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Emerging Methodologies and Applications in Modeling, Wentifcation and Control

Series Editor: Quan Min Zhu

System Assurances
Modeling and Management

Edited by
Prashant Johri, Adarsh Anand, Júri Vain,
Jagvinder Singh and Mohammad Tabrez Quasim

System Assurances

System Assurances
Modeling and Management

Edited by

Prashant Johri
Professor, School of Computing Science & Engineering, Galgotias
University, Greater Noida, India

Adarsh Anand

Assistant Professor, Department of Operational Research, University of
Delhi, New Delhi, India

Jüri Vain

Professor, Department of Software Science, Tallinn University of
Technology, Tallinn, Estonia

Jagvinder Singh

Assistant Profesor, USME, DTU East Delhi Campus, Delhi, India
Mohammad Tabrez Quasim

Assistant Professor, University of Bisha, Bish, Saudi Arabia

Series Editor
Quan Min Zhu

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Contributors

Number in parentheses indicate he pages on which he authors ontrbions hen.

Deepti Aggrawal (143), USME, DTU, East Delhi Campus, Delhi, India

Afag Ahmad (307, 47), Department of Electrical and Computer Engineering Sultan
Qaboos University, Muscat, Oman

Sridhar Akir (189), Department of Mathematics, GLS, GITAM (Deemed to be
University), Visakhapatnam, Andhra Pradesh, Ind

Sayyid Samir Al Busaldi (307), Department of Electrical and Computer Engineering,
‘Sultan Qaboos University, Muscat, Oman

‘Adarsh Anand (143), Department of Operational Research, Faculty of Mathematical
Sciences, University of Delhi Delhi, India

M. Arvindhan (531), Galgotias University, Greater Noida, India

R. Baby Chithra (123), Department of ECE, New Horizon College of Engineering,
Bengaluru, India

Ajay Sudhir Bale (123), Department of ECE, SOET, CMR Universi

Néstor Barraza (355), Departmen of Sciences and Technology, University of Tres de
Febrero, Caseros, Argentina; School of Engineering, University of Buenos Aire,
‘Autonomous City of Buenos Aires Argentina

Pratima Bavagosal (371), Department of Statistics, Faculty of Science, The Maharaja
Sayajiro University of Baroda, Vadodara, India

RAK. Bhardwaj (175), Department of Statistics, Punjabi University Patiala, Patiala,
Punjab, India

Iyotir Moy Chatterjee (403), Department of IT, LBEF, Kathmandu, Nepal

Nikesh Choudhary (11), Department of Operational Research, University of Delhi,
di

Arindam Chowdhury (513), Department of Electrical Engineering, Maryland Institute
of Technology and Management, Jamshedpur, India

Rajesh Kumar Dhanaraj (333), School of Computing Science and Engineering,
Galgotias University, Greater Noid, India

Suresh Gnana Dhas (503), Department of Computer Science, Ambo University,

‘Ambo, Ethiopia

Ashutosh Dist (103, 513), Department of Electrical Engineering, Graphic Era Deemed
10 be Univesity, Dehradun, Utarakhand, In

Bengaluru, India

Contibuton

‘Tadele Degefa Geleto (503), Deparment of Computer Science, Ambo University,
‘Ambo, Ethiopia

Vanceta Goel (11), Satyawati College, University of Delhi, India

Shaik Ashfaq Hussain (547), Department of Communications Engineering and
‘Advanced Telecommunicaions Technology. School of Electrical Engineering,
Faculty of Engineering, Universiti Teknologi Malaysia (UTM), Johor Bahr,
Malaysia

‘Shaik Mazhar Hussain (S47), Department of Communications Engineering. and
‘Advanced Telecommuniations Technology, Schoo! of Electrical Engineering,
Faculty of Engineering, Universit Teknologi Malaysia (UTM), Johor Bahru,
Malaysia

‘Shinji Inoue (155), Faculty of Informatics, Kansai University, Osaka, Japan

Prashant Johri (85), Galgtias University, Greater Noida, Utar Pradesh, India

$. Kala (437), Department of Electronics and Communication Engineering, Indian
Institute of Information Technology Kottayam, Kottayam, India

‘Swapnil Kamble (389), Mechanical Enginecring Department, Goa College of
Engineering, Ponda, Goa, India

Lenin Kanagasabai (323), Department of EEE, Prasad V. Potlri Siddhartha Institute of
‘Technology, Vijayawada, Andhra Pradesh India

Gert Kanter (67, 447), Department of Software Science, Tallinn University of
Technology, Tallin, Estonia

Jasmine Kaur (143), Department of Operational Research, Faculty of Mathematical
‘Sciences, University of Delhi, Delhi, Inia

Vandana Khaitan (nee Gupta) (1
‘of Delhi, India

Vyachestay Kharchenko (209), Department of Computer Systems, Networks and
(Cybersseuity, Nationa Aerospace University “KhAI", Kharkiv, Ukraine

‘Neeraj Khera (287), Department of ECE, Amity University, Noida, Utar Pradesh, India

NV. Kousik (503), School of Computing Science and Engineering, Galgotias
University, Greater Noida, Ur Pradesh, India

Abhishek Kumar (403), Department of CSE, Chitkara University Institute
of Engineering and Technology, Chitkara University, Bad, Himachal Pradesh,
India

Avneesh Kumar (88), Galgotis University, Greater Noida, Uttar Pradesh, India

Rupesh Kumtekar (389), Mechanical Engineering Deparment, Goa College of
Engineering, Ponda, Goa, India

Marti Ingmar Lübert (67), Insitute of Computer Science, University of Tatu, Tar,
Estonia

Palvinder Kaur Mangat (477), Univers
University, Chandigarh, India

Department of Operational Research, University

Institute of Computing. Chandigarh

‘Yuka Minamino (155), Graduate School of Engineering, Totori University, Tottori,
Japan

Verónica Moreno 355), Department of Sciencesand Technology, University of Tres de
Febrero, Caseros, Argentina

(Olga Morozova (209), Department of Computer Systems, Networks and Cybersecurity,
National Aerospace Univesity "KHAI”, Kharkiv, Ukraine

‘Anjali Munde (41), Amity University, Noida, Ur Pradesh, India

K. Muralidharan (371), Department of Statistics, Faculty of Science, The Maharaja
Sayajirso University of Baroda, Vadodara, India

Rohaila Nasz (229), Teonhanker Mahaveer University, Moradabad, Uttar Pradesh,
India

Nalesh (437), Department of Electronics, Cochin University of Science and
Technology, Koch, India

Sunay P. Pal (51), Institute of Maritime Su

+, Vasc-Da-Gama, Goa, Indi
‘Manju Payal (403), Software Developer Academic Hub, Ajmer, Rajasthan, India

Gabriel Pena (355), Department of Sciences and Technology, University of Tres de
Febrero, Caseros, Argentina

Yuriy Ponochovayi (209), Department of Information Systems and Technologies,
Poltava State Agrarian University, Poltava, Ukraine

Rajesh S. Prabhu Gaonkar (51, Indian Institute of Tecnology Goa (HT Goa),Ponda-
Goa, India

Pa Pravesh (123), Department of ECE, SoET, CMR University, Bengaluru, India

J Premalatha (333), Department of IT, Kongu Engineering College, Erode, Tamilnadu,
India

Vani Rajasekar (333), Department of CSE, Kongu Engineering College, Erode,
‘Tamilnadu, India

Muhammad Ehsan Rana (271), Asia Pacific University of Technology & Innovation
(APU), Technology Park Malaysia, Kuala Lumpur, Malaysia

Suraj Rane (389), Mechanical Engineering Department, Goa College of Engineering,
Ponda, Goa, Indi

Pramod Singh Rathore (403), Department of CSE, ACERC, Ajmer, Rajasthan, India

Dr, Kamaljit Singh Saini (477), University Institute of Computing, Chandigarh
University, Chandigarh, India

ech Saint (103,513), Department of Electrical Engineering, Graphic Era Deemed 10

be University, Dehradun, Unarakhand, India

Omar $. Saleh 271), Studies, Planning and Follow-Up
Education and Scientific Research, Baghdad, Ing

S. Saravana Kumar (123), Department of CSE, SOET, CMR University, Bengaluru,

orate, Ministry of Higher

Contributors

P. Sasikala (189), Department of Mathematics, GSS, GITAM (Deemed 10 be
University), Bangalore, Kamataka, Indi

Ashendra Kumar Saxena (229), Teerthanker Mahaveer Universit
‘Uttar Pradesh, Ind

Rajinder Sharma (563), CR Department, University of Technology and Applied
Seiences-Sohar, Sohar, Oman

IN. Singh (85), Galgoias University, Greater Noida, Uttar Pradesh, India

Ravinder Singh (175), Department of Statistics, Central University of Haryana,
Namaul, Haryana, India

Purnima Sonker (175), Department of Statistics, Punjabi University Pata, Pata,
Punjab, India

Pavan Kumar Subbara (189), Department of Mathematics, G.S:S, GITAM (Deemed to
be University), Bangalore, Kamatak, India

Yoshinobu Tamura (1), Yamaguchi University, Yamaguchi, Japan

Leonidas Tsiopoulos (447), Department of Software Science, Tallin University of
Technology, Tallin, Estonia

Juri Vain (447), Department of Software Science, Tallinn University of Technology,
Tallin, Estonia

Iharika Varshney (103), Department of Electrical Engineering, Graphic Era Deemed

to be University, Dehradun, Unarakhand, India

'S. Varun Yogi (123), Department of ECE, SOET, CMR University, Bengaluru, India

N. Vinay (123), Department of ECE, SORT, CMR University, Bengaluru, India

‘Swetha Vura (123), Department of ECE, SoET, CMR University, Bengaluru, India

‘Sudeept Singh Yaday (85), Galgotias University, Greater Noida, Uttar Pradesh, India

VSS Yadavall (189), Department of Industrial and Systems Engineering, Pretoria
University, Pretoria, South Afica

Shigeru Yamada (1, 155), Graduate School of Engineering, Tottori University,
“Toto Japan

Kamaludin Mohamad Yuso (547), Department of Communications Engineering and
‘Advanced Telecommunicaions Technology, School of Electrical Engineering,
Faculty of Engineering, Universit Teknologi Malaysia (UTM), Johor Bahru,
Malaysia

N. Yuvaraj (503), Research and Development, ICT Academy, Chennai India

,. Moradabad,

Preface

In today’s neck to neck competitive era, almost every system is facing tough
‘challenges for survival. These challenges include, maintaining the system per-
formance measures such as; reliability, availability, maintainability, cost &
failure factors, and many other factors associated with them. The last decade
has witnessed huge advancements and technological changes. As a result, more
robust and dynamic systems are required to have an overall better performance.
‘These analyses for a system can be performed by taking care of several areas
such as mathematical modeling for reliability maintenance, software reliability
‘engineering and standards, coding and cryptography, artificial intelligence and
expert systems, operations research and IT, IT in health care, and several others.

This edited issue of Emerging Methodologies and Applications in Model-
ing, Identification, and Control on System Assurances: Modeling and Manage-
‘ment includes invited papers appropriate to the theme and the complex solution
approaches to handle research challenges in the related domain. Emphasis has
been given 10 the original and qualitative work relevant 10 he theme, with par-
ticular importance given to system assurance.

Prashant Johri
Galgotias University, India

Adarsh Anand

University of Delhi, India

Jüri Vain

Tallinn University of Technology, Estonia
Jagvinder Singh

Delhi Technological University, India

Mohammad Tabrez Quasim

University of Bisha, Bisha, Saudi Arabia

Acknowledgments

We are grateful 10 various colleagues both in academia and in industry who
have contributed to this book. Our appreciation also goes out to Leticia Lima
for her cooperation through the publication process. In addition, we are honored
to be associated with Prof. Quan Min Zhu, who showed us for carrying.
out the book compilation work under his series.

(Of course, no author can successfully complete a book project without fam-
ily support. Our beloved appreciation to our respective families for affording us
their patience that allowed the compilation of this edited book

Prashant Johri

‘Adarsh Anand

Jari Vain

Jagvinder Singh
Mohammad Tabrez Quasim

Chapter 1

Statistical analysis approach
for the quality assessment
of open-source software

Yoshinobu Tamura’ and Shigeru Yamada”
“Yamaguchi Univers, Yamaguch Japan, "Graduate Schoo of Enginering. Tonor Universi,
Ter Japan

1.1. Introduction

At present, many OSS (open source software) are used in many software devel-
‘opment organizations. Also, many commercial software have been developed
by embedding several OSS components because of standardization, cost reduc~
tion, quick delivery, etc. Various methods for software reliability assessment of
(OSS system have been proposed by several researchers [1-3].

“Moreover, many OSS systems have used the fault tracking systems such as.
the Bugzilla. Also, many research papers have discussed the methods in terms
of the fault tracking system [4-13].

In this chapter, we discuss statistical analysis such as correspondence anal-

In particular, we apply correspondence analysis to the faul large-scale data
‘of OSS. Then the discussed method based on correspondence analysis can be
used to understand the whole trend ofthe fault large-scale data of OSS. Corre-
spondence analysis has been used in many marketing areas. Also, several
research papers have been proposed by using correspondence analysis [14-10].

