Table Of ContentLecture Notes in Computer Science 7314
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
AlfredKobsa
UniversityofCalifornia,Irvine,CA,USA
FriedemannMattern
ETHZurich,Switzerland
JohnC.Mitchell
StanfordUniversity,CA,USA
MoniNaor
WeizmannInstituteofScience,Rehovot,Israel
OscarNierstrasz
UniversityofBern,Switzerland
C.PanduRangan
IndianInstituteofTechnology,Madras,India
BernhardSteffen
TUDortmundUniversity,Germany
MadhuSudan
MicrosoftResearch,Cambridge,MA,USA
DemetriTerzopoulos
UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
MaxPlanckInstituteforInformatics,Saarbruecken,Germany
Khalid Al-Begain Dieter Fiems
Jean-Marc Vincent (Eds.)
Analytical and Stochastic
Modeling Techniques
and Applications
19th International Conference, ASMTA 2012
Grenoble, France, June 4-6, 2012
Proceedings
1 3
VolumeEditors
KhalidAl-Begain
UniversityofGlamorgan
FacultyofAdvancedTechnology
Pontypridd,UK
E-mail:[email protected]
DieterFiems
GhentUniversity
DepartmentTELIN
Gent,Belgium
E-mail:dieter.fi[email protected]
Jean-MarcVincent
LaboratoireLIG,projetMescal
Grenoble,France
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-30781-2 e-ISBN978-3-642-30782-9
DOI10.1007/978-3-642-30782-9
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2012938994
CRSubjectClassification(1998):C.2,D.2.4,D.2.8,D.4,C.4,H.3,F.1
LNCSSublibrary:SL2–ProgrammingandSoftwareEngineering
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Preface
It is our pleasure to present the proceedings of the 19th International Confer-
ence on Analytical and Stochastic Modelling and Applications (ASMTA 2012)
which was held in Grenoble, France. ASMTA conferences have become estab-
lishedqualityeventsinthecalendarofanalytical,numericalandevensimulation
experts in Europe and wellbeyond.In addition to regularparticipants fromthe
main centers of expertise from the UK, Belgium, Germany, Belarus, France,
Italy, Latvia, Hungary and many other countries, we received newcomers with
interestingcontributionsfromothercountriessuchasKorea,JapanandSweden.
The quality of this year’s program was exceptionally high. The conference
committee was extremely selective this year, accepting only 20 papers. As ever,
the International Program Committee reviewed the submissions critically and
in detail, thereby assisting the Program Chairs in making the final decision as
well as in providing the authors with useful comments to improve their papers.
We would therefore like to thank every member of the Program Committee for
their time and efforts.
WeareverygratefulforthegeneroussupportoftheUniversit´eJosephFourier,
and their efforts for organizing the conference.
We thank the authors and participants for their contribution to ASMTA
2012.
4 June 2012 Khalid Al-Begain
Dieter Fiems
Jean-Marc Vincent
Organization
Conference Chair
Khalid Al-Begain University of Glamorgan, UK
Program Chairs
Dieter Fiems Ghent University, Belgium
Jean-Marc Vincent Universit´e Joseph Fourier, France
Program Committee
Sergey Andreev Tampere University of Technology, Finland
Jonatha Anselmi BasqueCenterforAppliedMathematics,Spain
Konstantin Avrachenkov INRIA Sophia-Anitipolis, France
Jeremy Bradley Imperial College London, UK
Herwig Bruneel Ghent University, Belgium
Giuliano Casale Imperial College, UK
Hind Castel Institut Telecom-Telecom SudParis, France
Koen De Turck Ghent University, Belgium
Alexander Dudin Belarusian State University, Belarus
Antonis Economou University of Athens, Greece
Paulo Fernandes Pontifical Catholic University of Rio Grande
do Sul, Brazil
Jean-Michel Fourneau University of Versailles, France
Rossano Gaeta University of Turin, Italy
Marco Gribaudo Politecnico di Milano, Italy
Yezekael Hayel Univeristy of Avignon, France
Andras Horvath University of Turin, Italy
Helen Karatza Aristotle University of Thessaloniki, Greece
William Knottenbelt Imperial College, UK
Lasse Leskel¨a University of Jyva¨skyla¨, Finland
Remco Litjens TNO ICT, The Netherlands
Andrea Marin University Ca’ Foscari of Venice, Italy
Don McNickle University of Canterbury, New Zealand
Panayotis Mertikopoulos Ecole Polytechnique, Paris, France
Yoni Nazarathy Swinburne University of Technology, Australia
Jos´e Nin˜o-Mora Universidad Carlos III de Madrid, Spain
Antonio Pacheco Instituto Superior Tecnico, Portugal
Balakrishna Prabhu Laas-CNRS, France
Matteo Sereno University of Turin, Italy
VIII Organization
Bruno Sericola INRIA Rennes - Bretagne Atlantique, France
Janos Sztrik Lajos Kossuth University, Hungary
Miklo´s Telek Budapest University of Technology, Hungary
Nigel Thomas University of Newcastle, UK
Corinne Touati INRIA Grenoble, France
Dietmar Tutsch University of Wuppertal, Germany
Kurt Tutschku University of Vienna, Austria
Benny van Houdt University of Antwerp, Belgium
Sabine Wittevrongel Ghent University, Belgium
Katinka Wolter Humboldt University of Berlin, Germany
Michele Zorzi University of Padova, Italy
Table of Contents
Queueing Systems I
QueueingSystemMAP/M/N asaModelofCallCenterwithCall-Back
Option ......................................................... 1
Chesoong Kim, Olga Dudina, Alexander Dudin, and Sergey Dudin
Two Way Communication Retrial Queues with Balanced Call
Blending........................................................ 16
Tuan Phung-Duc and Wouter Rogiest
Analysis of a Two-Class FCFS Queueing System with Interclass
Correlation...................................................... 32
