## Plenary and keynote speakers

**Larisa G. Afanasyeva **(Moscow State University, RUSSIA)

**Yury Belyaev **(Umeå Universit, Sweden)

**Alexander Bulinski **(Moscow State University, RUSSIA)

**Bulinskaya Ekaterina Vadimovna **(Moscow State University, RUSSIA)

**Guy Fayolle **(INRIA, France)

**Erol Gelenbe** (Imperial College, London)

**Eberhard Knobloch **(Technical University of Berlin)

**Dimitrios George Konstantinides** (Department of Mathematics, University of the Aegean, Greece)

**Nikolaos Limnios **(University of Technology Compiègne, France)

**Vladimir I. Lotov **(Sobolev Institute of Mathematics, Russia)

**Stanislav Molchanov** (Laboratory of Stochastic Analysis and its Applications)

**Gerardo Rubino** (INRIA, France)

**Konstantin Samouylov** (RUDN University, RUSSIA)

**Albert N. Shiryaev **(Moscow State University, RUSSIA)

**Nozer D. Singpurwalla **(City University of Hong Kong)

**Hermann Thorisson **(University of Iceland)

**Elena Yarovaya **(Moscow State University, RUSSIA)

**Andrey M. Zubkov **(Moscow State University, RUSSIA)

**Larisa G. Afanasyeva – Professor of Department of Mechanics and Mathematics of Moscow State University
**

**Title: **Asymptotic Analysis of Queueing models based on Synchronization Methods

**Abstract: **We consider a multichannel queueing system with a regenerative input flow and heterogeneous servers. An auxiliary stochastic flow is defined as the number of customers that can be served by the system if there are always customers for service. Under some natural conditions this process is also regenerative one and we construct the common points of the regeneration for the both processes. Then the traffic rate of the system is defined with the help of rates of these processes. The first result is the stability criterion for the broad class of queueing models. Note that stability analysis is an essential and challenging stage of investigation of a stochastic model, however stability conditions may be of an independent interest. Basing on the main stability result we obtain stability criterion for

queueing systems with interruptions of service and as corollary for priority queueing models. A separate class of multiserver models allows a single customer to be served by a number of servers simultaneously. Currently the increasing interest to study such systems is mainly motivated by their importance in the modeling of high performance clusters containing a huge number of servers working in parallel. The main contribution of this work is an extension of the stability criterion to the cluster model with a regenerative input flow and PH-distribution of the service time. We consider systems with independent service as well as systems with concurrent service. It follows from our results that the structure of the input flow does not affect on the stability condition, only the rate of this input flow plays role. But the distribution of the service time is very important since stability criterion is not defined by the mean of the service time. We also prove limit theorems in the heavy-traffic situation basing on the synchronization approach.

**Biography: **Afanaseva Larisa G. works at Moscow State University since 1977 till now. PhD “Ergodicity conditions for queueing systems with balking”in 1966, Dr. Phys. Math. Science (Habilitation) “Cyclic queueing systems and applications” in 1991.

**Belyaev Yury – Professor emeritus at Department of Mathematics and Mathematical Statistics, Umeå University
**

**Abstract: **We introduce a novel parametric approach to estimate the parameters of a two component mixture distribution. The method combines a grid-based approach with the method of moments and reparametrization. The grid approach enables the use of parallel computing and the method can easily be combined with resampling techniques. We derive a reparametrization for the mixture of two Weibull distributions, and apply the method on gene expression data from one gene and 408 ER+ cancer patients.

**Biography: **Graduated in 1951 from secondary (high) school with a gold medal. He received an award at the Olympiad in Physics organized by the Physics Faculty of Moscow State University (MSU). He studied at the Faculty of Mechanics and Mathematics of MSU from 1951 to 1956. From 1956 to 1959 he was an aspirant at the Steklov Mathematical Institute of Academy of Sciences. Andrei Nikolayevich Kolmogorov was his scientific supervisor. In 1960 he defended there his candidate dissertation and worked as a junior researcher at the Steklov Mathematical Institute. From 1958 to 1962 he also worked as a consultant in applications of operations and queuing theories. From the end of 1960 he was the head of Laboratory of Statistical Methods of MSU and in 1965 he became senior researcher in this laboratory. In 1970 he defended, at the Institute of Applied Mathematics of Academy of Sciences, dissertation for degree of Doctor in Physics and Mathematics Sciences. In 1971 he received the title of Professor in Mathematical Statistics. At the Laboratory of Statistical Methods in MSU he was the head of the Department Queuing Theory and Reliability. He participated in organization series of all-Soviet Union conferences devoted to the queuing theory and the theory of stochastic processes. He read lectures and consulted engineers at the Chamber of Reliability in the Moscow Polytechnic Museum. He organized seminars at the Laboratory of Statistical Methods, which were recommended for pre-defense of dissertations. He was repeatedly invited for collaboration abroad, including a position of full professor at the Humboldt University in Berlin and University of Otto von Guericke in Magdeburg. He was a member of the editorial boards of a number of journals. Now he is editorial board member in the journal “Informatics and Applications”, Russian Academy of Sciences (RAN). Since 1993 he is professor of Umea University, Sweden. For his research work in the field of reliability and quality control in mass production he received the state award of the USSR. He is an elected member of the International Institute of Statistics (ISI), member (fellow 1968) of the Institute of Mathematical Statistics (IMS).