“Moreover, several numerical examples based on the Fault large-scale data in
actual OpenStack cloud projects of OSS are shown by using the statistical
method applied in this chapter. Then the numerical examples of visualization
based on correspondence analysis are shown inthis chapter. Finally, we show
thatthe applied method will be useful to understand the reliability trend of OSS
for the quality assessment of OSS developed under the OSS project.

1.2. Correspondence analysis

Correspondence analysis is well known as one of the multivariate analyses for
qualitative data. In particular, the main purpose of correspondence analysis is

Cogn Bena Le arc 1

2 System assurances

Visualization, In correspondence analysis, our methods make a visualization by
using the survey items and attribute ones. Then the correlation coefficient is
‘maximized for the data visualization,

‘This chapter focuses on the visualization of faut large-scale data of OSS by
using correspondence analysis. By using comespondence analysis, we can eas-
ily understand the whole reliability trend of OSS because of the bird's-eye view
‘of correspondence analysis. Many correspondence analyses are used in the mar-
keting area. However, we consider that the correspondence analysis is helpful to
understand the whole reliability trend. We use the fault count encoding for the
correspondence analysis of OSS fault large-scale data because the software
fault data have been used by many software reliability growth models. Thereby,
we can comprehend the whole reliability trend by using the fault collection data,
based on the fault count encoding one.

an

a

where 7, is the data for the first variable i and second variable j.
‘Then the mean values ofthe frst variable and the second variable j are as
follows:

aay

as

where p is the weight parameter in the first variable i, Similarly, y is the weight
parameter in the first variable js the number of variables. Therefore, the cor-
relation coefficient is given by

Era

ne se

‘The estimate of the correlation coefficient p° is the value making p of
Bq, (1.6) maximize, The estimate can be given from the solutions of the
following

de

Zi an

Statistical analysis approach Chapter | 1 3

1.3. Estimation procedure based on correspondence analysis

‘The estimation steps based on the correspondence analysis are as follows:
1. The raw fault large-scale data is obtained from the fault tracking system,
2. The count encoding data is converted from the raw fault large-scale data,
3. The pivot tables are made for each factor ofthe fault category.

4. We make a correspondence analysis by using the datasets in the pivot table.
5. We discuss the results of the correspondence anal

Moreover, we apply the following fault category data to the correspondence
analysis:

Nickname for fault assignee
Name for software component
Name for hardware

Name for OS

‚name for fault reporter
Fault severity level

Status for software fault
Number for software version

‘Then the data in each factor are encoded from the character data to the numer-
ical values by using the count encoding from the standpoint of the relationship
between the OSS reliability and OSS faul.

1.4 Numerical examples

‘This chapter shows several numerical illustrations for OpenStack Project [171 of
OSS development project. In particular, StarlingX included in OpenStack
projects are well known as the edge-OSS projects. At present, OpenStack pro-
jects that include StarlingX. It is useful to show several numerical illustrations
for the cloud software. We show several numerical illustrations by using the
StarlingX Project as the edge software.

Figs. 1.1-1.8 show the estimated results based on correspondence analysis
for assignee, component, hardware, OS, reporter, severity, status, and version.
We discuss the estimated results for each factor as follows:

+ Nickname of fault assignee:
Assignee and component exhibit a sim
+ Name of software component:
Assignee and component exhibit a similar tendency.
+ Name of hardware:
“ppe64le” and “x84_64" show different trends,
+ Name of operating system:
Hardware and OS exhibit a similar tendency.
+ Nickname of fault reporter:

tendency.

4 System assurances

FIG. 1.1 The estimated ests based on come pandence analysis fr sine

FIG. 1.2 The estimated eis ase on corspondene analysis fr component.

Hardware, OS, and reporter exhibit a similar tendency.
e Fault severity level:

‘The low level of fault severity is related to the Reporter.
© Status of software fault:

‘The reporter and assignee have a specific role.

Statistical analysis approach Chapter | 15

FIG. 1.3. Tho estimated ress based on cormspondenzs anal for hardware

FIG. 1.4, The estimated resis based on corespondence analy Fr OS,

+ Number of software version:
‘The old and new versions have a specific role for the assignee and the
reporter, respectively.

‘The correspondence analyses such as Figs. 1.1-1.8 will be highly useful for

the edge-OSS developers to understand the reliability of edge-OSS project

6 System assurances

Reponer

FIG. 1.5 The estimated results based on cospondene analysis fr reponer

Den

FIG. 1.6 The estimated eis based on come spandence anal for seve

from various perspectives. Especially, edge-OSS project is structured from
assignee, component, hardware, OS, reporter, severity, status, version, ec,
By focusing on various factors such as assignee, component, hardware, OS,
reporter, severity, status, and version, the edge-OSS developers can understand
the reliability of edge OSS from various perspectives.

Statistical analysis approach Chapter | 1 7.

Sa

FIG. 1.7. The estimated ress based on corspondene analysis fr sats

FIG. 1.8. The estimated resus based on corespondence analy for version

1.5 Concluding remarks

‘This chapter focuses on statistical analysis by using correspondence analysis
for OSS projects. The quality control for OSS is highly important for the
‘edge-OSS developers to manage the edge-OSS quality, software reliability,

8 System assurances

and cost saving of edge-OSS projects. This chapter has proposed the visualiza-
tion method based on the correspondence analysis for OSS assessment consid-
ering the whole OSS system. It is highly difficult for the edge-OSS project
managers to make a visualization of the reliability trend of whole OSS. Then

chapter has discussed several numerical illustrations of visualization based
‘on the correspondence analysis. The discussed method will be available as the
reliability visualization method based on the visualization considering the
‘component-based assessment for whole OSS.

Acknowledgment
“This work was suppored in par bythe JSPS KAKENHI Grant no. 20K 11799 in Japan

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7 The OpenStck projet, Build he future of Open Infrasutue ips pension

‘Yoshinobu Tamora recived the BSE, MS, and PAD degree from Toto University in 1998,
2000, and 2003, respectively. Prom 200310 2006, he was a esearch asian a Tor Uni
very of Environmental Studies. From 2006 102009 he was a Lecture and Associate Pro-
fessor at Hiroshima Institute of Technology. Hiroshima, Japan. From 2009102017, h was an
Associate Professor a the Graduate School of Sciences and Technology for Innovation,
‘Yamaguchi University, Ute, Japan. From 2017 19 2019, he has ben working asa professor
atthe Faculty of Knowledge Engineering, Tokyo City University, Tokyo, Japan, Since 2020,
he hasbeen working a a professor a he Faulty of Information Technology. Tokyo City
University, Tokyo, Japan, Since 2021, he hasbeen working asa profesor a the Grade
Schoo! of Sciences and Technology for Innovation, Yamaguchi University, Ube. Japan,
“The research interes of Yoshinobu Tamura include reliability assesment or edge compat
ing, cloud computing. big dt, optimization, and reliability. He is regular member ofthe
Institute of Electronic, the Information and Communication Engineers of Japan, the Opera»
tions Research Society of Japan. the Society of Projet Management of Japan, the Reliability
Engineering Association of Japan, andthe IEEE. He as authored the book ented OSS Rei
ability Measurement and Assessment (Springer International Publishing. 2016). Dr. Tamura
received the Presentation Award ofthe Seventh Intemational Conference an Industri Man:
agement in 2004, the IEEE Reliability Society Japan Chapter Awards 2007, the Reseach
Leadership Award in Area of Reliability from the ICRITO 2010, the Best Paper Award of
the IEEE International Conference on nus Engineering and Engineering Management
in 2012, etilo honorary profesor from Amity University of Inia in 2017, the Best Paper
Award fie 24th ISSAT International Conference on Reliability nd Quality in Design 2018,

Shigeru Yamada received the BSE, M.S. and PAD degrees from Hiroshima University,
Japan, in 1975, 1977, and 198S respectively Since 1993, he has been working as a professor
tthe Department of Soca! Management Engineering, Graduate Schoo! of Engineering. Tot
tori University Japan. He has published over 500 reviewed technical papers inthe area of
software reliability engineering, project management, reliability engineering, and quality

10. System assurances

‘contol He hs authored several books entitled Introduction to Software Management Model
‘(Kyorisu Shuppan, 1993), Software Reliability Models: Fundamentals and Applications
(USE, Tokyo, 1994), Statsical Quality Consol for TQM (Corona Publishing, Tokyo,
1998), Software Reliability: Model, Tool, Management (The Society of Project Manageme
204), Quliy-Oriened Sofware Management (Morikia Shuppan, 2007). Elements of Sof
‘ware Reliability Modeling Approach (Kyeritsu Shuppan 2011), Projet Management (Kyo.
isa Shuppan, 2012), Sofware Engineering: Fundamentals and Applications (Suurkougak
Publishing, 2013), Software Rebabilty Modeling: Fundamentals and Applications
(Springer-Verlag 2014), and OSS Reliability Measurement and Assessment (Springer Inter“
rational Publishing 2016) Dr, Yamada received the Best Autor Awad fromthe Information
Processing Society of Japan in 1992, he TELECOM System Technology Awanl from the
‘Telecommanications Advancement Foundation in 1993, the Best Paper Award fom the Rel
ability Engineering Association o Japan 199, he International Leadership Award in Rei
ability Engineering Research from the ICQRIT/SREQOM 2005, the Best Paper Award atthe
2004 Intemational Computer Symposium, the Best Paper Award rom the Society of Project
Management in 2006, the Leadership Award from the ISSAT 2007, the Outstanding Paper
‘Awad tthe IEE Intemational Conference on Industrial Engineering and Engineering Man
‘agement (IEEM2008) the Intemational Leadership and Pioncerng Research Award in Soft
‘ware Reliability Engineering from the SREQOMICQRIT 2009, the Exceptional Intemational
Leadership and Contribution Award in Software Reliability athe ICRITO" 2010, 2011 Best
Paper Award from the IEEE Reliability Society Japan Chapter 2012, the Laweship Award
fiom the ISSAT 2014, the Projet Management Service Award from the SPM 2014, the Con-
tributions Award fr Promoting OR from the ORS) 2017, and the Research Award from the
ISSAT 2017. He isa regalar member o the IEICE, the Information Processing Society of
Japan the Operations Research Society of Japan, the Reliability Engineering Association
‘of pan, the Japan Industrial Management Association the Japanese Society for Quality Con
‘wl the Society of Project Management, and tb IEEE.

Chapter 2

Analytical modeling

and performance evaluation
of SIP signaling protocol:
Analytical modeling of SIP

Nikesh Choudhary’, Vandana Khaitan (nee Gupta)’, and Vaneeta Goel!”
“Department of Operational Rescorch Universi of Deli, India "Satu College, University of
Delhi. Ind,

2.1 Introduction

Voice over Internet Protocol (VoIP) (also known as IP telephony) is an
approach and collection of technologies for transmitting voice and multimedia
sessions over IP networks. It has been actively used everywhere due o its
‘economical cost and noted flexibility related to Public Switched Telephone
Networks (PSTN) [1]. One of the most powerful VoIP signaling protocols is
the Session Initiation Protocol (SIP) 2] tis an application-layer signaling pro
tocol introduced by the Internet Engineering Task Force (IETF) considering
Request for Comments (RFC) 3261 in 2002. It was formery designed by the
Network Working Group (NWG) for creating, modifying, and teardown
multimedia sessions. This protocol can work on both Transmission Control
Protocol (TCP) and User Datagram Protocol (UDP). I also works with other

description protocol (SDP), real-time transmission
(RTP), resource reservation protocol (RSVP), session announcement protocol
(SAP), lightweight directory access protocol (LDAP), realtime steaming
protocol (RTSP), and remote authentication dial-in user service protocol
(RADIUS).

SIP is also known as a transaction-oriented protocol by which messages
ae carried out through different transactions. The transaction mechanism in
SIP controls the exchange of messages between the client and the server and
reliably delivers these messages. The two major SIP transactions are the
INVITE transaction and the non-INVITE transaction. For establishing a ses-
sion, the INVITE transaction is used, and for modifying and terminating a

Cogn Bena Le arc $"

12. System assurances

session, the non-INVITE transaction is used [3]. In the INVITE transaction,
the client sends the INVITE request or acknowledgments 10 the server, and
the server sends different types of responses corresponding to these requests
and acknowledgments. Predicting its importance and magnificent potential to
grow as a major signaling protocol, IETF chose to operate SIP over H.323 pro
tocol. Despite its potential to succeed H.323, many years of implementation
‘and experimentation have been conducted in the SIP specification, RFC 3261
[1]. The SIP architecture considered in the chapter is adopted from Ref. [4].

Modeling and interpreting SIP specifications using approved methods can
assist in ensuring thatthe phrasing of RFC 3261 is accurate, certain, and user
friendly. IETF has published a revised version of the SIP specification, RFC
16026 [5], in September 2010. It also invites people for unicast and multicast

2.2 Background work

Since put into operation in 2002, SIP has been an interesting research topic.
Most of the research articles in SIP are based on its working and services,
Suryawanshi etal. [2] described the architecture of SIP, its message types,
its applications, and many more, The authors in Ref. [3] discussed the call flow
setup in SIP, different servers asa proxy server, network server, registrar server,
and SIP security issues. The authors in Ref. [6] determined the potential
association between two objects in a social network represented by a graph
including edges and nodes. Howie e al. [7] described the advanced form of
SIP and its use in collaborating peer-to-peer applications on cellular phones.
‘The authors in Ref. [$] presented the communication protocol design to secure
SIP regulated communication of VoIP.

