# Program for Stochastic Modeling and Applied Research of TechnologY

Welcome Coffee

#### presented by Alexander Rumyantsev

Welcome Coffee

09:00 - 09:30 311 Student's DayOpening

#### presented by Alexander Rumyantsev

Opening

09:30 - 10:00 311 Student's DayMarkov Decision Theory

#### presented by Rein Nobel

By using Markov Decision Theory (MDT) the optimal strategy is calculated for activating and switching off servers in a call centre, which is modelled as a retrial queue.

10:00 - 11:00 311 Student's DayCoffee Break 1 - 21

#### presented by Alexander Rumyantsev

Coffee Break 1 - 21

11:00 - 11:20 311 Student's DayPhase type distribution generated by a second order Markov Chain

#### presented by Achyutha Krishnamoorthy

The phase type distribution gives the time till absorption in a finite state space Markov chain with one absorbing state (or a set of absorbing states). The sojourn time and transitions among the states are governed by a semi-Markov process with sojourn time exponentially distributed. Thus it is generated by a Markov chain of order 1. Now consider a second order Markov chain on a finite stat...

more 11:20 - 12:20 311 Student's DayThree Levels of Stochastic Modeling

#### presented by Alexander Rumyantsev

In this short motivating presentation I will try to focus on a possibility to build a system of models which connect the general theory to applications.

12:20 - 12:50 311 Student's DayLunch Break 21

#### presented by Alexander Rumyantsev

Lunch Break

12:50 - 13:50 311 Student's DayVerification of the stability of a two-server queueing system with static priority

#### presented by Mariia

In this work, we explore the so called N-model, which consists of 2 servers and 2 classes of external customers, both generated by Poisson inputs. When server 1 is occupied and there are waiting customers in queue of the first server, then class-1 customer jumps to server 2. We consider a non-preemptive service priority: a class-1 customer starts service in server 2, when a class-2 customer fin...

more 13:50 - 14:10 311 Student's DayTasksBag Runtime estimation in a Desktop Grid

A mathematical model and software tool

#### presented by Valentina Litovchenko

Work is devoted to a set of tasks (tasksbag) runtime estimation in a Desktop Grid. We present a mathematical model of point prediction and confidence intervals calculation based on mean-square deviation minimization. An algorithm of runtime estimation including scaling and parameters adjust- ment is described. The notes on BOINC module implementation and perfor- mance optimization are give...

more 14:10 - 14:30 311 Student's DayLogistic regression: hyperparameters and cats.

Small talk about hyperparameters and how the influence on test and training error.

#### presented by Roman

Deep learning is an active field of research, so i decided to examine some subtleties in this domain. My task was to make a binary classfication network which would be able to distinguish cats from dogs in photos i had. I implemented a logistic regression model and tried out a few architectural decisions such as number of hidden units in different layers, number of these layers and activation f...

more 14:30 - 14:50 311 Student's DayDiscrete Time Queue in a Random Environment

#### presented by Rein Nobel

TBA

09:00 - 10:00 311 1. Stochastic Modeling and ApplicationsCoffee Break 1 - 22

#### presented by Alexander Rumyantsev

Coffee Break 1 - 22

10:00 - 10:20 311 1. Stochastic Modeling and ApplicationsEffectiveness of Stochastic Modeling

#### presented by Varghese C. Joshua

TBA

10:20 - 10:50 311 1. Stochastic Modeling and ApplicationsAnalysis of customer induced interruption and retrial of interrupted customers

#### presented by Varghese Jacob

We consider a single server retrial queue with infinite capacity of pri- mary buffer and finite capacity orbit to which customers arrive according to a Poisson process and the service time follows Phase type distribution. The customer induced interruption while in service occurs according to a Poisson process. The self interrupted customers enter into orbit. Any inter- rupted customer, fin...

more 10:50 - 11:10 311 1. Stochastic Modeling and ApplicationsPerformance analysis and stability of a multiclass system with constant retrial rates

#### presented by Evsey Morozov

We consider a single-server retrial model with many classes of customers. The arriving customers follow independent Poisson inputs and, a new customer meeting server busy may join the corresponding (class-dependent) orbit queue with a class-dependent probability. Otherwise, this (blocked) customer leaves the system. We consider constant retrial rate discipline, when only one (the oldest) or...

more 11:10 - 11:40 311 1. Stochastic Modeling and ApplicationsCoffee Break 2 - 22

#### presented by Alexander Rumyantsev

Coffee Break

11:40 - 12:00 311 1. Stochastic Modeling and ApplicationsA tandem queue with a specialist server operating with a vacation strategy

#### presented by Varghese C. Joshua

In the queueing system considered, service is provided at two stations, station 1 and station 2 operating in tandem. The station 1 is a multiserver station, where c identical exponential servers work in parallel. Station 2 is equipped with a single phase type server called specialist server. Customers arrive to the station 1 according to a Markovian Arrival Process. An arriving customer direct...