**Areas of expertise: **His works relate to the theory of Gaussian processes and fields theory, statistical methods of empirical data analysis, informatics methods in estimating the distribution parameters and the accuracy of estimates with implementation of computer computation tools, and methods for mass production quality control. He obtained significant results in queuing and reliability theory, as well as in methods of planning and observed data processing.

**Alexander Bulinski ** – Dr. Sc. Phys-Math. (Habilitation), Professor at the Department of Probability Theory (Faculty of Mathematics and Mechanics of the Lomonosov Moscow State University)

**Title: **Asymptotic Methods and Limit Theorem

**Abstract:** The talk is devoted to problems related to asymptotic analysis of dependent functions constructed by means of arrays of independent observations. Such functions are employed in statistics, e.g., in the framework of regression analysis, and have a number of applications in medical and biological studies. A new version of the conditional central limit theorem is established and applied to data analysis. The feature selection problems are considered as well.

**Biography.** A.V.Bulinski graduated from the Faculty of Mathematics and Mechanics of the Lomonosov Moscow State University in 1974 with superior marks in all the disciplines. He was a PhD student of Professor A.N.Kolmogorov during 1974 – 1977. In 1977 he defended the PhD thesis and in 1990 the Doctor Sc. thesis (Habilitation). Since 1977 he works at the Faculty as Assistant Professor, Associate Professor and starting from 1994 as Full Professor of the Probability Theory Department. He is an author of more than 150 publications (among them 5 books). The textbook “Theory of Stochastic Processes” by A.V.Bulinski and A.N.Shiryaev (FIZMATLIT 2003, 2005) is included in the series “Classical University Textbook”. In 1998 A.V.Bulinski was awarded the State scholarship for eminent researchers, in 2000 – Diploma of the International Science Foundation for outstanding contributions to world science and education. In 2009 he was awarded the Lomonosov prize in science. Under his direction 15 PhD theses were written and 4 are in preparation. He delivered courses of lectures in France (Paris-6), Netherlands (TU Delft), UK (Heriot – Watt University), Germany (Ulm University) etc. He was a plenary and invited speaker at a number of International conferences and he was (and is) a member of the Program Committee of many International conferences, e.g., the European Meeting of Statisticians (Budapest, Hungary, 2013), 1st BRICS Mathematics conference (Beijing, China, 2017) etc. Since 2000 he is regularly elected as a member of the Board of the Moscow Mathematical Society. Member of the Expert Council for Higher Qualification Committee of Russia (since 2006). Head of the Federal Teaching Union on Mathematics and Mechanics in the Higher Education System of Russia (since 2015). He is a member of the Editorial Boards of 6 international mathematical journals.

**Areas of Expertise**. Limit theorems for stochastic processes and random fields. Stochastic geometry, development of the modern statistical methods of data analysis

**Bulinskaya Ekaterina Vadimovna – Professor of the Probability Department of the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University**

**Title: **Stability Problems in Modern Actuarial Sciences

**Biography: **After graduating from a high school with a gold medal she entered the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University and all her subsequent life is connected with MSU. Her scientific work has begun from the third study year under supervision of Professor Yu.V.Prokhorov (who became later the academician of the Academy of Sciences of the USSR). Her student work “On the mean number of crossings of a level by a stationary Gaussian process” was published in the journal Probability Theory and its Applications. The main result was included in the book by H. Cramer and M. Leadbetter “Stationary and Related Stochastic Processes” and called Bulinskaya’s theorem. Her PhD thesis “Some problems of optimal inventory control” was the first work on the mathematical inventory theory written in the Soviet Union. After graduation she was invited to work at the Department of Probability Theory as an assistant, then associate Professor and full Professor. Awarded the medal “For outstanding contribution to the mathematical theory of inventory” of the International Society for Inventory Research. She actively participated in the seminar chaired by academician of UkrSSR B. V. Gnedenko, Professor Y. K. Belyaev and Professor A. D. Soloviev. It is worth mentioning that B. V. Gnedenko and A. D. Solov’ev drew her attention to the similarity of the problems arising in the inventory theory, queuing theory and insurance. Therefore, since the introduction of the teaching of actuarial mathematics in 1993, E. V. Bulinskaya takes an active part in this process. On the recommendation of academician A. N. Shiryaev, who in 1996 organized at the Department of Probability Theory the specialization “actuarial-financial analyst”, she was on traineeship in France and in the UK through cooperation with the actuarial societies of these countries, made a presentation at the world Congress of actuaries in Birmingham in 1998. E. V. Bulinskaya is the author of three books on mathematical risk theory and reinsurance and more than 200 papers. She is a member of three scientific societies, participated in the program Committees of several international conferences, was sections organizer and the invited speaker. Conducts active research and pedagogical work, has a large number of students.