Herwig Bruneel, Tom Maertens, Bart Steyaert, Dieter Claeys,
Dieter Fiems, and Joris Walraevens
The Virtual Waiting Time in a Finite-Buffer Queue with a Single
Vacation Policy.................................................. 47
Wojciech M. Kempa
Networking Applications
Analysis of Periodically Gated Vacation Model and Its Application to
IEEE 802.16 Network ............................................ 61
Zsolt Saffer, Sergey Andreev, and Yevgeni Koucheryavy
Combined CAC and Forced Handoff for Mobile Network
Performability................................................... 76
Idriss-Ismael Aouled and Hind Castel-Taleb
Modeling CSMA/CA in VANET................................... 91
Anh Tuan Giang and Anthony Busson
Consolidation and Replication of VMs Matching Performance
Objectives ...................................................... 106
Marco Gribaudo, Pietro Piazzolla, and Giuseppe Serazzi
Queueing Systems II
Analysis of a Discrete-Time Queue with Geometrically Distributed
Service Capacities................................................ 121
Herwig Bruneel, Joris Walraevens, Dieter Claeys, and
Sabine Wittevrongel
X Table of Contents
Perfect Sampling of Networks with Finite and Infinite Capacity
Queues ......................................................... 136
Ana Buˇsi´c, Bruno Gaujal, and Florence Perronnin
A Queueing Theoretic Approach to Decoupling Inventory ............. 150
Eline De Cuypere, Koen De Turck, and Dieter Fiems
Controlling Variability in Split-Merge Systems....................... 165
Iryna Tsimashenka, William Knottenbelt, and Peter Harrison
Markov Chains
Some Improvements for the Computation of the Steady-State
Distribution of a Markov Chain by Monotone Sequences of Vectors..... 178
Jean-Michel Fourneau and Franck Quessette
Mean-Field Analysis of Markov Models with Reward Feedback......... 193
Anton Stefanek, Richard A. Hayden, Mark Mac Gonagle, and
Jeremy T. Bradley
Lumping and Reversed Processes in Cooperating Automata ........... 212
Simonetta Balsamo, Gian-Luca Dei Rossi, and Andrea Marin
Transform-Domain Solutions of Poisson’s Equation with Applications
to the Asymptotic Variance ....................................... 227
Koen De Turck, Sofian De Clercq, Sabine Wittevrongel,
Herwig Bruneel, and Dieter Fiems
Stochastic Modelling
Analytical and Stochastic Modelling of Battery Cell Dynamics......... 240
Ingemar Kaj and Victorien Konan´e
Branching Processes,the Max-Plus Algebra and Network Calculus ..... 255
Eitan Altman and Dieter Fiems
Efficient Generation of PH-Distributed Random Variates.............. 271
Ga´bor Horva´th, Philipp Reinecke, Miklo´s Telek, and Katinka Wolter
Finding Prediction Limits for a Future Number of Failures in the
Prescribed Time Interval under Parametric Uncertainty............... 286
Nicholas Nechval, Maris Purgailis, Uldis Rozevskis, Inta Bruna, and
Konstantin Nechval
Author Index.................................................. 303
Queueing System MAP/M/N as a Model
of Call Center with Call-Back Option
Chesoong Kim1, Olga Dudina2, Alexander Dudin2,(cid:2), and Sergey Dudin2
1 Sangji University,Wonju,Kangwon, 220-702, Korea
2 Belarusian StateUniversity,4, Nezavisimosti Ave., Minsk, 220030, Belarus
[email protected], dudina [email protected],
[email protected], [email protected]
Abstract. A multi-server queueing system with a Markovian Arrival
Process (MAP), an infinite buffer and impatient customers useful in
modelingacallcenterwithacall-backoptionisinvestigated.Theservice
time of a customer by a server has an exponential distribution. If all
servers are busy at a customer arrival epoch, the customer may leave
the system forever or move to the buffer (such a customer is referred
to as a real customer), or, alternatively, request for call-back (such a
customer is referred to as a virtual customer). During a waiting period,
the real customer can be impatient and can leave the system without
the service or request for call-back (becomes a virtual customer). An
efficient algorithm for calculating the stationary probabilities of system
states is proposed. Some key performance measures are calculated. The
Laplace-Stieltjes transform of the sojourn time distribution for virtual
customers is derived.Some numerical results are presented.
Keywords: Call Center, Call-Back, Markovian Arrival Process, Multi-
ServerQueueing System.
1 Introduction
Acallcenterisacentralisedofficeusedbycompaniesforreceivingandservicing
their clients’ requests by telephone. The call centers are an integral part of the
companies whose activities are directly related to the contact with their cus-
tomers. Under increasing competition among the companies, customer’s service
is becoming increasingly important, so not only the image but also the profit of
thecompanydependsontheeffectiveoperationofitscallcenter.Theproblemof
the effective service of a large number of calls with minimal losses of customers
and minimal operating costs is of primary importance. This problem can be
successfully solved by means of informing the customers about the anticipated
delaysandprovidinga so calledcall-backoption. This means that the customer
whodoesnotwanttowaitonthelinehasanopportunitytoleavehis(her)phone
number and an operator of the call center will contact him (her) for the service
(cid:2) Corresponding author.
K.Al-Begain,D.Fiems,andJ.-M.Vincent(Eds.):ASMTA2012,LNCS7314,pp.1–15,2012.
(cid:2)c Springer-VerlagBerlinHeidelberg2012
