need my faith, my boy, if you’ve got faith of your own, but I give it to you gladly. Give me your hand.” He got up and the two men clasped hands, and Phil Gallatin’s eyes did not flicker or fade before the searching gaze of the other man. It was a pact, none the less solemn for the silence with which one of them entered into it. “You’re awake, Phil?” he asked. “Yes, that’s it, Uncle John. Awake,” said Gallatin. “I’m glad—I’m very glad. And I believe it. I’ve never been able to get used to the idea of your being really out of here. We need you, my boy, and I’ve got work for you, of the kind that will put your mettle to the test. There’s a great opportunity in it, and I’ll gladly turn it over to you. ‘Sic itur ad astra,’ my boy. Will you take it?” “Gladly. A corporation case?”
- 37. “Sanborn et al.vs. The Sanborn Mining Company. Sit here and I’ll explain it to you.”
- 38. W XV DISCOVERED omen have acode of their own, a system of signals, a lip and sign language perfectly intelligible among themselves, but mystifying, as they purpose it to be, to mere man. Overweening husbands, with a fine air of letting the cat out of the bag, have been known to whisper that these carefully guarded secrets are no secrets at all, and that women are merely children of a larger growth, playing at hide and seek with one another (and with their common enemy) for the mere love of the game, that there are no mysteries in their natures to be solved, and that the vaunted woman’s instinct, like the child’s, is as apt to be wrong as often as it is right. Of course, no one believes this, and even if one did, man would go his way and woman hers. Woman would continue to believe in the accuracy of her intuitions and man would continue to marvel at them. Woman would continue to play at hide and seek, and man would continue to enjoy the game. Call them by what name you please, instinct, intuition, or guesswork, Mrs. Richard Pennington had succeeded by methods entirely feminine, in discovering that Phil Gallatin’s Dryad was Jane Loring, that he was badly in love with her and that Jane was not indifferent to his attentions. Phil Gallatin had not been difficult to read, and Mrs. Pennington took a greater pride in the discovery of Jane’s share in the romance, for she knew when Jane left her house in company with Phil that her intuition had not erred. Jane Loring had kissed her on both cheeks and called her “odious.”
- 39. This in itselfwas almost enough, but to complete the chain of evidence, she learned that Dawson, her head coachman, in the course of execution of her orders, had gone as far North as 125th Street before his unfortunate mistake of Miss Loring’s number had been discovered by the occupants of the brougham. Mrs. Pennington realized that this last bit of evidence had been obtained at the expense of a breach of hospitality, for she was not a woman who made a practice of talking with her servants, but she was sure that the ends had justified the means and the complete success of her maneuver more than compensated for her slight loss of self-respect in its accomplishment. But while her discovery pleased her, she was not without a sense of responsibility in the matter. She had been hoping for a year that a girl of the right kind would come between Phil and the fate he seemed to be courting, for since his mother’s death he had lived alone, and seclusion was not good for men of his habits. She had wanted Phil to meet Jane Loring, and her object in bringing them together had been expressed in a definite hope that they would learn to like each other a great deal. But now that she knew what their relations were, she was slightly oppressed by the thought of unpleasant possibilities. It was in the midst of these reflections that Miss Jaffray was announced, and in a moment she entered the room with a long half- mannish, half-feline stride and took up her place before the mantelpiece where she stood, her feet apart, toasting her back at the open fire. Mrs. Pennington indicated the cigarettes, and Nina Jaffray took one, rolling it in her fingers and tapping the end of it on her wrist to shake out the loose dust as a man would do. “I’m flattered, Nina,” said Nellie Pennington. “To what virtue of mine am I indebted for the earliness of this visit?” “I slept badly,” said Nina laconically. “And I’m the anodyne? Thanks.” “Oh, no; merely an antidote.”