**Areas of expertise: **stochastic processes and limit theorems, inventory theory and actuarial mathematics

**Stanisław Domoradzki – University of Rzeszów, Poland**

**Title:** Mathematics in Lviv from the second half of 19th century till WWII

**Abstract:** В докладе будет представлен процесс развития математики и математического сообщества во Львове в период так называемой Галицкой автономии (1868 – 1918) – когда император Франц-Иосиф отдал образование и науку в Галиции в ведение Львовского Краевого Сейма. В частности, мы осветим деятельность математиков Львова, их большую приверженность науке, покажем важность их работы для повышения уровня математической культуры в Польше во второй половине девятнадцатого и начале двадцатого века. В результате во Львове была подготовлена почва для возникновения в 20-ых годах научной школы мирового значения – Львовской математической школы (В. Серпинский, Г. Штейнхауз, С. Банах, Ю. Шаудер, В. Орлич, С. Улам и др.). Одна из целей доклада – анализ основных направлений деятельности школы в контексте развития математики в ХХ веке.

Biography. Доморадзкий Станислав (Domoradzki Stanisław) родился в 1955 году, закончил Краковский университет. Автор нескольких монографий и многочисленных статей по истории математической мысли в польском научном сообществе в 19 – первой половине 20 века. Наиболее известны его исследования по зарождению львовского математического центра в первой трети 20-го столетия (С. Банах и др.). Профессор факультета математики и естествознания Жешовского университета (Rzeszów University, Faculty of Mathematicsand NaturalSciences, Rzeszów, Poland).

**Title:** Functional equations as an important analytic method in stochastic telecommunication systems and in combinatorics

**Abstract:** Functional equations arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to determine the probability generating function of some positive random vector in Z n +. Although the reader might be familiar with the situation n = 1, we quote first an interesting non local functional equation appearing in modelling a protocol for a muti-access broadcast channel. As for n = 2, starting from examples, we outline the theory which consists in reducing these linear functional equations of two complex variables to solutions of boundary value problems of Riemann-Hilbert-Carleman type, which are given in terms of closed form integrals. Sometimes it is also possible to determine the nature of the functions (e.g., rational, algebraic, holonomic). To conclude, we give some prospective remarks for n ≥ 3, since in this case no concrete theory exists.

**Biography:** He graduated from École Centrale (Lille 1967). Docteur-Ingénieur thesis (Univ. Paris VI, Dept. of Applied Maths., 1975). Doctorat d’État ès-Sciences Mathématiques (Univ. Paris VI, Dept. of Probability, 1979). He has been at INRIA since 1971, and project-team scientific leader from 1981 to 2007. Currently, he is Research Director Emeritus at INRIA, and Scientific Advisor at the Robotics Laboratory of Mines ParisTech. He gave regular lectures and courses on probability and stochastic modelling at several universities (Paris XI-Orsay, Paris VI) and High Schools (École Polytechnique, École Nationale Supérieure des Télécommunications). He co-organised about 10 International Conferences and Workshops. He authored and co-authored 2 books and more than 100 scientific papers.

**Areas of expertise:** Probability calculus and stochastic processes (Markov chains, ergodicity conditions, Lyapunov functions, random walks in an orthant), Analytic methods and Functional equations, Mathematical modelling of large systems, Statistical physics (propagation of chaos, scaling, exclusion processes, hydrodynamic limits, interplay between discrete and continuous description), Analytic combinatorics

**Erol Gelenbe – Imperial College, London**

**Title**: **“Product form solution of tightly coupled G-networks”**

**Biography**: Erol Gelenbe is the Dennis Gabor Professor in the Electrical and Electronic Engineering Department at Imperial College London. He is also a Member of the Scientific Council of the Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences. Known for

developing mathematical and simulation methods for the analysis and performance optimisation of computer systems and networks, Erol’s current interests concern the interaction of energy with computer systems and networks, including at the nanoscopic level regarding communications with spins, as well as deep learning with random neural networks. For his contributions to higher education and research, Erol was awarded Chevalier de la Legion d’Honneur by the French government, and Commander of Merit by the government of Italy.

He has been elected to Fellowship of the Royal Academy of Belgium, the Science Academies of Hungary, Poland and Turkey, and the National Academy of Technologies of France. He has received several scientific awards from France, the UK, and from ACM. He is a Fellow of both ACM and IEEE.