However, we observed that when it comes to the analysis and modeling of
SIP, only a few research anicles are available inthe literature [9, 10]. Lin [9]
suggested colored petri nets (CPNs) to design and analyze the INVITE transac-
tion of SIP over the unreliable medium in which messages are reordered and
lost. Barakovic et al. [10] considered the simulation model of SIP INVITE.
transaction designed using CPNs. According to this model, they concluded that
the SIP INVITE transactions ae free from live locks and dead codes and also
observed that these dead codes are both desirable and undesirable atthe same
time, They also suggested that the INVITE transaction of SIP ought to be sup-
pressed for further improvement to reduce unwanted deadlock. Filal and Bouh-
dadi [11] considered the reliable and unreliable medium of the SIP INVITE
transaction and verified it by using the simulation technique of “Event-B” using
the Rodin platform. Kizmaz and Kirei [12] accomplished that the timed colored
per nets (TCPNS) can be used to analyze the functional properties of SIP
INVITE transactions.

Analytical modeling of SIP Chapter |2 13

Inthe literature discussed earlier, we observe that most of the work on SIPis.
based on simulation. This inspired us to propose an analytical model for the
performance analysis of the protocol.

2.2.1. Motivation

“There is plenty of simulation-based research on SIP, but very les literature is
available on the analytical modeling of the SIP INVITE transaction. This
‘encouraged us to develop an analytical model for the SIP invite transaction
because analytical models provide an absolutely precise connection between
the inputs and the outputs. On the contrary, results obtained from simulation
models ae required to be statistically explained Moreover, the results of the
simulation model are time consuming, error prone, and expensive. The anlyt-
ical model explains and concentrates on the esearch procedure “mathem
cally and statistically.” In contrast, the simulation model compares the
research work to another related work following the equivalent simulators
ation having similar parameters to test its performance. Hence in this chapter,
we construct an analytical model that provides an abstract representation ofthe
SIP INVITE transaction and helps in analyzing its performance,

Keeping in mind the dynamic behavior of SIP, a stochastic process, speif-

inyous-time Markov chain (CTMC), seems appropriate to develop

1 model. However, the CTMC model is quite far away from the
al feel ofthe system being modeled. Moreover, because of the com-
plex functionality of the SIP, the comesponding CTMC is expected to have a
very large state space. To overcome this issue of large state space, we consider
proposing a stochastic reward net (SRN) model which is more rip in its spec-
fications and is almost same asthe designers perception of the system. Also,
many software packages are available that can spontaneously transform the
SRN model
the SRN modeling technique has been effectively used
analyze the performance measures of different protocols, such as TCP (15),
‘TCP NewReno [14], IEEES02.11 MAC [15], RLC protocol of LTE [16], et
“The SRN has provento be the most suitable too to serie the dynamic behav-
ior ofthese protocols by providing graphical understanding ofthe packet or
message transmission. Hence, we propose an SRN model forthe SIP INVITE
transaction. Major features of SIP such as various timers, INVITE retransmis-
sion, response retransmission, together with the arival of extra acknowledg-
ments during retransmission are considered inthe proposed model, SHARPE.
117) software is then used for the numerical analysis of the suggested
model. A brief introduction of SRN and its components is given in
Section 2.3. For a detailed study on the SRN modeling technique, the reader
‘ean refer 10 Ref. [17]

14. System assurances

2.2.2 Main contribution

‘The important contributions of this chapter are as follows:

1. The chapter proposes an analytical model that provides an abstract represen-
tation of SIP INVITE transaction.

2. The analytical model is developed for the SIP INVITE transaction over the
unreliable medium using SRN modeling technique.

3. All important features of SIP INVITE transaction such as timers,
re-INVITEs, and retransmissions are incorporated in the SRN model.

4. Performance measures such as throughput and latency of the SIP INVITE
transaction are determined.

‘The analytical results are validated with the help of diserete-event simula-

tion performed using MATLAB.

‘The remainder of this chapter is structured in the following manner. In
Section 2.3.1, various types of SIP responses are discussed, Section 2.3.2 briefly
presents the SIP layered structure and its working. The introduction of SRN and.
its basic components are discussed in Section 24.1, Section 2.4.2 presents the
proposed SRN of the SIP INVITE transaction. In Section 2.5, the performance
measures of the protocol are discussed. Section 2.6 represents the numerical
‘observations corresponding to the measures of performances discussed in
Section 2.5. In Section 2.7, the model validation detail are presented. Finally,
the chapter is concluded in Section 2.8.

2.3. SIP layered structure and its working

In this section, we discuss the layered structure of SIP INVITE request and its
working in correspondence with the client and the server transactions. The SIP
architecture we are considering in this chapter is adopted from Ref. [4].

2.3.1. Types of responses of SIP

Before beginning with SIP working, we first need to understand the various
types of responses used in the protocol. When the client transaction transfers
the INVITE request to the server transaction, the server transfers some
responses to this INVITE request (see Table 2.1). These responses are described
as follows:
xx (100-199) responses: These responses are called provisional responses.
No or numerous provisional responses may appear before single or multiple
successful or unsuccessful responses are accepted. Provisional responses.
‘meant for an INVITE request can produce “early messages.” These early
messages in the ongoing session are represented by the 100 trying response
toquench the INVITE request retransmission. These early messages will be
required ifthe server requires to transmit a response to its client inside the
message before the primary INVITE transaction ends. Provisional responses.

Analytical modeling of SIP Chapter |2 15

TABLE 2.1 Types of SIP response messages.

Responses — Functions

tex Provisional response ques received despite that not approved)

zu Success rıponse (quest fic received and approved)

E Redirection response (some actions are intended o fll he request

4x Roques failure response (some actions are needed to complete the
request

5 Server err response (server is unsuccesdal to respond o the request)

ES Global failure response not single seers avale 0 respond tothe
request

are also called “informational responses.” Ixx contains different responses
such as /80-ringing, 181-call is being forwarded, 182-queued, ec.

2x (200-299) responses: These responses are called successful responses.
“There is a response in 2xx, which is represented as 200 OK. Ifthe client
receives 200 OK response from the server, it represents that the server
successfully accepts the request. After receiving this successful response,
the client sends an acknowledgment to the server.

xe (300-399) responses: 3c responses provide details regarding the
‘server's position or optional settings that can probably complete the cal.
xx contains different responses such as 300-multiple responses, 301-moved
permanently, 302-moved temporarily, et.

dar (400-499) responses: dax responses are the server’s complete failure
responses, The client cannot retransmit similar request unless required cor-
rections are done (eg. attaching relevant authorization). xx includes.
responses such as 400 bad request, 401 unauthorized, ec.

Sut (500-599) responses: These are the failure responses generated when
the server encounters some errors. Sxx contains responses namely
500-server internal error, SOI-not implemented, 502-bad gateway, et.
‘xx (600-699) responses: Gux responses show that the server contains
comprehensive details regarding an appropriate client, and not merely the
particular situation shown in the request. Different responses in 6x are
600 busy everywhere, 603 decline, 604 does not exist anywhere, etc.

All the responses from 3x t0 6xx (3ex-Gxx) are called unsuccessful responses.

2.3.2 Layered structure and working of SIP

We discuss the layered structure and functioning of the SIP protocol in this
section, SIP is structured into four layers, each performing a special task

16. System assurances

mai
Tr
Amann >

AG. 2. SIP yer arte

(see Fig. 2.1). Syntax and encoding is the lowest layer ofthe SIP layered struc-
ture. Augmented Backus-Naur Form (ABNF) grammar is used to specify the
‘encoding of the lowest layer. The transport layer is the second layer from bot-
tom 10 top. As mentioned easier, his layer represents how a client transmits
requests and accepts responses, as well as how a server accepts requests and!
‘transmits responses across the network. The third layer is Ihe transaction layer
which lies above the transport layer. This layer manages retransmission by the
application layer and matches the responses to the requests and time-outs by the
application layer in case of initiation and termination ofa session. The topmost
layer ofthe SIP layered structure is called the transaction user (TU). The TU
‘generates and abandons transactions of SIP and makes use of services provided
by the transaction layer.

SIP isa ransaction-oriented protocol that performs tasks from one transac-
tion to another transaction, Therefore, among all the layers of SIP, the ransac-
tion layer is the most significant layer. There is only one INVITE request
message in the SIP transaction, and corresponding to this INVITE request mes-
sage, there are many response messages. The transaction is carried out through
two sides: he client side and server side. The transactions that occur on the cli-
em side are known as client transactions, and the transactions that occur on the
server side are known as server transactions. Requests are sent through client
‘transactions, and responses are sent through server transactions. The objective
‘of a client transaction is to create the INVITE request and transmit the request
message 10 the server transaction. On the other hand, the server transaction
accepts a request from the transaction layer and transfers it 10 its TU.

Analytical modeling of IP Chapter | 217

Also, it takes responses from the TU and transfers these responses 10 he trans-
‘action ayer. Depending onthe pattern of the requests and responses received by
the client TU and the server TU, there exist two kinds o client transactions, hat
is, INVITE client transaction and non-INVITE client transaction. INVITE cli-
‘ent transaction is used to handle the INVITE requests, and the non-INVITE
‘ent transaction is used to handle all types of requests other than the INVITE
requests and acknowledgments. Similarly, a server transaction is also of two
kinds, INVITE server transaction and non-INVITE server transaction. The
INVITE server transaction handles the responses regarding INVITE requests,
and the non-INVITE server transaction is used to handle all types of responses.
other than the INVITE requests and acknowledgments. Fig. 2.2 presents a stan-
‘dard SIP message transaction to establish a session. The illustration comprises
wo user agents, client and server, and a proxy server. The client transmits an
“INVITE” request showing thatthe client is ready to set up a session with the
server. The server then sends different responses, a 100-trying response before
sending a 200-OK, or Zxx-Gxx response, which is used to quench the requested
transmission. The 100-1rying response symbolizes that the server has taken the
INVITE request; the server sends the 200-OK to represent that he/she isready to
participate in this multimedia session, whereas 300-600 responses are

cr PROXY SERVER
head. 8 hed.
pe
ine
om
=
LL u “=
pan
a
HOR + ACK

Bye

18. System assurances

‘comprised of many responses which represent that there is some error in the
request. Upon acceptance of the 200-OK or 300-600 responses, the client for-
wards an “ACK" to acknowledge the acceptance ofthese responses. SIP man-
ages bidirectional handshakes to set up a session: “INVITE request-/00-Trying
response” and *200-OK (or 300-600) responses-ACK” handshake. The former
handshake is among adjacent SIP nodes such asthe client and the proxy, and the
latter handshake is among the proxy and its ultimate destination, that is, server.
‘The session is set up by receiving 200 OK responses from the server, Then the
client begins the audio/video conversation. The audio/video data packets are
transmitted by following transport protocols such as TCP, UDP, ete. When
the client wants to terminate the call, a BYE message is transmitted to the
server. The server approves the BYE message by sending a 200 OK response
that tears down a session.

2.4 Proposed SRN model of SIP INVITE transaction

Before presenting the SRN model for the SIP-INVITE-transaction, we fi
discuss the basics of the SRN modeling technique.

2.4.1 SRN and its attributes

SRN is an enhanced version of stochastic petri nets (SPNs), and SPN is an
extension of petri net (PN). PN is a bipartite directed graph in which the nodes
are segregated into two disjoint sets, namely, places and transitions. PN is
extended to SPN with time involvement, and a further extension of SPN is
known as SRN. For complex systems, it is a top-level descriptive language.
SRN has been established as a strong modeling tool for the performance anal:
ysis and reliability and availability computation of communication networks.
ig. 23 shows the general attributes of an SRN model, which are described
as given below:

— ol 0

AG. 23 SRN componen

Analytical modeling of IP Chapter | 219

1. Places: Places are represented by circles that indicate the state of the
system. It can hold tokens and has infinite capacity by default. Tokens

are illustrated as dots or numbers in the places,

Transitions: A transition is represented by a rectangular bar and indicates

an action o be performed. It has no capacity and cannot store tokens at al.

3. Types of places and arcs:

+ Places and transitions are linked through directed ares. An are links a
place toa transition and a transition toa place, but no arc can link a tran
sition to a transition ora place to à place. The ares directed toward the
transitions are known as input ares and their corresponding places are
known as input places. Each arc has some multiplicity, which is repre-
sented as a number.

The ares directed out of the transitions are called as output arcs and their
equivalent places are called as ouput places.

Enabling of transition: M every input place of a transition holds as many

tokens, which are atleast equal tothe input ares multiplicities (a postive

integer associated with each input arc), then the transition is said to be
enabled.