- 40. “For what?” “Myself. I’vegot the blues.” “You! Impossible.” “Oh, yes. It’s quite true. I’m quite wretched.” “Dressmaker or milliner?” “Neither. Just bored, I think. You know I’ve been out five years now. Think of it! And I’m twenty-four. Isn’t that enough to make an angel weep?” “It’s too sad to mention,” said Mrs. Pennington. “You used to be such a nice little thing, too.” Nina Jaffray raised a hand in protest. “Don’t, Nellie, it’s no joke, I can tell you. I’m not a nice little thing any longer, and I know it. I’m a hoydenish, hard-riding, loud-spoken vixen, and that’s the truth. I wish I was a ‘nice little thing’ as you call it, like Jane Loring for instance, with illusions and hopes and a proclivity for virtue. I’m not. I like the talk of men——” “That’s not unnatural—so do I.” “I mean the talk of men among men. They interest me, more what they say than what they are. They’re genuine, somehow. You can get the worst and the best of them at a sitting. One can’t do that with women. Most of us are forever purring and pawing and my-dearing one another when we know that what we want to do is to spit and claw. I like the easy ways of men—collectively, Nellie, not individually, and I’ve come and gone among them because it seemed the most natural thing in the world to do. I’ve made a mistake. I know it now. When a girl gets to be ‘a good fellow’ she does it at the expense either of her femininity or her morals. And men make the distinction without difficulty. I’m ‘a good fellow,’” she said scornfully, “and I’m decent. Men know it, but they know, too, that I have no individual appeal. Why only last week at the Breakfast the Sackett boy clapped me on the back and called me ‘a jolly fine chap.’ I put
- 41. him down, Ican tell you. I’d rather he’d called me anything— anything—even something dreadful—if it had only been feminine.” She flicked her cigarette into the fire and dropped into a chair. Mrs. Pennington laughed. “All this is very unmanly of you, Nina.” “Oh, I’m not joking. You’re like the others. Just because I’ve ridden through life with a light hand, you think I’m in no danger of a cropper. Well, I am. I’ve had too light a hand, and I’m out in the back-stretch with a winded horse. You didn’t make that mistake, Nellie. Why couldn’t you have warned me?” Mrs. Pennington held off the embroidery frame at arm’s length and examined it with interest. “You didn’t ask me to, Nina,” she replied quietly. “No, I didn’t. I never ask advice. When I do, it’s only to do the other thing. But you might have offered it just the same.” “I might have, if I knew you wouldn’t have followed it.” “No,” reflectively. “I think I’d have done what you said. I like you immensely, you know, Nellie. You’re a good sort—besides being everything I’m not.” “Meaning—what?” “Oh, I don’t know. You’re all woman, for one thing.” “I have had two children,” smiled the other toward the ceiling. “I could hardly be anything else.” “Is that it?” asked the visitor; and then after a pause, “I don’t like children.” “Not other people’s. You’d adore your own.” “I wonder.” Mrs. Pennington’s pretty shoulders gave an expressive shrug.
- 42. “Marry, my dear.Nothing defines one’s sex so accurately. Marry for love if you can, marry for money if you must, but marry just the same. You may be unhappy, but you’ll never be bored.” Nina Jaffray gazed long into the fire. “I’ve been thinking about it,” she said. “That’s what I came to see you about.” “Oh, Nina, I’m delighted!” cried Nellie Pennington genuinely, “and so flattered. Who, my dear child?” “I’ve been thinking—seriously.” “You must have had dozens of offers.” “Oh, yes, from fortune hunters and gentlemen jockeys, but I’m not a philanthropic institution. Curiously enough my taste is quite conventional. I want a New Yorker—a man with a mind—with a future, perhaps, neither a prig nor a rake—human enough not to be too good, decent enough not to be burdensome—a man with weaknesses, if you like, a poor man, perhaps——” “Nina. Who?” Miss Jaffray paused. “I thought I’d marry Phil Gallatin,” she said quietly. Mrs. Pennington laid her embroidery frame down and looked up quickly. Nina Jaffray’s long legs were extended toward the blaze, but her head was lowered and her eyes gazed steadily before her. It was easily to be seen that she was quite serious—more serious than Mrs. Pennington liked. “Phil Gallatin! Oh, Nina, you can’t mean it?” “I do. There isn’t a man in New York I’d rather marry than Phil.” “Does he know it?” “No. But I mean that he shall.” “Don’t be foolish. You two would end in the ditch in no time.”