**Eberhard Knobloch **– Professor of History of Science and Technology at the Technical University of Berlin

**Title:** Leibniz’s contributions to financial and insurance mathematics

**Biography: **Prof. Dr. Eberhard Knobloch is a leading contemporary German historian of science and mathematics. From 1973 he was professor of mathematics at the College of Education in Berlin . In 1976 he qualified as a professor in Berlin and was a visiting scholar at Oxford, London and Edinburgh. Since 1976 he is head of the math sections of the Academy edition of the works of Gottfried Wilhelm Leibniz (and later the technical-scientific parts). In 1981 he became professor of history of science at the Technical University of Berlin (since 2002 academy professor); retiring in 2009. In 1984 he was a visiting professor at the Russian Academy of Sciences in Leningrad. Since 1999 he has been a regular guest professor at Northwestern Polytechnical University in Xian, China. He also was a visiting professor at the Ecole Normale Supérieure in Paris. He is a member of the International Academy of the History of Science in Paris (corresponding member since 1984, member since 1988, 2001 to 2005 as Vice President and later its president). Since 1996, a member of the Leopoldina, corresponding member of the Saxon Academy of Sciences, Member of Academia Scientiarum et Artium Europaea since 1997 and the Berlin-Brandenburg Academy of Sciences . From 2001 to 2005 he was president of the German National Committee for the History of Science. In 2006 he became president of the European Society for the History of Science.

**Areas of expertise: **History of mathematical sciences, of cosmologies; Probability theory, infinitesimal mathematics; Renaissance technology; Philosophy of mathematics; Alexander von Humboldt, Kepler, Leibniz; Jesuit science.

**Dimitrios George Konstantinides ** – Full Professor of Department of Mathematics, University of the Aegean, Greece

**Biography: **Dimitrios George Konstantinides, born 15.09.1958 in Thessaloniki, Greece, is a full Professor of Department of Mathematics, University of the Aegean since 2014. **His previous full-time positions are at Department of Sciences, Technical University of Crete: Assistant Professor with annual contract 1992 – 1998, at Department of Mathematics, University of the Aegean: Assistant Professor with annual contract 1998 – 2001. Department of Statistics and Actuarial Science, University of the Aegean: Lecturer 2001 – 2003, Assistant Professor 2003 – 2009, Associate Professor 2009 – 2014.**

Academic degrees: University of Athens: Dept. Mathematics, B.Sc., 1982, Kiev State University: Dept. Mechanics-Mathematics, M.Sc., 1984, Moscow State University: Dept. Mechanics-Mathematics, Ph.D., 1990. His supervisor at MSU was Professor A.D.Soloviev. Teaching experience: *Undergraduate level* – Probability Theory, Statistics, Stochastic Processes, Operation Research, Queuing Theory, Inventory Theory, Actuarial Mathematics, Financial Mathematics, Extreme Value Theory, Introduction to Insurance, Risk Theory, Modeling of Extremal Events, Life Insurance Mathematics, Macroeconomics. *Post graduate level – *Actuarial Mathematics, Theory of Extremal Events, Non-life Insurance Mathematics, Interest Rate and Bonds. 3 Doctoral students. Memberships in 5 professional organizations: Greek Statistical Institute, Greek Mathematical Society, Pythagorean Academy, Bernoulli Society, Bachelier Finance Society. He is the member of Organizing and Scientific Committees of well-known Conferences in Actuarial Science & Finance on Samos (next year 2018 there will be the 10th Conference), as well as, Participant of International conferences, among them World Congresses of Bachelier Finance Society, International Congresses on Insurance: Mathematics and Economics, ASMDA 2015 and 2009 and many others. D.Konstantinides is author of 11 books and 32 papers. Among his coauthors A.D.Soloviev, V.V.Kalashnikov, V.I.Piterbarg, G.Sh.Tsitsiashvili.

**Nikolaos Limnios **– Professor Classe Exceptionnelle at University of Technology Compiègne (UTC) Sorbonne University

**Title**: Discrete-Time Semi-Markov Random Evolutions: Asymptotics and Applications

**Abstract: ** This talk presents a study of discrete-time semi-Markov random evolution and study asymptotic properties, namely, averaging and diffusion approximation by martingale

weak convergence method. Applications given concern averaging and diffusion approximations for discrete-time dynamical systems and additive functionals. We also present some estimation problem.

**Biography: **Professor Classe Exceptionnelle at University of Technology Compiègne (UTC) Sorbonne University and Director of the Laboratoty of Applied Mathematics. He has obtained his diploma (1979) AUTh Greece, PhD (1983) and Doctorat d’Etat (1991) UTC France. He was appointed Maitre de conférences (1988) and Professor (1993) in UTC in the Laboratoty of Applied Mathematics. His research interest include stochastic processes and statistics with applications (reliability, statistical seismology, biology, etc.). He published more than 150 journal papers and several books in theory and applications of stochastic processes.