5. Inhibitor are: An are connecting a place and a transition along with the

y hollow ring rather than the arrows at the terminating end, having

muliplicty k > 1 is called an inhibitor arc. If no multiplicity is
‘mentioned on the ar, then itis assumed to be 1. IF an inhibitor arc has.
‘multiplicity n, and its input place contains tokens which are greater than.
or equal to, then the transition, in spite of being enabled, is inhibited.
Firing ofa transition can take place only when itis enabled and not inhib-
ited. On firing ofa transition, amount of tokens same asthe multiplicity
of the input ares is li
tokens same as the multiplicity of the output arcs is transferred to all
its output places.

6. Types of transition:

+ The transition having some random firing time (distributed exponen-
tially) other than zero is called a timed transition.

+ The transition with zero firing time is called an inmediate transition.
Immediate transition possesses higher priority than he timed transition.

Guard function: The Guard function “g” is a Boolean expression associ-

ated with a transition, say 7. A transition Tis enabled ¡its guard function,

Lis satisfied (ic, g = 1) and disabled if the guard function g = 0.

8. Marking: The state of a PN having N places is represented as a marking
IN) which contains N tuples, Cr (0,Ma(0....1u(0) of positive integers
{including zero), where 10% (1 < 1 < M indicates the amount of tokens
in the th place at any given time, ¢. The starting state of the PN is
represented by the initial marking denoted by “M(t)" which is at time
1=0,

2

4

7.

20. System assurances

9. Reward rate: The reward is a positive (including zero) weight allocated to
every single marking, and the reward rate is defined asthe overall marking
fof the weighted mean of the amount of tokens in the specified place.

10. Firing probability: “If multiple transitions struggle for firing, then some
‘weights are needed to be specified to resolve these conflicts” [15]. These
Weights are known as firing probabilities. The probabilities associated
‘withthe firing rates of the transition sum up to I.

2.4.2. Proposed SRN model of SIP INVITE transaction

We now develop an SRN model forthe SIP INVITE client transaction and SIP
INVITE server transaction based on its work discussed earlier. For a compre-
hensive study on modeling using SRN, one can refer to Ref. [18]. Though we
have worked with SRN as a modeling tool, we do not use rewards in this model
However, we use other notions such as guard functions that ae assisted only by
‘an SRN model but not by a generalized stochastic petri net (GSPN) model. The
SRN model depicting the SIP INVITE transaction is shown in Fig. 2.4. This
model consists of mainly two pars, namely the client side and the server side
‘The meanings of each timed transition, place, guard functions, and immediate
transitions used in the SRN model ae illustrated in Tables 2.2-2.5, respectively.
Further, it is 10 be noted here that even though some functions in the SIP
INVITE transaction can be deterministic such as different types of timers such
as mer M, timer H, timer L, etc i is assumed thatthe firing times of each and
every timed transition are distributed exponentially 10 facilitate modeling
using SRN.

‘The INVITE client transaction and server transaction ae initiated by the TU
at client and server sides, respectively. When the client’s TU wishes to start a
session, it creates an INVITE request depicted by the firing ofthe timed tran-
Sition Ten (See Fig. 2.4). This transition has exponentially distributed firing
time with mean 2y, The INVITE client transaction goes through five different
stages one by one after initiating a session. These five stages are:

1.Calling 2. Proceeding 3. Accepted 4. Completed 5. Terminated

‘These five stages are represented by the places Pour. Prrcc Parcs
Paume 308 Print.

‘When a transition 7. fires, atoken is transferred tothe place Pr. T
means thatthe client creates an INVITE request, and the initial calling state is
reached. A token in he place Pu, enables the transition Ty, Which repre-
sents that the INVITE request is delivered to server side through the transport

Analytical modeling of SIP Chapter | 2 21

FIG. 2.4 SRN model of SIP INVITE want,

layer. As soon as the transition Thine gets enabled, the guard function
probability gy2 checks whether the place Py rg Is empty or not. IF the place
is empty, then the transition Tera Wil fie and the token moves from Pang
either Pier Of Pras With probabilities p and (1 — p), respectively. A token
in the place Pons represents thatthe INVITE request is successfully received
by the server TU, and a token inthe place Prep describes thatthe client is
waiting for the response while the INVITE request is handled by the server
transaction

22. System assurances

TABLE 2.2 Transitions and their meaning.

Transition

Tre ning

Tox

Tae
Tw

De
Tin

Trt

Tas
Tac med

Tax

Tee

Tears
Tapar?
Tampons
Toone me
i

Tes

Tucson
Tra

Tat

Tame

Meaning,

Provisional response needed to quench INVITE
Fequestrevansmision

‘ox responses generated by the server
Ta rspane scie the cnt ansction
a reponse generated by the server

Zn response eceiveby the client tansacón
aa responses are generated by the server

30x60 responses ae received by the client
transition

Server stat entering in he accepted tate

Acknowledgments generate by the client

‘Acknowledgments sent to server transaction

Client transaction creates an INVITE request

Server transaction star entering inthe
completed Sate

Transport err occu in the proceeding state
Transport emor occur in the completed state
INVITE request is eceve by the server

Successul ransmision of acknowledgment to
Server transaction

Successful ransmision of acknowledgment to
serve transición

Server sta entering in the proceeding Sate
INVITE request retransmission
x response is again received by the cent

xx response sent transpor layer
INVITE request retransmission

Average time
Rate’) (ns)

0.000048

0.000055
‘2.000060

0.000058
0.000058
0.000060
0.000060

0.00008
0.00003

0.00003,

0.00001
0.00008

0.000065
0.000065
0.000085
0.000060
0.000060

0.00005,
0.0002

0.000062

0.00008
0.0002

Tom

To

res

There

Thu
oo

Tao mes

Tiana

Tra ed

Tom

Tins
Tage
Trap ct
Tima
Tina

Tai

Analytical modeling of SIP Chapter | 2 23

Meaning

2XX response received by the client TU afer
entering in he proceeding ate

Retransmission of Zu response

responses are eliveredto transport layer

Rereceving o 2 response by he cen

Se responses agin received by clint
transition

x responses received by client TU afer
“entering in the proceeding sate

INVITE request retransmission
INVITE request delivered to server transaction

Transport enor occur while inthe tanspon
layer’

Requests dle o transport aye ater
proceeding site

Transaction time-out

Transport error occur before ctering the
accepted sate

Waiting ime fo retransmission of u response

“Amount of me thatthe TU wil wat for
retranamision of 2x response

Transport error occur when acknowledgments

Transport error occur before eteing in the
completed state

Response is pase to ranspon layer for
retransmission

‘Amountoftime that the server TU wil emi in
the completed sate

Sewer transaction abandons retransmiting the
Soe responses

Average time
(Rate) (ms)
0.00004

0.000062

0.00008
0.000060

0.000062
0.00004

0.0002
0.00008
0.000065

0.000052

000003125
0.000065;

0.00003125
000003125.

0.000065
6.000065,
0.000022
0.000022

000003125

24. System assurances

TABLE 2.3 Places and their meaning.

Pro new
Po
Pa

Prat

Pare
Pons
Poe
Peon
Pons

Prete

Pc
Ps

Prop
Es

e

ares
Pane
ee

Pam

100 Ting responses generate to quench request transmission
os response is generated by the server transaction

x responses generated bythe server Iansacion

ab responses generated by the server transaction
Acknowledgments generated rom the client transaction

Accepted ate is entered when the server transaction generates 2x
response successfully

Accepted sat is entered when the cient transaction receives 20x
response fom the server transaction

Acknowledgment recived he sever tansction ombctampor
layer

Inia calling states etre when the INVITE lent wansaction is
crested

Completed state is entered when the clint wansaction receives,
ab response fom the server ansaction

Complete state is entered when the sever transaction generates
ab response success

Conf statis entered to absor ational acknowledgment
messages that ative fom rtransmisson of final response

INVITE request is received by he server transaction

Proceeding sat is entered when the client transaction receives Tax
response fom the server transaction

Intl proceeding tate is entered when INVITE ever transaction is
ested

Response awaited afer sending INVITE request
INVITE request is sent to server transaction

Generated acknowledgment is sento server transaction through
transpor layer

Response sento transpor layer (1)
Response sento transpor layer (2x)

Response sento transport ayer ex)
Finally de INVITE request gts terminate

Analytical modeling of SIP Chapter | 2 25

TABLE 2.8 Guard functions.

Guard function
8

A

a

a

a

se

e

=

»

so Ma)

A (Page) 2107 Pam) > 1
sa Poste me) ==

sa Pan) 21 06 Paca

TABLE 2.5 Immediate transition and their meaning.

Guard
Transition Meaning function
6 Flushing ofeinated place E
. Flushing of extra generated acknowledgments »
anne Servertransacton recive acknowledgment and sendit Ar
to the confrmed ate
pe (Detemines thatthe server changes is tate from =
confirmed to terminated

A token in the place Pre. wi enables four other transitions, namely Tin es
Ta cs Tere Ad Time With probabilities ps, Pa; ps, and pa, respectively.
‘The fring of the transition Pise implies thatthe client transaction receives
xx response from the server side through transport layer. Similarly, the firing
of the transition Tascr and Those represent that the client transaction

26. System assurances

receives 2uvand 3ex6xx responses, respectively, from te server side through its
transport layer. I, however, the transitions a, fies fist, his indicates that
the clients not received any response from the server transactions, and atime-
out has occurred.

If the place Pen has a token, then the transitions Tyanperteront and
Tire get enabled with probabilities psand (I ~ ps, respectively. The ring
ofthe transition Trouper aro. epreents hat when an INVITE request is set
to the server transaction, it encounters an emor, and due to this enor, the request
enters the erminated tate at si the trasto omo Ares st with the
probability sa token is transfered to the place Pern stead, the Fring oF
the transition Tree describes that the server receives the INVITE request
successfully from the client transaction and a token is transferred 10 he place
Prove re withthe probability (1 ~ po.

‘When the place Pare re has a token, it enables the transition Tina
‘The transition Tun ming res fer an exponential time and atoken is transferred
to the place Poo nine Which indicates thatthe server transaction sends the 100
Ain response tothe client sde to quench the INVITE request retransmission
‘The INVITE server transaction enter these five different sates one by one after
receiving an INVITE request from the client's TU:

1.Proceeding 2. Accepted 3. Completed 4.Confirmed 5. Terminated

These five stages are represented by the places Pre Parcs Pas:
Pons 806 Parmnae the place Pic sig Contains a token, it enables the
transition Ts and on firing ofthis transition a token is transferred to the place
Phyo. A token in he place Ppracs indicates thatthe server enters into the state
proceeding by receiving the INVITE request, and by sending the 100 tying
response within 200 ms. When a token is transfered to the place Prrus, it
enables four other transitions, namely Tir t+ Tirmportoos Taco and
Tague With probabilities Ps, Pr, ps. and po, respectively. Ifthe transition
Trang iger ies first, it implies thatthe x response is transmitted 10 the
transport layer and a token is transferred tothe place Prraspr ine tf the place
Privy 1.1 ontains token, it enables two other transiiOnS Frame 2
and Tc, With probabilities pro and (1 — pro) respectively. Ifthe transition
Trango eme. fies, à token is transfered o the place Pr again (depicting
that the transport error occurs when x response is sent 10 the transpor layer)
If the transition Ty fies, a token is transfered tothe place Pie If the place
Pi contains a token, it represents that the Lc response is successfully gener-
ated by the server transaction, I he place Pia already contains a token and à
tokenentersin the place Prep mar then the transition Tye ree gets enabled. When
‘the transition Tice fire, represents that the client has received x response
from the server transaction. Now, when the transition Tie fires, a token gets
‘ransferred o the place Prac. representing that after receiving xx response
from the server transaction the client enters the proceeding state. If the place
Pros already has a token and another token enters in the place Pre e

Analytical modeling of IP Chapter | 2 27

simultaneously, then the transition Tre ware fire frst, representing that the
server accepts the INVITE request repeatedly while is inthe proceeding state,
anda token is again transferred tothe place Ps. This condition is managed by
the guard function gu

‘The firing ofthe transition 72. transfers atoken tothe place Pau represente
ing thatthe server generates a 2ex (successful) response. As a token is trans-
ferred to the place Pau, the transition Tia is enabled representing that the
response is transfered 0 the transpor layer. When the transition Tun fire, a
token is transferred 10 the place Pri U the Place Phan 2 BAS 2
token, it enables two other transitions namely, Trage are nd Tone With
probabilities pu and (I — pan) respectivel. the transition Tryon amr 3 Fires
first, a token is transferred 10 the place Pas Which implies that à transport
error has occurred while the response is delivered to the transpor layer. On
the other hand, if the transition Tacs res first, a token is transferred 10
the same place Paces indicating thatthe 2xx response is successfully delivered
by the transpor layer. Now. the place Pays contains a token which enables
the other transitions, namely Te ar 2 The 2 04 Time. With probabilities
ras Piss and pis respectively. If there i a token inthe place Pace and atthe
same time if there ae one or more tokens in the place Prey mai the client side,
the transition Tze gts enabled inthe client side. Simultaneously, if there is
token in the place Pacs and if there are some tokens in the place Pc the
client side, this enables the transition Tye, (representing that the’ client has
received 2x response after entering in the proceeding state) in the cient side.
Also ifthe place Paces already contains atoken and another token enters the
place Pre eat the same time, then the transition Tre avere will fire, repre-
Senting thatthe server transaction again receives the INVITE request while in
the accepted state, and a token is again transferred to the place Pacos. This
‘condition is managed through the guard function gı on Tre aire >. Similarly,
ifinthe accepted state the server generates Zu responses repeatedly, it remains

the accepted state. Thais, ifthe place Pep already has token and another
token enters in the place Pa, atthe same time, then the transition The u Will
fire, representing the repeated generation of 2xx responses on the server side
while in the accepted state, and atoken is again transfered tothe place Pase
‘This condition is managed through the guard function gy on Trea. Also, he
transition pe, ies, token enters the place Preminaess where the firing time
ofthe transition Timer represents the waiting time forthe retransmission of 2e
(success) response.