- 43. Nina straightened andexamined her hostess calmly. “Do you think so?” she asked at last. “Yes, I think so——” Nellie Pennington paused, and whatever it was that she had in mind to say remained unspoken. Instinct had already warned her that Nina was the kind of girl who is only encouraged by obstacles, and it was not her duty to impose them. “Stranger things have happened, Nellie,” she laughed. “But are you sure Phil will—er—accept you?” “Oh, no, and I shan’t be discouraged if he refuses,” she went on oblivious of Nellie Pennington’s humor. “Then you do mean to speak to him?” “Of course.” Nina’s eyes showed only grave surprise at the question. “How should he know it otherwise?” “Your methods are nothing, if not direct.” “Phil would never guess unless I told him. For a clever man he’s singularly stupid about women. I think that’s why I like him. Why shouldn’t I tell him? What’s the use of beating around the bush? It’s such a waste of time and energy.” Mrs. Pennington’s laugh threw discretion to the winds. “Oh, Nina, you’ll be the death of me yet. There never was such a passion since the beginning of Time.” “I didn’t say I loved Phil Gallatin,” corrected Nina promptly. “I said I’d decided to marry him.” “And have you any reason to suppose that he shares your—er— nubile emotions?” “None whatever. He has always been quite indifferent to me—to all women. I think the arrangement might be advantageous to him. He’s quite poor and I’ve got more money than I know what to do with. He’s not a fool, and I’m—Nellie, I’m not old-looking or ugly, am I? Why shouldn’t he like me, if he doesn’t like any one else?”
- 44. “No reason inthe world, dear. I’d marry you, if I were a man.” Mrs. Pennington took to cover uneasily, conscious that here was a situation over which she could have no control. She was not in Phil Gallatin’s confidence or in Jane Loring’s, and the only kind of discouragement she could offer must fail of effectiveness with a girl who all her life had done everything in the world that she wanted to do, and who had apparently decided that what she now wanted was Phil Gallatin. Nina’s plans would have been amusing had they not been rather pathetic, for Nellie Pennington had sought and found below her visitor’s calm exterior, a vein of seriousness, of regret and self-reproach, which was not to be diverted by the usual methods. Did she really care for Phil? Clever as Mrs. Pennington was, she could not answer that. But she knew that it was a part of Nina Jaffray’s methods to do the unexpected thing, so that her sincerity was therefore always open to question. Nellie Pennington took the benefit of that doubt. “Has it occurred to you, Nina, that he may care for some one else?” Her visitor turned quickly. “You don’t think so, do you?” she asked sharply. “How should I know?” Mrs. Pennington evaded. “I’ve thought of that, Nellie. Who was Phil’s wood-nymph? He’s very secretive about it. I wonder why.” “I don’t believe there was a wood-nymph,” said Mrs. Pennington slowly. “Besides, Phil would hardly be in love with that sort of girl.” “That’s just the point. What sort of a girl was she? What reason could Phil have for keeping the thing a secret? Was it an amourette? If it was, then it’s Phil Gallatin’s business and nobody else’s. But if the girl was one of Phil’s own class and station, like——” “Miss Loring,” announced the French maid softly from the doorway.