**Vladimir I. Lotov **– Head of Laboratory of Probability and Statistics, Sobolev Institute of Mathematics, Novosibirsk

**Title:** Factorization method in boundary crossing problems for random walks

**Abstract: **We demonstrate an analytical approach to a number of problems related to crossing linear boundaries by the trajectory of a random walk. Main results consist in finding explicit expressions and asymptotic expansions for distributions of various boundary functionals such as first exit time and overshoot, the crossing number of a strip, sojourn time, etc. The method includes several steps. We start with the identities containing Laplace transforms of joint distributions under study. The use of the Wiener-Hopf factorization is the main instrument to solve these identities. Thus we obtain explicit expressions for the Laplace transforms in terms of factorization components. It turns out that in many cases Laplace transforms are expressed through the special factorization operators which are of particular interest. We further discuss possibilities of exact expressions for these operators, analyze their analytic structure, and obtain asymptotic representations for them under the assumption that the boundaries tend to infinity. After that we invert Laplace transforms asymptotically to get limit theorems and asymptotic expansions, including complete asymptotic expansions.

**Biography:**Doctor of Science (1989) Steklov Mathematical Institute, Moscow. (Limit Theorems in Two-sided Boundary Crossing Problems for Random Walks).

Candidate of Science (PhD) (1977), Steklov Mathematical Institute, Moscow. (Asymptotic Expansions in Two-sided Boundary Crossing Problems for Random Walks: with B.A.Rogozin).

M.Sc. (1971), Novosibirsk State University. (Limit Properties of the Concentration Functions: with B.A.Rogozin)

Currently professor Vladimir Lotov is the head of the Laboratory of Probability and Statistics, Sobolev Institute of Mathematics, Novosibirsk, and Professor of Novosibirsk State University. Author of more than 100 pulications.

**Areas of expertise: **Boundary Crossing Problems for Random Walks and Stochastic Processes, Factorization Methods, Limit Theorems and Asymptotic Expansions for Distributions of Boundary Functionals; Sequential Analysis.

**Anatolii Mogulskii (Novosibirsk State University, Russia)**

**Title:** Integro-local limit theorems for multidimensional compound renewal processes

**Abstract:** Let (τ, ζ),(τ1, ζ1 ),(τ2, ζ2 ), · · · be a sequence of i.i.d. random vectors in R × R d , τ > 0, T0 := 0, Tn := Xn j=1 τj , Z0 := 0, Zn := Xn j=1 ζj ; η(t) := max{k ≥ 0 : Tk < t}, ν(t) := min{k ≥ 0 : Tk ≥ t}. The compound renewal processes Z(t), Y(t) for the sequence (τj , ζj ), j ≥ 1, are defined as Z(t) := Zη(t) , Y(t) := Zν(t) , t ≥ 0. Let the Cram´er moment condition for (τ, ζ) hold. For a vector x = (x(1), · · · , x(d)) ∈ R d put ∆[x) := [x(1), x(1) + ∆) × [x(2), x(2) + ∆) × · · · × [x(d) , x(d) + ∆), ∆ > 0. We establish the exact asymptotics for the probabilities P(Z(t) ∈ ∆[x)), P(Y(t) ∈ ∆[x)), as t → ∞ in the range of normal and large deviations. It is a joint work with E.I.Prokopenko.

**Biography:** Doctor of Science (1983), Candidate of Science (PhD, 1973), Graduated from Novosibirsk State University (1969). Anatolii Mogulskii is Top-level Research Fellow in Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics; Professor in Chair of Probability Theory and Mathematical Statistics, Novosibirsk State University. Author of more than 100 publications.

** Stanislav Molchanov – ** Laboratory of Stochastic Analysis and its Applications

**Title: **Central Limit Theorem of Turing’s Formula (joint work with *Zhang Zh., Zheng L.*)

**Biography: **Academic Supervisor Laboratory of Stochastic Analysis and its Applications.

EDUCATION:

1958-1963: Student, Mathematical and Mechanical faculty, Moscow State University, Master thesis “On one problem from the diffusion process theory.” Supervisor: Professor E. Dynkin (now a professor at Cornell University, USA).

1963-1966: Graduate student of the Department of Probability theory and Mathematical Statistics, MSU. Supervisor: Professor E. Dynkin.

1967: Ph.D. degree I (Candidate of Sciences) Title of thesis: “Some problems in the Martin boundary theory.”

1983: Ph.D degree II (Doctor of Sciences) Title of thesis: “Spectral theory of random operators.”

PROFESIONAL ACHIEVEMENTS AND EXPERIENCE:

Markov processes – geometrical approach (Martin boundaries, diffusion on the Riemannian

manifolds.

Spectral theory (localization in random media, spectral properties of the Riemannian manifolds)

Physical processes and fields in disordered structures (averaging, intermittency with applications to geophysics, astrophysics, oceanography).

Wave processes in periodic and random media, quantum graphs, applications to optics.