‘When the place Pens has a token, the transition Txus gets enabled and
fires, and then token is transferred to the place Pau indicating that the server
transaction generates the JG (unsuccessful) responses. These unsuccessful
responses are generated because the server is moved temporarily or perma-
nently or maybe the server is busy anywhere else as there could be other rar
sons. Ifthe place Pas Contains a token, it enables the transition 7 yy and
when this transition fires, a token is transferred 10 the place Prunpurt ayer 3

28. System assurances

(deseribing that response is sent to the transport layer). If the place
Pranger iners contains a token, it enables two other transitions, namely
Tiranpetare à 300 Temps With probabilities pas and (1 — prs), respectively.
If the transition Tranpor ero + fires fist, a token is transferred to the place
Poe: presenting that some transport error has occurred while moving
through the transport layer. If the transition Temps fies, a token is transferred
tothe place Pens. When the transition Teams fre, it represents that the trans-
pont layer successfully sends the Jaxfax response to the client side and the
server enters into the completed state. Ihe place Pops contains a token three
‘other transitions, namely Tir 4 Trina Ad Trine get enabled with prob-
abilities pig, Pur, and pre respectively. Also, if here isa token in the place
Pam and ifthe place Pr way Contains atoken inthe client sie, the transition
These: gts enabled. Simultaneously, if there is a token in the place Pump
and there are one or more token inthe place Pyac then the transition Fr gets
‘enabled. Now, if the place Pcomps already contains a token and an extra token
enter in the place Pare mes then the transition Tre wires at he server side
will fire and a token is transferred tothe place Prune. for transmission,
‘This condition is managed through the guard function gı on Tre wire s. The
firing of the transition Treswres represents that the server receives the
INVITE request repeatedly from the client transaction. If the transition mer
(representing that the 3xx6xx response is passed to the transpor layer again for
retransmission) fies, then the token gets transferred tothe place Pme er
‘This condition is managed through the guard function /3 09 Tyner Mf the tran-
Siion mr fires indicating that time-out has occurred, token ges transferred
tothe place Prrmintad-

In the proceeding state of client transaction, there are three possibilities:
First, the client can accept any number of /ax (provisional) responses and
remain in proceeding state. Second, it can receive 2xx (successful) responses
and enter the accepted state, create and send acknowledgment for successful
response, And lastly, the client can receive xx6xx (unsuccessful) responses
and move to the completed state, and create and send acknowledgment for
the unsuccessful response. We now consider these three cases one by one. Case
1: A token remains in the place Pp, and it enables three other transitions,
namely, Tete res Tome 804 Try With probabilitis py, Pao, and Par respec-
tively. If there is already one token in the place Pc and simultaneously
another token arrives in the place Pi then the transition Te tee Wil fie,
‘representing that the client receives the Zu responses repeatedly from the server
side, anda token is again transfered 10 the place Prac: This condition is man-
‘aged through the guard function g2 on Tre tse. Case 2: 1 the place Pre
already contains a token and simultaneously another token enters the place
Pacs On the server side, then th transition Tq will fre, and token is then
transferred 10 the place Parce (depicting thatthe client receives Zur response
after receiving /xx response from the server transaction). This condition is man-
aged through the guard function #6 on 7,n. The firing ofthe transition Tye,

Analytical modeling of IP Chapter | 2 29

represents that the client is waiting for the response from the server transaction
and the server sends response along with the xx response. Case 3: When the
place Prrc contains a token and another token enters the place Pcomps at the
serverside, then the transition Try Will fie, representing thatthe client receives
3xx6xx responses along with the xv response from the server side, and a token
is transfered tothe place Peony. This condition is managed through the guard
funetion 700 Ty Now, if the place Prep Contain a token and at the same
time another token enters the place Pac hen the transition Taser Will fire
and a token is transferred 10 the place Pac. This condition is managed
through the guard function On Te a The firing ofthe transition Tac TeP-
resents that the client is waiting for response and receives 2xx response from the
server transaction.

If the place Pape contains a token, it enables three other transitions,
namely Tre2ceees DCi os And Tama With probabilies pas pas and
as, respectively. Ifthe place Pac contains a token and an extra token enters
in the place Pacs simultancously, then the transition Tre x re Will fire,
representing thatthe client receives 2xx response repeatedly from the server
transaction, and a token is again transferred tothe place Parce. This condition
is managed through the guard function 6 on Trev e. Also, if the place
Parc contains a token and simultaneously extra token enters the places
Pas then the transition Taca gmeaed Wi fre and a token is transferred 10
the place Pack. This condition is managed through the guard function gı, on
Tack gewnant: The fring of the transition Tack enana represents that the client
transfers an acknowledgment for Zu response t the server transaction. On the
other hand, when the transition Tyna fies fist a token is transferred to the
terminated place Per. The fing time Of Tamer is same as the period
of time thatthe TU will hold on for retransmission of 2xx response,

‘When the place Pye mur contains a token and simultaneously another token
arrives in he place Pronps, then the transition Tuer Will fire, and a token is
transferred to the place Plonpe (depicting thatthe client transaction receives
3064 response from the server transaction and enters the completed stat).
‘This condition is managed through the guard function g7 On Tics. THE
firing ofthe transition Taare represents that the client i waiting for some
response and the server transition transfers Sta response to the client trans-
action. The client's TU will enter the completed state directly by getting the
response 3xx6xx from the server transaction or indirectly by getting Ze
response after the provisional (Zxx) response. IF the place Peony contains
2 token, it enables four other transitions, namely Te suture TACK orando
Trapt ons. ss nd Timer With probabilities pa, Das, Pay and pas, respectively.
Ifthe place Pc yc contains atoken and an extra token entes he place Pcunpsat
the same time, hen the transition Tre xg will fire, representing thatthe client
receives 3x response repeatedly from the server transaction. This condition is
managed through the guard function 4, On Tre u Also, if there is one token
in the place Pape and simultaneously another token arrives in the places

30. System assurances

Peng then the transition Tac. gerd Willie and one token is transfered to
the place Pacy. This situation i managed by the guard function gy, on
Tack gran. When the transition Tac. naa Fes, it represents that he client
sends an acknowledgment for xx response 10 he server transaction, I tran-
Sition uma. ors ies representing hat the acknowledgment fom the client
‘transaction encounters transport eror before reaching the server transaction,
‘one token is transfered tothe place Pam When the pice Pronyc contains
‘one token and the place Pcunps is emptied, the transition Tamer ges enabled.
‘This condition is managed through the guard function g imposed on the tran:
Sition Zim. The fring time of this transition represents the waiting time for
Sexe response retransmission.

No, a token is there inthe place Pack and this enables two other trans
tions: the transition Tack son and the immediate transition 1 with probabilities
pas and (1 — pas), respectively. The acknowledgments that are created by the
lient transaction is then sent tothe transport layer to transfer them to the server
transaction, that is, ifthe transition Tac. fres,one token is transfered to the
place Pronpwciyrs and this enables two other transitions, namely
Trance Und Trogr With probabilities pao and (1 — pao) respectively
But ifthe place Pack already contains a token and an extra token enters
the place Pycy simultaneously, then the firing of immediate transition £ will
stat, andthe token gets flushed fom the place Pac because only one acknowl
‘edgment is required for one INVITE request and more than one acknowledg-
ments get flushed out. This condition is managed through the guard function
49 0n ff a transport erorhas occurred at the transpor layer, the acknowledg-
ments generated by the client transaction enters the terminated state and gets
destroyed, that i, ifthe transition Tracparcener6 Mies, a token is transferred
10 the place Parme

‘When the transition Tan. fires, a token is transfered to the place
Pack we implying that the acknowledgment is delivered tothe transport layer
to transfer it 1 the server transaction, and no error has occurred at the time of
Transmission). As a token enters the place Pack; and simultaneously another
token arrivesin te place Pcanysthen the firing of immediate transition cx ec
will start and a token is transferred 10 the place Pcs. When the immediate
transition 13 fires, it represents that as the acknowledgment is accepted by the
server transaction, the server TU changes its tate from completed to confirmed.
‘Tis condition is managed through the guard function gy on tack. rn he com
firmed state, there is an absorption of any additional acknowledgments that are
triggered by the retransmission of the final response. When the token enters
the place Pewgns it enables the immediate transition fm. The fing of the
immediate transition oy Will transfer a token 10 the place Premise When
the immediate transition jer ie, it represents hat the server changes its state
from confirmed o terminated and the multimedia sesion is over. On the con-
trary, if the client does not receive any response from the server transaction,
then the transition Tyne vil fire representing that the client transaction

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kung, nar man ar i fängelse, ty kungen fick ej ens titta ut i gángen
utan vakt, och der sitter herr Erik ofta flere timmar;" knekten hade
ock tillagt, att det kunde han gema f8 góra, ty nog ar den gángen
lika sáker som hvarje annat fängelse, nar vakt stár utom dórrn. Nog
stá de gamla, manga aln tjocka, grástens murarna báde mot herre
och kung. I skymningen lástes dock fängelsets inre dérr och för
natten var herr Erik instángd i kung Eriks fängelse.

En liten strále af hopp började gry för Sigrid. S8 ringa den án var,
sá kunde hon ej underláta att fasta sig dervid. Sá fullt upptagen an
hennes sjál var af tanken pá fadren, sá glómde hon dock icke, att
äfven frága hvad qvinnan visste sága om Johan Fleming. Hon
lugnades ganska mycket, i afseende & hans öde, genom den
beráttelse qvinnan afgaf, om huru fruarna i slottet sagt, att de
hoppades, det han icke skulle behófva lida nägot.

Sigrid fann snart ett hem i samma boning, der hon, genom master
Sigfrids bemedling, hade funnit en fristad, dä hon ur slottet
bortförde den svärt särade Enevald Fincke. Det var hos en gammal,
stilla enka, af borgerligt stand. Gumman tog nu helt kärligen och
vánligen emot den unga, blida jungfrun, hvilken hon bitrádt med att
skóta hennes sjuke fästman, till dess han hunnit bli sá mycket
bättre, att gumman ensam kunde värda honom. Har hade Sigrid
tilfälle, att i lugn ófvervága den plan, hon börjat att uppgöra. Skulle
hon Iyckas att ur fängelset rädda sin far, sá hade hon för honom till
en början ett säkert gómstálle i Nádendals Kloster, till dess utväg
blefve, att fly lángre bort fran det farliga grannskapet af Abo.

XIII.

Sigrid öfverlade noga allt. Den fara hon sjelf utsatte sig för, fall hon
blefve upptäckt, den aktade hon icke. Hon tánkte blott pá
möjligheten af, att kunna rädda sin far.

En ytterst liten bát med tvenne áror, anskaffades af mor Anna, och
gómdes under ett skjul vid ástranden. Sá snart det blef mörkt, var
Sigrid i ordning till sin äfventyrliga fárd. Hennes mod var nara att
svika, dá hon skulle bege sig ut, men innan hon lemnade sitt rum,
knäföll hon och bad länge och varmt om hjelp och stöd, att hon, den
svaga flickan, matte kunna lyckas i sitt svära företag.

Nágot lugnad begaf hon sig nu pá vag. Det var endast den noga
kännedom Sigrid hade om lokalen, som kunde géra méjligt för
henne ett försök att befria sin far, innan hertigens ankomst skulle
gôra det fór sent.

Med tysta ärtag nalkades hon slottet. Det hade emellertid blifvit
alldeles mérkt. Den vanliga farleden gick omkring slottsudden. Att en
bat färdades der, väckte ingen uppmärksamhet, om an nágon skulle
varsnat den. Ytterst pá udden läg slottsträdgärden, omgifven af en
hg och fast halfcirkelformig mur. Att denna mur var slat, i godt skick

och omöjlig att öfverstiga, visste Sigrid, den var för icke lángesedan
ányo uppförd. Hvarje fórsók att bestiga den, om an med en
repstege, skulle látt hafva väckt uppmarksamhet. Men den lila
luckan i muren! Hon visste hvar den fanns, ehuru den Iäg alldeles
nere vid marken och var gémd af násslor och ris pá yttre sidan. Hon
kände dess hemliga mekanik och kunde öppna den.