- 45. Nina Jaffray pausedand an expression of annoyance crossed her face. She straightened slowly in her chair, then rose and walked across the room. Mrs. Pennington hoped that she would go, but she only took another cigarette and lit it carefully. “You’re too popular, Nellie,” she said, taking a chair by the fire. Mrs. Pennington raised a protesting hand. “Don’t say that, Nina. For years I’ve been dreading that adjective. When a woman finds herself popular with her own sex it means that she’s either too passée to be dangerous, too staid to be interesting, or too stupid to be either. Morning, Jane! So glad! Is it chilly out or are those cheeks your impersonal expression of the joy of living?” “Both, you lazy creature! How do you do, Nina? This is my dinner call, Mrs. Pennington. I simply couldn’t wait to be formal.” “I’m glad, dear.” And then mischievously, “Did you get home safely?” “Oh, yes, but it was a pity to take poor Mr. Gallatin so far out of his way,” she replied carelessly. “Poor Phil! That’s the fate of these stupid ineligible bachelors—to act as postilion to the chariot of Venus. Awfully nice boy, but so uninteresting at times.” “Is he? I thought him very attractive,” said Jane. “He’s one of the Gallatins, isn’t he?” “Yes, dear, the last of them. I was afraid you wouldn’t like him.” “Oh, yes, I do. Quite a great deal. He’s a friend of yours, isn’t he, Nina?” “I’ve known him for ages,” said Miss Jaffray dryly; and then to Mrs. Pennington, “Why shouldn’t Jane like him, Nellie?” “Oh, I don’t know,” she finished with a gesture of graceful retirement. Their game of hide and seek was amusing, but
- 46. hazardous in thepresent company, so she quickly turned the conversation into other channels. Nina Jaffray and Jane Loring had met in the late autumn at a house party at the Ledyards’ place in Virginia, and while their natures were hardly concordant, each had found in the other some ingredients which made for amiability. Jane’s interest had been dictated by curiosity rather than approval, for Nina Jaffray was like no other girl she had ever met before. Whatever her manners, and these, Jane discovered, could be atrocious, her instincts were good, and her intentions seemed of the best. To Miss Jaffray, Jane Loring was ‘a nice little thing’ who had shown a disposition not to interfere with other people’s plans, a nice little thing, amiable and a trifle prudish, for whom Nina’s kind of men hadn’t seemed to care. They had not been, and could never be intimate, but upon a basis of good fellowship, they existed with mutual toleration and regard. Nellie Pennington, from her shadowed corner, watched the two girls with the keenest of interest and curiosity. Nina Jaffray sat with hands clasped around one upraised knee, her head on one side listening carelessly to Jane’s enthusiastic account of the Ledyards’ ball, commenting only in monosyllables, but interested in spite of herself in Jane’s ingenuous point of view, aware in her own heart of a slight sense of envy that she no longer possessed a susceptibility to those fresh impressions. Nina was not pretty this morning, Nellie Pennington thought. Hers was the effectiveness of midnight which requires a spot-light and accessories and, unless in the hunting field, midday was unkind to her; while Jane who had danced late brought with her all the freshness of early blossoms. But she liked Nina, and that remarkable confession, however stagy and Nina-esque, had set her thinking about Jane Loring and Mr. Gallatin. It was a pretty triangle and promised interesting possibilities. Jane was still speaking when Nina interrupted, as though through all that she had heard, one train of thought had persisted.
- 47. “What did youmean, Nellie, about Phil Gallatin being ineligible?” she asked. “And I know you don’t think him stupid. And why shouldn’t Jane Loring like him? I don’t think I understand?” Nellie Pennington smiled. She had made a mistake. Hide and seek as a game depends for its success upon the elimination of the bystander. “I am afraid, of course, that Jane would be falling in love with him,” she said lightly. And then, “That would have been a pity. Don’t you think so, Nina?” “There’s hardly a danger of that,” laughed Jane, “seeing that I’ve just—just been introduced to the man. You needn’t be at all afraid, Nina.” “I’m not. Besides he’s awfully gone on a wood-nymph. You saw him blush when I spoke of it at dinner here—didn’t you, Jane?” “Yes, I did,” said Jane, now quite rosy herself. “Phil wouldn’t have blushed you know,” said Nina confidently, “unless he was terribly rattled. He was rattled. That’s what I can’t understand. Suppose he did find a girl who was lost in the woods. What of it? It’s nobody’s business but his own and the girl’s. I’d be furious if people talked about me the way they’re talking about Phil and that girl. I was lost once in the Adirondacks. You were, too, in Canada only last summer, Jane. You told me so down in Virginia and ——” Jane Loring had struggled hard to control her emotion, and bent her head forward to conceal her discomposure, but Nina’s eyes caught the rising color which had flowed to the very tips of her ears. “Jane!” cried Nina in sharp accents of amazed discovery. “It was you!” The game of hide and seek had terminated disastrously for Jane, and her system of signals, useful to deceive as well as reveal had betrayed her. It was clearly to be seen that further dissimulation
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