2012: Fellowship by AMS

**Michele Pagano (University of Pisa, Italy)**

**Title:** Network architectures evolution and teletraffic theory: general principles and open issues

**Abstract:** Teletraffic theory, based on traffic measurements and theoretical contributions by Agner Krarup Erlang, has played a major role in the development of public switched telephone networks. Indeed, Erlang B formula, which gives the (steady-state) probability that a trunk is not available as a function of the load and the number of trunks in a loss system, has been widely used for network dimensioning purposes.

Computer networks use a completely different architectural approach (packet switching instead of circuit switching) and a direct application of classical teletraffic results has led to a dramatic under-dimensioning of network resources and, as a reaction, to a marginal interest for mathematical results: “We believe in: rough consensus and running code” is frequently cited as the motto of the Internet engineering community.

Several traffic measurement campaigns highlighted that well-established assumptions, such as limited variability, Poisson nature of call arrivals, and exponential distribution of call holding times, must be substituted by new concepts, such as burstiness, long range dependence, and heavy tails.

The goal of this talk, addressed to non specialists in the field of computer networks, is to provides a heuristic justification for the need of such a “paradigm shift”, highlighting at the same time the limited analytical tractability of the corresponding traffic models.

**Biography:** Michele Pagano received laurea (cum laude) in Electronics Engineering in 1994 and a Ph.D. in Electronics Engineering in 1998, both from the University of Pisa. Since 2007, he is an associate professor at the Dipartimento di Ingegneria dell’Informazione of the University of Pisa, where he is the official lecturer of the courses of “Telematics”, “Performance of Multimedia Networks” and “Network Security”. His teaching experience includes tutorials and lectures on traffic modelling, rare event simulations, and anomaly detection, given in different countries (France, Poland, Russia and Uzbekistan).

His primary research interests are related to statistical characterization of traffic flows and network performance analysis. Performance evaluation has been carried through analytical approaches as well as by means of discrete event simulation. In the last years he extended his research interests to statistical traffic classification and network security issues (mainly in the framework of anomaly–based Intrusion Detection Systems), and to Green Networking (energy efficiency of current network devices and planning of energy-aware routing algorithms).

He has co-authored more than 200 papers published in international journals and presented in leading international conferences.

**Gerardo Rubino** – Senior Researcher at INRIA, France

**Title: **New results on the transient analysis of some fundamental queuing systems

**Abstract:** Understanding the transient behavior of queuing systems, or more generally, of resource sharing systems, is important in many application areas, where we want to control the system not only in equilibrium but also in its initial phase. With some exceptions pretty known in probability (such as the pure delay queue), known explicit closed-form expressions for the distributions associated with a queue at an arbitrary point in time needed some efforts to be derived, and these expressions are available only for a small number of models. In this talk, after reviewing the main results in the area, we will present some generalizations of an approach based on the Uniformization idea that can be applied on dynamical systems more general than queues. We will also explain how to perform other forms of analysis of queuing systems in their transient phases, again based in the same starting idea of considering the uniformized versions of the associated stochastic processes.