Sigrid steg försigtigt ur sin lilla bät, som hon laggt just under
muren, der vattnet gick nästan anda intill. Äfven detta ställe kände
hon förut, och visste huru hon har lätt kunde fasta sin lilla julle.
Smygande längs muren, kände hon för sig utmed jorden, till dess
hon vidrórde luckan, hon öppnade den och fann med glädje, att hon
hade sá godt utrymme att slippa igenom den, att hon hoppades, det
hennes far áfven skulle kunna tránga sig ut derigenom. Med tysta
steg hann Sigrid snart öfver den lilla trádgárden. Har kände hon sá
val hvarje buske, hvarje grásfláck, sá att hon med látthet kunde
komma fram, utan att góra buller. Framfér henne reste sig, hógt och
kalt, den áldsta delen af fástet, det sákallade gamla slottet. Endast
nágra fa gluggar, högt oppe, voro anbragta, för att insläppa dager
och luft, ibland dem det lilla fónster, som gaf dag t gängen till kung
Eriks fängelse.

Sigrids hjerta slog sá häftigt, att det nástan betog henne
andedrágten. Nu hann hon rénnen, kung Eriks rônn. Hon hade
alltfór ofta besókt den, för att taga misste om dess plats. Hon
uppsteg pá en sten, derifrän hon visste sig kunna uppná de krokar,
som fasthóllo trádet, ryckte och vred pá dem och, hvad hon hade
beráknat inträffade, de hade redan tagit nágon röta, eller gifvit vika,
sá att hon utan svárighet fick dem att lossna ur den remna, deri de
blifvit indrifna; och trádet ágde ännu nog spánstighet qvar, for att till
nágon del ätertaga sin férra ställning.

Sà varsamt án Sigrid förfarit, kunde ej detta ske utan buller. Hon
märkte rórelse utanföre; trädgärdsporten, en liten tung port i muren,
gick opp och tvenne karlar intrádde.

"Ja, var säker du, att jag hörde nágot buller, hität."

"Ja, du hör sá mycket du i drómmen, der du stár och sofver. Jag
undrar hvem har skulle róras. Och kan tánka om án sjelfva
polackkungen skulle skicka hit alla sina hejduker, sá kunde de fá roa
sig bast de gitte, har i kryddgárden. Kanske tror du, de ska sid häl
pä de fyra aln tjocka grästensmurarna har pà slottet."

"N nä, det láter han vail sakta bli att snusa hit, nar hertig Carl har
fástet inne. Men hur tror du det ska gá med oss, om nágon varit har,
utan att vi skulle markt det?"

"Näja, jag tanker man finge visa vágen ät de der herrame, som
sitta deroppe, till ett hetare stálle, än har ar i natt."

Emellertid kommo de talande allt närmare Sigrid. Mánen började
svagt genombryta molnen. Sigrid kröp ihop bakom det utspráng af
stenen hvarpá hon státt. FA steg till, och karlarne skulle hafva
upptäckt henne.

Men nu skymtade en person fram fran ett annat hall. Karlarne
sprungo till, grepo denna och bórjade slápa henne emot porten.

“Hi, hi, hi. Jag tanker ni bli feta pá fyndet“, skrattade mor Annikas
röst, "jo, jo, jag undrar just hur mycket besvär det vore, att blása
ner kráknástet ert der, til straff för att ni inte láta folk gä i fred och
sóka rótter."

Emellertid hade karlarne med sin fángst hunnit utom porten, den
de noga tilláste, och dä nu mánen sken allt klarare, sägo de den lla,
torra gumman, som skrattade och hánade dem.

“Hur kom du in, käring", frágade den ena karlen.

"Ja si det var durm det! Jaha, ja det var storkonsten. Finns det
inte stickor och strá att rida pá? Bättre hästar an dem ha ni, edra
glopar, aldrig ridit. Jo, jo. Tokiga ä' ni, som tror, ni kan stánga ut den,
som nägot vet, hi, hi, hi. Men si, nu hade jag nástan lust att g8 in i
táppan igen."

"Pass pá, lät bli med det, mor."

"NS, nog kunde jag nu val ocksá spá er en smula, innan jag gär
tillbaka, sá lar ni val inte neka mig, att der söka nágra rötter, som
inte växa annestäns."

Härom parlamenterades nu en stund, karlarne gäfvo icke med sig,
men Annika lofvade slutligen, att ändä spá &t dem och s& hade hon
Iyckats, att för en ganska lng stund upptaga deras uppmärksamhet,
s8 att Sigrid fann lágenhet, att utfóra sitt várf.

Sedan porten blifvit tillstängd, fórsummade hon intet ögonblick,
ehuru hon darrade só, att hon knappt kunde halla sig oppe. Som
fórut blifvit anmárkt, stod kung Eriks rénn sálunda bakom ett hör af
byggnaden, att den icke bemárktes, fórr an man hunnit nágra steg
framom porten. Af vakten vid porten kunde Sigrid sáledes icke
varseblifvas, der hon nu stod, áfven nar mánan lyste. Men var
hennes far ánnu ute i gángen? Skulle en vaktknekt bli den, som
stode deroppe vid fönstret? Utan att betánka vádan deraf för sig

sjelf, hviskade hon sakta uppät "fader", och med outsäglig glädje säg
hon en hand stickas ut genom gallret och liksom vinka.

Nu vágade hon det sista steget. Rónnen hade rest sig sá mycket,
att hon, pa dess nu löflösa grenar, lyckades hjelpa sig opp till en liten
afsats i muren, dit hon i sjelfva verket slutligen hann, och der hon
äfven lyckades finna ett knappt fotfäste, s3 säkert, att hon med stód
af trádet, der kunde hálla sig fast. Ur sin kjolsáck upptog hon nu ett
nystan, som hade en sten till káma, och kastade det opp mot
gluggen. Tre gänger misslyckades det och nystanet föll till jorden;
men hon hade fast sin trad sá val, att hon äter kunde uppdraga det
till sig. Nu sladdrade och trátte och skrattade Annika med soldaterna
Ijudeligt, och deras skrattsalfvor bevisade, att de voro längt ifrän att
vara uppmärksamma pä nägot annat. Anda till Sigrid trángde Ijudet
af deras röster och lugnade henne betydligt. Hon bjöd nu till, att
Kasta sin slunga med lika kall blod, som hon varit van att, vid lekarna
pá ängen, kasta bollen och — nu kunde hon knappt äterhälla ett
gládjerop, handen deroppe fick tag i nystanet. Nu klángde hon sá
fort, som mójligt, ned till marken och fáste der skyndsamt vid
trádens andra ánda ett bref och ett lángt, fint och starkt rep, som
handen deroppe drog till sig. Vid repets nedra anda band hon âter
nâgra smá verktyg, som kunde bli nyttiga vid gallrets lösbrytande,
äfvensä en fil.

Sedan allt detta fórsvunnit inom gallret, skyndade sig Sigrid ned
genom trádgárden. Just dá hon lutade sig ned, för att krypa ut
genom luckan, kastade hon en blick mot fadrens fängelse och säg
med bäfvan ett matt ljus Iysa derifrán. Att fángvakten med sin Iykta,
nu kommit för att instánga hennes far för natten, tog hon för gifvet.
Hade han lyckats hinna pá nágot sätt gómma de nyss emottagna

sakerna, det frágade hon sig otaliga gánger, utan att kunna besvara
sin frága.

Snart satt Sigrid ater i sin lila bât, men nar hon hunnit sá lángt ut
i farleden, att faran af upptäckt, för denna gang, var förbi, kände
hon sig nara att förlora sansningen. Hon drog in äroma i bäten,
nástan utan att hon sjelf visste deraf, och sjönk ned i dess botten.
Efter en liten stund ätervaknade hon till s8 mycken sans, att hon
kunde lösa af sitt hufvud den duk hon bundit deréfver, doppade den
i vattnet ófver bátkanten och lade sedan den vata duken ófver sin
panna. Detta uppfriskade och ätergaf henne full sans. Nu márkte
hon att ansigte och hinder blödde, men det var endast skrámor.
Sedan hon nägra gánger med den vata duken aftvättat dem,
upphórde de att bléda. Hon hade förmodligen skrapat sig vid det
arbete, hon förehaft.

Hennes första känsla nar hon äterbefann sig i sin lilla kammare
hos enkan, var att utgjuta sitt hjerta i en varm tackságelsebón, for
att hon hade sá längt Iyckats utföra sitt varf, och hon började nu att
hoppas, det herr Erik hunnit délja, hvad hon lemnat honom. Hon
fattade tilfórsigt till att hon skulle kunna utfóra sitt varf, hon tyckte
sig sáker att hon hade välsignelse med sig, dá allt hitils gätt henne i
hander.

Hon lade sig nu och bjöd till att betvinga sin oro, för att kunna
sofva. Hon visste att hon, kanske redan päföljande dag, skulle
behófva all sin styrka.

Att anlita nágon annan om hjelp, vägade hon icke. Herr Erik hade
mänga vanner; hon skulle kanske kunnat lyckas förmä nägon, att
utsátta sig fór de faror, som hotade hvemhelst, som skulle varit
henne behjelplig, men hon kunde icke éfvertala sig till, att vilja

utsätta nägon, för att kanske offras &t en plägsam död. Dessutom
skulle den, som hjelpt hennes far pá flykten, säkerligen genom tortyr
hafva blifvit tvingad att uppge hvar herr Erik funnit tilfiykt, sá framt
man kommit pá spáren hvem, som varit honom behjelplig. Det
säkraste var att icke äga nágon förtrogen, annan än mor Annika,
hviken tycktes ha sá noga reda p3 alla Sigrids steg, äfven dem,
hvika hon ej anfértrodde gumman, sá att allt döljande för denna
syntes vara fäfängt. Hon hade ock bevisat Sigrid sá stora tjenster, att
det tycktes vara fôga skál att misstro henne.

Följande natt lág sá sotmörk ófver vattnet, som en natt i
November
plágar vara nár regnet faller i strida skurar. Genomvat hukade sig
Sigrid ned pá marken vid den éppnade luckan i slottsmuren och
Iyddes.
Hon kunde ej annat höra an regnets plaskande.

Hade hennes far fätt behälla, hvad hon sändt honom? Skulle han
komma i afton? Kunde han ens i mérkret hitta til luckan? Men äfven
han var ju sá hemmastadd pá slottet, att detta sista borde gà för sig.
Hon ville ej krypa in, för att icke ka vádan af upptäckt. Hade herr
Erik fätt vara sá mycket ensam, som erfodrats, för att fä lós gallret?
Och hade han verkligen fätt löst det, áfven om han fätt försöka det?
Tusende ängestfulla tankar plägade henne, och den späda flickan,
som man ofta beskylit för att vara rädd och tafatt, tánkte nu ej ens
pá hvad hon sjelf led, huru hemskt det var i den öde qvällen, huru
stor hennes egen fara var. Stundom bäfvade hon dock tillsammans,
hon tyckte att hennes hjerta nástan sammankrymptes, hon fruktade
att fórlora sansningen. Áter tog hon sin tillfiykt till bón.

Nu tyckte hon sig héra ett sakta prassel bland de nedfallna léfven
som lágo pá trádgárdens gángar och sade nástan ohörbart: "Far
"Bam", svarades nästan lika sakta. Med möda lyckades riddarn
tránga sig ut genom den lilla luckan, och innan kort sutto far och
dotter, utan att vidare hafva vexlat ett ord, bäda i den lila bäten,
som ej var större an att den jemnt bar dem.

Sigrid fattade 8rorna och rodde utät. Hvar vägen rätteligen gick,
var ej lätt att skönja i mörkret; men den lilla ekan gick fram äfven
der det var grundt, och herr Erik kánde val farvattnet. De mörka
massorna af krigsskeppen syntes skymta emot himmelen, huru
mörkt det án var, sá att det lat sig göra att undvika dem. En gáng
kommo de resande dock nog nára ett fartyg, fór att bli anropade,
men Sigrid hvilade dá ett ögonblick p& Aroma och fortsatte sedan
fárden med ytterst tysta ártag, och vakten pá skeppet trodde sig
hafva hört miste nar han tyckt sig förnimma Ijud, bland smattret af
det fallande regnet.

Andteligen hade flyktingarna hunnit fórbi Runsala och bäda
började nu smáningom andas lättare. Nu begärte herr Erik ärorna
och Sigrid, som fann att hennes hander ej länge mera skulle fórmá
sköta dem, var villig att ge dem ifrän sig. Dessa ord voro de fórsta,
som vexlades mellan far och dotter. Sedan de i tysthet, med nágon
svärighet bytt plats i den lilla b&ten, grep fadren med kraft i ärorna
och nu gick fárden raskt framát, allt ánnu under tystnad. Han valde
vägen genom smärre sund, som sällan besöktes af bátar, hvilket
numera, sedan regnet smáningom upphôrt, icke var omójligt, ty man
började dock kunna urskilja konturerna af fóremálen.

Natten var láng, som November-natten är En stund hvilade
fiyktingarna i en lada, men vágade icke försöka att göra opp eld, för

att torka sig vid. Herr Erik ikládde sig en grá vadmals rock och
mössa med stora öronlappar, som Sigrid medfórt i báten. Snart
begäfvo de sig ater à vag.