**Vladimir Rykov (RUDN University, and Gubkin Russian State University of Oil&Gas, Moscow, Russia)**

**Title:** Sensitivity analysis of renewable reliability systems

**Abstract:** Stability of different systems characteristics to the changes in initial states or exterior factors are the key problems in all natural sciences. For stochastic systems stability often means insensitivity or low sensitivity of their output characteristics to the shapes of some input distributions. One of the earliest results concerning insensitivity of systems’ characteristics to the shape of service time distribution has been obtained by [ B. Sevast’yanovAn Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals. Theory of Probability and its Applications ], who proved the insensitivity of Erlang formulas to the shape of service time distribution with fixed mean value for loss queueing systems with Poisson input flow. In [ I.N. Kovalenko.Investigations on Analysis of Complex Systems Reliability.] I.Kovalenko found the necessary and sufficient conditions for insensitivity of stationary reliability characteristics of redundant renewable system with exponential life time and general repair time distributions of its components to the shape of the latter. These conditions consist in sufficient amount of repairing facilities, i.e. in possibility of immediate start to repair any of failed element. The sufficiency of this condition for the case of general life and repair time distributions has been found in [ V. Rykov. Multidimensional Alternative Processes as Reliability Models. Modern Probabilistic Methods for Analysis of Telecommunication Networks ] with the help of multi-dimensional alternative processes theory. However, in the case of limited possibilities for restoration these results do not hold, as it was shown, for example, in [ D. Koenig, V. Rykov, D. Schtoyn. Queueing Theory. ] with the help of additional variable method. Moreover, in this case the problem of the reliability function calculation does not solved yet, and it is considered in the talk for the simplest case of double redundant hot standby system with only one repairman. On the other hand in series of work of B.V. Gnedenko, A.D. Solov’ev and others it was shown that under “quick” restoration the reliability characteristics become asymptotically insensitive to the shapes of their elements life and repair times distributions. In papers [V. Rykov, Tran Ahn Ngia. On sensitivity of systems reliability characteristics to the shape of their elements life and repair time distributions; V. Rykov, Tran Ahn Ngia. On sensitivity of systems reliability characteristics to the shape of their elements life and repair time distributions; Dmitry Efrosinin, Vladimir Rykov and Vladimir Vishnevskiy. Sensitivity of Reliability Models to the Shape of Life and Repair Time Distributions.] the problem of system’s steady state reliability characteristics sensitivity to the shape of life and repair time distributions of its components has been considered for the simple case of a cold standby double redundant system when one of the input distributions (either of life or repair time lengths) is exponential. For these models explicit expressions for stationary probabilities have been obtained which show their evident dependence on the non-exponential distributions in the form of their Laplace-Stiltjes transforms. At that the numerical investigations, proposed in [D.V. Kozyrev. Analysis of Asymptotic Behavior of Reliability Properties of Redundant Systems under the Fast Recovery; V. Rykov, D. Kozyrev. On sensitivity of steady state probabilities of a cold redundant system to the shape of life and repair times distributions of its elements. Submitted to the Proceedings of the Eights International Workshop on Simulation; V Rykov, D Kozyrev, E Zaripova. Modeling and simulation of reliability function of a homogeneous hot double redundant repairable system.] show that this dependence becomes vanishingly small under “quick” restoration also in the case, when both life and repair time distributions are non-exponential. The problem of the rate of convergence is enough complicated and does not enough investigated. In the paper of Kalashnikov [ V.V. Kalashnikov. Geometric Sums: Bounds for Rare Events with Applications: Risk Analysis, Reliability, Queueing. Dordrecht. ] the evaluation of the convergence rate has been done in terms of moments of appropriate distributions. The numerical investigation and simulation results, given in [V. Rykov, D. Kozyrev. On sensitivity of steady state probabilities of a cold redundant system to the shape of life and repair times distributions of its elements. Submitted to the Proceedings of the Eights International Workshop on Simulation; V Rykov, D Kozyrev, E Zaripova. Modeling and simulation of reliability function of a homogeneous hot double redundant repairable system.] demonstrate enough quick appearance of practical insensitivity of the time dependent as well as stationary reliability characteristics of the shapes of life and repair time distributions with fixed their mean values. In the talk the previous results will be extended for the case of heterogeneous double redundant standby renewable systems. The reliability function in terms of their Laplace transforms for the systems under consideration for the cases of full and partial restoration will be proposed. Explicit expressions for steady state and quasi stationary system state probabilities will be done and their asymptotic insensitivity to the shapes of life and repair times distributions under rare failures will be shown. The talk ends with conclusion and some problems description.

**Konstantin Samouylov – ** RUDN University

**Title: **Mathematical Modeling Issues in the Future Mobile Networks

**Biography: **Konstantin Samouylov received his Ph.D. from the Moscow State University and a Doctor of Sciences degree from the Moscow Technical University of Communications and Informatics. During 1985-1996 he held several positions at the Faculty of Science of the Peoples’ Friendship University of Russia where he became a head of Telecommunication System Department in 1996. Since 2014 he is a head of the Department of Applied Probability and Informatics. His current research interests are probability theory and theory of queuing systems, performance analysis of 4G/5G networks, teletraffic of triple play networks, and signaling networks planning. He is the author of more than 150 scientific and conference papers and six books.

**Abstract: **Over the past few years, there has been an increasing level of research activities worldwide to design and performance analysis for the future multiservice networks. The presentation outlines how mathematical models are being used to address current issues concerning quality of service and performance parameters of the modern and future networks. We shall show models based on the teletraffic and queuing theory and reflecting key features of admission control mechanisms in the future mobile network. There should be great opportunities for the scientific community to contribute to solution of these problems in the forthcoming decade.

**Albert N. Shiryaev **– Head of Department of Mechanics and Mathematics of Moscow State University

**Biography: **He graduated from the M.V. Lomonosov Moscow State University in 1957. From that time till now he has been working in Steklov Mathematical Institute. He earned his candidate degree in 1961 (Andrey Kolmogorov was his advisor) and a doctoral degree in 1967 for his work “On statistical sequential analysis”. He is a full professor at the department of mechanics and mathematics of Moscow State University, since 1971. He was elected a corresponding member of the Russian Academy of Sciences in 1997 and a full member in 2011. As of 2007 Shiryaev holds a 20% permanent professorial position at the School of Mathematics, University of Manchester.

**Areas of expertise:** Nonlinear theory of stationary stochastic processes, Problems of fast detection of random effects, Problems of optimal nonlinear filtration, stochastic differential equations, Problems of stochastic optimization, Problems of general stochastic theory and martingale theory, Problems of stochastic finance

**Nozer D. Singpurwalla **– Chair Professor of Risk Analysis and Management at the City University of Hong Kong

**Title:** Subjective Probability: Its Axioms and Operationalization

**Biography:** Nozer D. Singpurwalla is an Emeritus Professor of Statistics and Distinguished Research Professor at the George Washington University in Washington, D.C. He has been Visiting Professor at Carnegie-Mellon University, Stanford University, the Universityof Florida at Tallahassee, the University of California at Berkeley, the Santa Fe Institute and Oxford University (UK). During Fall 1991, he was the first C. C. Garvin Visiting Endowed Professor in the Mathematical Sciences at the Virginia Polytechnic Institute and State University. He is Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the American Association for the Advancement of Science, and he is an elected member of the International Statistical Institute. He is the 1984 recipient of the U.S. Army’s S. S. Wilks Award for Contributions to Statistical Methodologies in Army Research, Development and Testing, and the first recipient of The George Washington University’s Oscar and Shoshana Trachtenberg Prize for Faculty Scholarship. He has coauthored two books in reliability and has published over 175 papers on reliability theory, warranties, failure data analysis, Bayesian statistical inference, dynamic models and time series analysis, quality control and statistical aspects of software engineering. In 1993 he was selected by the National Science Foundation, the American Statistical Association and the National Institute of Standards and Technology as the ASA/NIST/NSF Senior Research Fellow. In 1993 he was awarded a Rockefeller Foundation Grant as a Scholar in Residence at the Bellagio, Italy Center.

**Areas of expertise: **Bayesian statistics, Reliability, Life testing, Risk analysis, Time series, Quality control.

**Hermann Thorisson – Professor, Department of Mathematics, University of Iceland**

**Title: **On Coupling and Convergence in Density and in Distribution

**Abstract:** According to the Skorohod representation theorem, convergence in distribution to a limit in a separable set is equivalent to the existence of a coupling with elements converging a.s. in the metric. A density analogue of this theorem says that a sequence of probability densities on a general measurable space has a probability density as a pointwise lower limit if and only if there exists a coupling with elements converging a.s. in the discrete metric. In this talk the discrete-metric theorem is extended to stochastic processes considered in a widening time window. The extension is then used to prove the Skorohod representation theorem.

**Biography:**Ph.D. from the Department of Mathematics, University of Göteborg, in 1981. Worked at the University of Göteborg, at Chalmers University of Technology, and at Stanford University, until returning home in 1990 to become a research professor at the Science Institute, University of Iceland.

Professor at the Department of Mathematics, University of Iceland, from 2004. Author of the book “Coupling, Stationarity, and Regeneration” (2000) and of more than 40 publications in the leading journals in probability theory.

**Areas of expertise: **Coupling, Stationarity, Regeneration, Markov Chains, Palm theory, Ergodicity.

**Vladimir Vatutin (Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia)**

**Title:** Branching Processes in Random Environment

**Abstract:** The talk presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID (independent and identically distributed) random environments. This is a natural generalization of the time inhomogeneous branching processes. The key assumptions of the family of population models in question are: non-overlapping generations, discrete time.

**Biography:** Graduated from the Faculty of Mechanics and Mathematics of the Moscow Lomonosov State University in 1974. A Phd student of the Steklov Mathematical Institute of the Academy of Sciences of the USSR from 1974 till 1977. From 1977 till now a researcher of the Steklov Mathematical Institute of the Academy of Sciences of the USSR and the Russian Academy of Sciences. Defended the PhD dissertation “Limit theorems for branching processes” in 1977 (the superwiser B.A.Sevastyanov). Has a doctor degree in mathematics (“Critical branching processes with regularly varying generating functions” (defended in 1987). Vatutin has got in 1988 an award of the Academy of Sciences of the USSR for important results in mathematics.

A member of the Editorial Board of the journals “Theory of Probability and its Applications”; “Markov processes and related fields”; “Discrete Mathematics and Applications”; “Pliska Studia Mathematica Bulgarica”.

**Elena Yarovaya **– Professor of the Probability Department of the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University (MSU, Russia)

**Title**: Survival Analysis and Recurrence Criteria for Branching Random Walks

**Abstract: **The models of symmetric continuous-time branching random walks on a multidimensional lattice with a few sources of particle birth and death are studied. Emphasis is made on the survival analysis and study of branching random walk properties depending on the configuration of the sources and their intensities. In particular, we will try to describe how the properties of a branching random walk depend on such characteristics of an underlying branching walk as finiteness or infiniteness of the variance of jumps. The presented results are based on Green’s functions representations of transition probabilities of a branching random walk.

**Andrey M. Zubkov **– Head of Department of mathematical statistics and stochastic processes** **of Moscow State University

**Title**: On the life and scientific activity of A.D. Soloviev

**Biography: **Andrey M. Zubkov graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University in 1970 (department of probability theory). Ph.D. thesis was defended in 1972. D.Sci. thesis was defended in 1982.

**Areas of expertise: **branching processes, limit theorems, combinatorics, Markov chains, extremal problems, statistics.