Andteligen hunno de málet för sin färd: Nádendals i ruiner fallande
Kloster. Enligt sin gamla fránkas anvisning, uppsókte Sigrid nu i
mörkret de hemliga dórrens fjáder. Sedan den var funnen sade hon:
"Nu, farkär, vill jag hoppas, att med Guds hjelp det vársta ar
öfverständet. Men icke ar det nédigt att nu i sádant mörker gâ in i
detta gómstálle. Ingen vistas har. Klostret förfaller allt mer, men
kyrkan, der vi nu befinna oss, är uppreparerad och har hálles om
séndagarna gudstjenst; säkert ar att före dager ingen kommer hit.
Skulle dock nágot ljud höras, sá máste vi hasta in i gômman."

Sedan Sigrid hade uttalat dessa ord, vacklade hon och nedfäll
afsvimmad. Naturen hade tagit ut sin rátt Den hégsta
själsansträngning hade hällit henne oppe, vida utöfver hvad hennes
krafter egentligen skulle förmätt. Nu brast den sá länge spánda
fjedern, och hon föll tillsamman, som ett kläde faller, nar det slappes
ur handen.

Under herr Eriks ömma omsorger vaknade hon dock slutligen ater
till medvetande, men hon kánde sig sá matt och liksom sénderfallen,
att det var henne oméjligt att uppstiga. En flaska vin, som hon laggt
i báten jemte ett bréd, kom nu val till pass, dä Sigrid ej orkade bege
sig ut, fór att anskaffa mat, och sá tillbringade far och dotter sin dag
tillsamman i sitt säkra gömställe.

XXXIII.

P& slottet hade emellertid fängens flykt blifvit upptäckt. Det
fängelse, som hyst den afsatte monarken, ansägs allt för svärt för
hvem som helst annan, genom sin brist pá luft och jus. Men dá nu
sá mánga fängar voro pá slottet, och man icke ville tiláta dem att fà
bo tvänne tillsamman, sá mäste áfven kung Eriks fängelse begagnas.
Och dä äfven den yttre gängen anságs lika fast, som hvarje annat
fängelse, sá tyckte man sig tryggt kunna fórunna fängen den
lindring, att man om dagarna lemnade dörren frán fángelserummet
till gángen olást. Sälunda var det egentligen den, som utgjorde hans
fängelse, och kung Eriks rum blott det ställe, der han för natten
inlástes. Herr Erik hade just jemnt hunnit i sin sang kasta, hvad han
af Sigrid emottagit, dá vaktknekten med sin Iykta inträdde.

Päföljande dag hade han lätsat vara sjuk, för att kunna ligga pá
den halm, som gömde repet. Dessutom anság han denna
förevändning lämplig, för att góra vakten obekymrad om honom.
Under loppet af dagen lyckades herr Erik att inskjuta nágra smulor
murbruk i l8set; och dá om aftonen vaktknekten, som vanligt, kom
for att stánga dérren, och nyckeln tog emot, férlorade han
t8lamodet, vred sá väldsamt, att axet brast, och máste bege sig till
slottssmedjan för att f& skadan hjelpt. Att emellertid ordna om

nágon vaktkarls utstállande i gángen, anság han sá mycket mindre
nédigt, som herr Erik nu var sjuk; och att dérren stode en timma
längre olást án vanligt, kunde ej vara farligt. Icke eller var han mon
om att inrapportera om nyckelns férvridande, hvilket han nódgats
göra, ifall han hade fordrat hit en ny postkarl. Det kunde ju aflöpa
utan allt detta trakasseri och dessutom utan nägon fara.

Nu var dock ingen i smedjan till hands. Arbetet drog ut pá tiden,
och först efter ett par timmar áterkom vaktkarlen med sin nyckel och
Iykta, och fann d8 till sin förfäran, buren tom.

Hans förskräckelse var gränslös. Hvilken vag fängen tagit, var lätt
att se. Han tyckte sig redan kánna tortyrredskapen gripa sig. Man
skulle naturligtvis anse honom hafva hjelpt fängen pá fiykten. Det
var ingen nád att vánta. Han ófverlade lange om han nu borde
anmäla saken, men fann slutligen pá en utväg, den han beslót att
försöka. Han kunde ándá knappt förvärra sitt öde.

Den första omsorgen var att draga in det qvarhängande repet,
hvarpä herr Erik slagit en mängd knutar. Derpá ställde han ater
gallret pá sitt ställe och injemkade de stenflisor, som vid utbrytandet
fallit ur muren.

Fängnekten hade redan om morgonen inrapporterat sin fänge
säsom sjuk. En man af gamisonen hade nyss dött och lág redan i sin
kista, fardig att begrafvas. Vaktkarlen, som bevakat trappans yttre
dörr, och sälunda var utsatt för fara genom fängens fiykt, intogs i
förtroendet. I soldatens likkista lades en stock, och den döde bars
opp i kung Eriks fängelse, lades i sängen och ikläddes nägra af herr
Eriks qvarlemnade klädesplagg. Här och skägg klipptes och ordnades
till ikhet med herr Eriks, och fängknekten anmälte fóljande morgon,
det fängen hade aflidit under natten.

Ett par personer afsándes fór att fórvissa sig om sanningen af
uppgiften. Under vágen talade vaktknekten mycket om, huruvida
han icke äfven torde insjukna, ty han började känna till just samma
onda, hvaröfver den aflidne klagat. De begge herrarne tycktes äfven
tro, att sjukdomen kunde vara smittosam, kastade endast pá afstánd
en blick pá den döde, och sá skumt det var i deta ohyggliga
fängelse, var det icke látt att upptäcka misstaget, isynnerhet för
personer, som icke mycket sett herr Erik Liljeholm och icke eller hade
nägot skal till misstanke. Fángknekten fick befallning att nedlägga
den döde i en kista, hvilken befallning han sá fort som möjligt
utfórde, och tillspikade sedan kistan val pà alla sidor.

XXXIV.

Nu randades den af sá mánga med báfvas rantade dag, dá hertig
Carl intráffade i Abo. Han fóregicks af blodiga rykten. Alla som retat
hans vrede genom trohet mot Sigismund, och synnerligen de, hvilka
genom sin börd eller större förmäga kunde blifva farliga, fóllo offer
för hans hámd. Halshuggning, stegling, fórlust af all egendom
drabbade tätt, och de lifdómdes familjer befunno sig i sin djupa sorg,
med detsamma de förlorade makar, söner eller bröder, tilika försatta
i den yttersta fattigdom.

Hustrur och barn till de fángne herrarne pá Abo slott omgáfvo
hertigen vid hans ankomst och bádo knäböjande om näd för de sina.
Hertigen svarade: "Hvi bedjen och anropen J mig? Jag kan intet, det
är lagen, som skall dömma dem. De hafva brutit mot konungens ed,
gjort uppror mot fäderneslandet och státt mig efter lifvet; deras dom
mäste lagen fälla."

Hertigen gick nu opp i sina rum och lát genast infóra Arvid
Eriksson Stálarm, som vardigt och lugnt besvarade hertigens háftiga
tilltal, och skyndade sig att begagna tillfállet för att fä framstálla
Johan Fleming, sásom af honom lockad och ófvertalad att
qvarstadna. "Han hade kommit till Finland för att ordna enskilda

angelágenheter och skaffa sig nágot penningar, dermed han skulle
bege sig i fremmande land, att der öfva och försöka sig, sásom unge
adelsmän bruka, hvarigenom han i framtiden battre kunde tjena sit
fádernesland."

Sedan Stälarm blifvit bortfórd, befallte hertigen att Johan Fleming
skulle infóras. Hertig Carl vandrade fram och äter med stora steg.
Adrorna pá hans tinningar svállde. Gäng efter annan sammanknöt
han handen. Nu intrádde Johan Fleming och bugade sig djupt.
Hertigen gick häftigt emot honom. I hans öga strálade segerglädje,
dá han sade: "Ha, detta ár sáledes Klas Flemings son!" Det var som
om han nu först skulle hafva känt sig rätt sáker om den krona, han
efterstráfvat, och dock rórde sig i hans inre en dunkel ónskan att
skona den älsklige ynglingens blod. Nar Johan sä stod infór fursten,
pá en gäng ödmjuk och stolt, och det behagliga, ungdomliga anletet
hójde sig bónfallande emot honom, dá vek for ett égonblick
sjelfviskhetens blodlystna demon frán Carl och han sade: "Det synes
mig dock härdt, att förgöra detta unga lif. Välan, vill du, som en ärlig
och adelig yngling, lofva och förpligta dig for framtiden, att troget
tjena mig och riket, s3 vill jag, för din ungdoms skull, láta nád gä för
rátt och skánka dig lif och frihet."

“Mot mig har min herre, konung Sigismundus, alltid varit en nádig
herre; det vore af mig otacksamt att ófverge hans tjenst, och jag
ger dertill ngen skálig orsak, och dock", tillade Johan, bójande knä,
"beder jag, att Eders Furstliga näde mätte bevilja mig nád, emedan
jag till Finland kommit endast fór att skaffa mig medel att fórsóka
min lycka i fremmande land."

"Du, Johan Fleming, beder om nád och böjer blott ett kná!
Hvarfóre vördar du mig icke med tvánne knán?"

Öppet och rent strálade Johans blick, dä han svarade: "Endast &t
Gud och min konung sparar jag denna vördnad."

Nu trädde Carl ett steg tillbaka: "Ha, sá ar det. Af ormaägg
komma ormaungar. En sädan var din fader och sádan blir du sjelf,
om du far lefva; men du skall icke váxa mig éfver hufvudet, som
han. Hade icke den öfvermodige och bälstore tyrannen, som aktade
hvarken Gud, konung eller land, satt sig opp emot mig och farit fram
som ett vilddjur, och dräpit och slagit ihjäl fattige bónder och godt
folk, som ville försvara rikets lag och regering, sá skulle längesedan
fred och rolighet herskat. Men du gifver nogsamt tillkánna, att du af
din fader ärft natur och sinne, och varnar oss för det vi, i ika motto,
skole förvänta af dig. Derfére má du vara beredd att svara för rátta
med de andre finnarne, med hvilka du dig förbundit hafver, och stá
din egen fara." Vakten slöt sig kring Johan Fleming och han
nedfórdes &ter i sitt fángelse.

Hertigen stod en stund qvar pá samma plats, men började sedan
g8 fram och äter i det han sade: "Hade icke den fórrádarn nara
narrat mig med sitt fagra anlete och blida min, att gifva honom fri.
Herren fórláte mig, att jag sá ernade lemna mina och riksens fiender
var, för att stámpla ondt och fóra oskyldiga menniskor i olycka,
genom sina illfundigheter. Herren känner mig och vet, att jag icke
eftersträfvat regementet, utan fast mer gjort allt hvad i min förmäga
státt, för att bibehálla det át min broders son, konungen i Polen;
men att han, mot all ed och fôrsäkran, som en menedare och
förrädare, sitt eget fádemesland med krigsfolk ófverfaller, och vill
med papisteri och svek oss alla i olyckan föra, och sätter till
befallningsmän sádane, som den blodhunden Klas Fleming och
dylika. Nej, visserligen máste de ogerningsmännen alla fórgóras. Sá
länge adeln ar för mäktig i landet, ager kronan ingen makt." De sista

orden uttalades halfhógt, men om fôr resten detta tal var ernadt att
höras af var Herre, eller af den tjenare, som stod vid dörren, eller af
hertigens eget samvete, ar ej latt att afgóra. Kanske det var ernadt
litet át dem hvarje.

Den utnámnda domstolen hade sin session pá rádhuset i Abo.
Joachim Scheel, Bjelkar, Lejonhufvud, Brahe och flere andra, sutto
kring bordet. Fängarne fördes nu ófver torget, mellan led af soldater,
under ljud af trummor och pipor, opp till rádstugan.

Anklagelsen upplástes. Nio punkter, alla rigtade mot Arvid Eriksson
Stälarm. Han hade fort afvig sköld emot fäderneslandet, hade státt
Hans Furstliga näde efter lifvet, och sá vidare. De andres brott
omtalades icke.

Nu framsteg Stälarm och talade: "Ädle herrar, som till domare
tillsatte aren, hvad jag án kan hafva brutit, denne unge herre, herr
Johan Klasson Fleming, han ar dock till allt oskyldig, och hvad det
anbelangar, som blifvit honom lagdt till last, att han med konung
Sigismund fólide vid dennes infall i Sverige, sá máste honom
tillgodoraknas, det lagen, som fäller den, som med fremmande
krigshár gár emot fäderneslandet, dock har tillägger: ‘med mindre
han var sjelf med, som näste var till riket.' Och hafver herr Johan,
som dá hade tjenst invid sin konungs person, náppeligen spánnt en
béssa emot Hans Furstliga náde eller hans folk."

Joachim Scheel lofvade att framstálla allt detta for Hans Fursteliga
nade, och sá fullfólides ransakningen, med att punkt för punkt
upptaga beskyliningarna emot Arvid Eriksson. De ófrige anklagades
brott omtalades icke ens, utan syntes deras dom komma att
innefattas i Stálarms.

Nar alla de nio anklagelsepunkterna voro genomgängna,
framträdde äter Stálarm: “Adle och välbördige herrar, beder jag
ödmjukligen, att J viljen hos Hans Furstliga nde understédja min
ödmjuka bôn. Icke beder jag om nágon annan nád, an den, att han
ville mig den gunst och nád bevisa, att láta mig ensam dé, och
skona dessa andra mina medfángne herrar, emedan jag hafver varit
den, som hafver fórestátt den högsta makten i Finland, och de
endast hafva följt mig och mina föreskrifter; och aro de sáledes att
ursäkta för hvad de mig till &tlydnad hafva brutit. Derhos matte det
cock högeligen beklagas, att J, ädle och välbördige herrar, eder
fórhastat, i det J endast mina brott och min skuld undersókt, men
icke ransakat dessa mina medfängars, hvilka J nu, jemte mig, viljen
démma."

Grefve Mauritz Lejonhufvud svarade: "Det hafva alla finnarne varit
om ett rád uti det, som J uti landet bedrifvit, och dertill med behöfva
icke vetterlige gerningar stor ransakning."

Följande morgon uppställdes hertigens krigsmakt i en krets
utanfór slottet. En otalig folkmassa af alla stánd samlades der
utanföre. Inuti ringen stodo alla fängarne pá knä. Cancelliskrifvaren
uppláste domen: Alla de uppraknade tjugutvä herrarna skulle
halshuggas, deras hufvuden uppsättas pá pikar, kropparna steglas
och deras egendom konfiskeras.

Hertigen kom derpá ned fran slottet och emottog af alla
närvarande hyllnings ed. Men nar han áter skulle tráda ur ringen
hójde Johan Fleming sin róst och bad, att "Hans Fursteliga náde ville
Iäta nád gá för ratt."

Fursten gick honom fórbi och svarade: "Du har fórkastat min nád
och fórlátelse, dá den erbjóds dig; nu ár det fór sent. Domen ár

fálld. Jag har icke mera makt att efterläta landsens rätt. Tanker
numera icke pá annat án huru J magen bereda eder att svara för
edra gerningar i en annan verid."

Det var dagen efter den, dá domen hade fallt. I sitt fängelse satt
Johan Fleming vid ett bord. Han hade pá begäran erhâlit
skriftilbehör. Hufvudet hvilade en stund i handen, innan han fattade
pennan. Det var sitt testamente den tjuguettärige ynglingen skulle
skrifva. Han började nu:

'Gud den allrahégste han vare min hjertans kara morkárs trést uti
hennes bedrôfvelse, och tvina intet att domarena skola svara mig for
Guds stránga dom, huru de mig dómt hafva.

'Derpá anbefallte han sina tjenare ät sin moder, och bad att sásom
de alla honom troligen tjenat, de ock mátte bli ärligen och val lönta.
Äfven nägra smá skulder uppgaf han, som borde betalas,
recommenderade til sin moders godhet personer, som hade bevisat
honom välvilja, i denna min bedröfvelses tid, och hafva mig hulpit
med mat och él, sásom ock hafva tillsagt att efter yttersta rád hjelpa
mitt lik til sin lágerstad, efter som mig kan undtvara.

"Till konungen beder han "för sin salige faders trogna tjenster, sá
ock min egen intill denna stund, att min hjertans kara morkär och
systrar má njuta det till godo, som de hafva mist bade árfdt och
förvärfdt, att de ej má behöfva lida nöd och spott." Nágra andra
punkter, alla bevisande hans ádia, varma hjerta, tilade han
yttermera, och slutade med följande ord: 'Láter jag min hjertans
kära morkär fómimma, att hvem hon hafver att beskylla för min död,
kan jag intet annat sága, utan att den trángtan och &stundan, som
hans furstliga náde hafver haft, till att ódelágga och fórdámpa min
slägt, hafver varit orsaken till det förnämsta, hvilket nu efter hans

vilja gänget ar. Gud tróste eder, min hjertans kara morkär, samt mina
kära syskon, och late oss finnas i den eviga glädjen. Gifvet uti min
eftersta stund pá Abo slott den 10:de November Anno 1599.

Eder ödmjuke son hafver jag varit.
Johan Fleming.

Sedan detta var skrifvet, vande sig Johan Fleming till sin gamle
tjenare och sade: "Nu har jag allt ordnadt, och beder dig blott ánnu
en gang, att du, om dig méjligt blifver, má framföra mina hjertliga
och kärleksfulla helsningar till alla dem, du vet att jag hällit kár, och
att du má berätta dem om mina sista stunder."

XXXV.

Sigrid och hennes fader hade emellertid tillbragt tiden i sitt mérka,
unkna gômställe. En afton i mérkningen hade Sigrid vägat sig in till
den lila staden, för att fd köpa mat, men snart blef det lila förrädet
slut. Hon mäste nu äter försöka att skaffa mera. Dessutom blef det
allt mer af néden, att sóka en annan tillflyktsort, ty det blef allt
kallare i luften. Derfóre máste fiyktingarne bjuda till att fä hora
nägot frán den yttre verlden, hvilket áfven eljest var för dem af
högsta intresse. Herr Erik fogade sig med sin vanliga, lugna
bekymmerslóshet uti det ingalunda behagliga láget, att tillbringa sina
dagar i det mérka och unkna, källarlika rummet; och Sigrid tánkte
alldeles icke pà att hon sjelf led obehag deraf. Men hon fruktade för
fadrens hälsa och tálamod, och funderade ideligt pá utvágar att
komma hádan. Fór Sigrid hade visserligen ingen fara varit att vandra
bort och aterbege sig till sitt hem, men att lemna sin far, kunde hon
ejsätta i fraga.

DA nu matförrädet var slut, fanns ingen annan utvag, an att Sigrid
ter i skymningen begaf sig till staden med duken tätt knuten om

ansiktet. Hon lyckades snart nog att fá uppköpt hvad hon behöfde,
men hvad hon i nyhetsväg kunde fä höra, var af sá förfärande art,

att hon endast med méda kunde hälla sig upprätt, för att bjuda til
att áter hinna till sin far.

“Ah häh, hvad J ar högfärdig, jungfru Sigrid", ropade en róst
bakom henne.

Sigrid spratt förskräckt till och ság sig om, men lugnade sig
genast, ty hon igenkände gamla mor Annika, som med detsamma
upphann henne.

"NA, mor, hvadan kommer ni?" frágade Sigrid vänligt.

“Ah jo, kommer frán blod, mycket blod, nástan for mycket. Nar
hertigen häller kalas, sá bestär han sá det käns. Fy, det börjar ratt
äckla till slut, det blir för mycket af det goda. Hi, hi, hi, der kasta' de
boll med hufvun och satte dem pá pikar. Huu, icke var den leken
ändä sá rolig, som jag tánkte, fast sjelfvaste herr Klases son var lika
blodig som han — han — hon vet, jungfru, fast man intet námner
simpelt folk i bredd med de förnämare. Men han var allt fager och
ung, herrn der ocksä, och manga sade, att det finns folk som máste
grata efter honom, lika bittert, som... äh.

"Johan Fleming, i himlens namn ar det dä sannt?"

"Ah jo, áh jo, liksom alla de andre. Ah jo, Olof Klasson, Nils
Ivarsson Stjernkors, Michel Päfvelson Munck, Sten Fincke, och
mänga, manga, hela länga raden. Bara Kurcken och Arvid Eriksson
fórde de in tillbaka igen, just som de vántade att mista nacken. Ah
háh, men det var otáckt! Tror jungfrun, att allt vattnet der borta i
fjärden, kan tvätta bort all den bloden? Anej, intet gár det med salt
vatten. Nah, kanske stora Näsijärvi? Nej, det ar sá stilla, sá mildt,
icke förslär det. Men Kyrönkoski, ja, eller Imatravattnet; husch hvad

det skummar i tvattbaljan! Ser J, jungfru, blod ville jag ha, det brann
i mig efter blod, men detta blef dock för mycket."

Ater började Annika: "Och herr Erik Liljeholm, ja, han ar déd han,
och honom söker ingen. Men domen fall ándá, att hans lik skulle
nedgráfvas i galgbacken och hans gods falla andra herrar till. Ah ha,
men si, jungfru Sigrid gráter icke efter far sin änd2. Hi, hi, hi. Huu,
änej, Annikamor har icke lust att skratta, der var ett sá ungt hufvud
och vackert; och det var en annan ocksä, som var ung och vacker,
som de sköto der pá Aland, nog vet jungfrun, den der gossen som
ville gifta sig med Storklasens flicka. NA, vill 3 veta nágot, jungfru,
kan J lása, kan J den trollkonsten? Nog skylla de att lila mor Annika
borde bránnas fér att hon kan mer an andra, men hvad straff borde
dä den fä, som kan läsa? Det ar val várre trolleri, det! Der har hon
papper, lás, lás. Jo si, Johan Bertilsson, han lar val f3 ska papperet
sitt, han."

Mekaniskt emottog Sigrid pappersrullan, utan att ens veta af det.

"Ack, de arma. Gud hjelpe dem. Fru Ebba, Karin! O, Gud styrk dem.
Kunde jag dock pá ett ögonblick komma till dem. Huru skola de bara
allt detta?" utbrast hon.

"Ah, storfolket, hvad felas val dem?"

"Mor Annika, häna icke de olyckliga, har ni ej sjelf lidit nog bittert
af att fórlora den ni anság som edert barn. Har ni i ert hjerta ingen
annan känsla, an hämd, och ni har dock varit sá válvilig emot mig",
utbrast Sigrid, som mer an en gäng förut sökt förhälla mor Annika
hennes ohyggliga hämdlängtan.

"Ah há, jungfru, hvar och en sitt, hvar och en sitt. Herr Erik var
god emot honom — honom, som jag ej térs námna; men —

Flemingen, var han ocksá god mot honom, han som... huu nej; hvar
och en sitt der

"Och derfére vill ni att de, som eder intet ondt gjort, skola lida.
Fru Ebba, alla lidandes beskyddarinna, den unga Katharina, ja, den
unge Welam de Wyks mor, ty áfven han hade en mor. Har J, mor,
tänkt p3 alla de sorger, alla de tárar, de fálla, har J tánkt p& alla de
enkor och barn, til de manga hertigens offer, öfver hvilka J
triumferat. Mor, mor, kom ihäg, att dessa alla och mánga, mánga
utom dem, hafva grátit, hafva lidit samma qval och samma sorg,
som J icke kunde bara; för hvilka J sökt hämd; hvilka J velat släcka i
blod. — Har ni nog nu af eder hämd?"

"Det gár sá underligt omkring i mitt hufvud. Det började sá ren
der i Abo, der, jungfrun vet, huu, der som det forssade sá mycket
blod. Tala inte sá der, jungfru. Huu, jag vill inte hórat. Anej, ánej,
Annika gár hem. Dit, dit, vet hon jungfru, icke till stugan i
Tavastskogen, men dit, der hon sprang som liten flicka. Vet J,
jungfru, lila mor Annika hon var ánnu mindre dá. Hon var sá der
liten. Det var en söndagsmorgon, hon hade ett helt rent linne pá sig,
det var sá hvitt, sá hvitt; hennes fötter voro sá hvita, de voro nyss
tváttade. Hennes har var ocksä hvitt, det var kammadt och benadt
och hennes kinder voro sá réda som äpplen. Ack, jag minns, jag säg
henne sá val i bácken vid var stuga. Jungfru, jungfru, Annika mäste
sóka opp hvar den hvita, rena flickan gômt sig. Farval, jungfru
Sigrid, mor Annika kan ej hjelpa er mera nu, hon hiner inte sóka sin
makt mera, hon mäste söka den hvita, lila flickan. Farval, farväl!"
och bort hastade mor Annika och férsvann fér Sigrid i skogen, dit
Sigrids blick följde henne, ehuru hon med sina tankar icke uppfattat
gummans ord, ty de voro helt och hället upptagna af de rysliga
nyheter, hon just hade hért.

Sigrid begaf sig, full af &ngest, till sin far. Hon berättade honom
först, att mor Annika hade uppgifvit, det man trodde herr Erik vara
déd och att hans egendom fórklarats fórbruten.

"Ja sá, säger gumman sant, sá ar jag sáledes déd! N3, det gár
an att jag ej kánner mig dess várre, och den dóde söker ingen efter.
Godsen, nä, det mäste val s3 vara, det kan ej hjelpas. Mina armar
ro ännu starka. Men mor Metta, det ar allt bra tungt for henne, och
du, kara barn! Herr Enevald matte dock val icke rygga, för det du ar
fattig. Nunnans lilla gods lar val bli allt, hvad du ger. Det kostar pá
hôgmodet att ej ha nágot att lemna dig. Fór mor matte val nágon
utväg bli; s3 má vi dock tacka Gud att det gick sä, som det gick, för
mig. Men visste hon intet saga om vára vánner, som lemnade qvar i
faran?

“Ack, fader, rysligt sladdrade hon tillsammans om blod och mord.
Jag bäfvar att sága det hon sade. Jag vet ej om man bér tro henne."

"Dödade?" frägade herr Erik dystert.

"Alla", svarade Sigrid, i det hon sammanknáppte sina hander.
"Johan Fleming?"

"Fader, afven han."

En lang tystnad rádde. Ingendera sade ett ord, Slutligen brat
Sigrid tystnaden.

"Fader, har ar ett papper, som mor Annika gaf mig, det lár
innehálla nármare upplysning:

System Assurances: Modeling and Management 1st Edition Prashant Johri (Editor)

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