more 12:00 - 12:20 311 1. Stochastic Modeling and ApplicationsA game-theoretic approach to task scheduling for efficient search of diverse results in a Desktop Grid

#### presented by Natalia Nikitina

This work describes a congestion game model aimed at optimizing virtual screening process. In this game-theoretical mathematical model computing nodes act as players, and in the equilibrium situation the balance is reached between the results retrieval rate and the search space coverage. Experimental analysis shows that the scheduling algorithm based on the proposed model allows to adjust the r...

more 12:20 - 12:40 311 1. Stochastic Modeling and ApplicationsGame-theoretic model of a volunteer computing grid

Replication vs Intrusion

#### presented by Ilya A. Chernov

Volunteer computing has been used for solving important problems for a few decades and its potential is growing due to increasing number of computers and their growing performance. An important challenge is possible activity of adversaries who try to spoil the computing process on purpose by returning wrong answers. We propose a simple model of such a grid considered from the point of view of t...

more 12:40 - 13:00 311 1. Stochastic Modeling and ApplicationsLunch Break 22

#### presented by Alexander Rumyantsev

Lunch Break

13:00 - 14:00 311 1. Stochastic Modeling and ApplicationsStability analysis of the multiclass coupled orbits by simulation

#### presented by Taisia Morozova

In this work, we verify by simulation some recent theoretical results describing the dynamics of the the retrial system with coupled orbits. In such a system, retransmission rate of customers blocked in a virtual orbit depends in general on the binary state, busy or idle, of other orbits. We consider a system with N classes of customers, where an arriving customer which meets server busy, join...

more 14:00 - 14:20 311 1. Stochastic Modeling and ApplicationsOn the large deviation analysis of retrial models

#### presented by Ksenia Zhukova

We consider constant retrial rate model and focus on the probability that the orbit size of the system reaches a high level N within busy period. Under natural assumptions, it is shown that, as N increases, this probability has an exponential decay rate. We apply the regenerative technique to analyze large deviation. Simulation results are also included to demonstrate the accuracy of ...

more 14:20 - 14:40 311 1. Stochastic Modeling and ApplicationsVerification of stability of a general multiclass system with classical retrial rates by simulation

#### presented by Ruslana Nekrasova

We study K-class single server retrial queueing system with classical retrial policy. If new arrival of class i=1,..., K finds the server busy, it joins to i-th infinite capacity orbit and then retry to attack server after random delay. Each class of customers is characterized by its own set of parameters (input rate, service time and orbit rate). Note, that only source of instability of su...

more 14:40 - 15:00 311 1. Stochastic Modeling and ApplicationsAsympotic Properties of Discrete and Pice-wise Models of Additive Increse Multiplicative Decrese Algorithm

#### presented by Bogoiavlenskaia Olga

Random walks with additive increase and multiplicative decrease are widely used in the modern networking environments for distributed control of the communication parties activity. Thus Additive Increase Multiplicative Decrease algorithm implements the random walk to provide flow control at the Internet transport layer. Different variations of the algorithm are used by more than ten TCP protoco...

more 15:00 - 15:20 311 1. Stochastic Modeling and ApplicationsCoffee Break 3 - 22

#### presented by Alexander Rumyantsev

Coffee Break

15:20 - 15:40 311 1. Stochastic Modeling and ApplicationsOn the splitting method application for random walk crawling

#### presented by Alexandra Borodina

In this work it is proposed to apply the technique of the splitting method to accelerate a random walk to study characteristics in large graphs. In particular, we use this approach to estimate the probability of hitting a given node (or group of nodes) before returning to the starter node. Such an approach can have advantages if the estimated probabilities are small, and the period of return to...

more 15:40 - 16:00 311 1. Stochastic Modeling and ApplicationsPiecewise linear approximation of time series on the base of the Weierstrass-Mandelbrot function

#### presented by schegoleva

E.A.Pitukhin, L.V.Shchegoleva

The paper is devoted to the construction of the algorithm of piecewise linear approximation of time series, the distinctive feature of which is the preservation of sharp "peaks" and data outliers. As a basis, the iterative algorithm of piecewise linear approximation proposed by E. K. Bely in 1994 was taken. This algorithm was used to smooth the experimental medi...

more 16:00 - 16:20 311 1. Stochastic Modeling and ApplicationsThe Selection Problem in Distributed Computing Systems with Application to Internet Environments

#### presented by Dmitry Korzun

Components of a distributed system are subject to autonomous and cooperative activity within the system. To implement this activity, a component applies an individual strategy when some reasonable actions are selected based on the observed system state and other components' activity. In the Internet case, this selection problem widely accepts the multi-agents system approach from Artificial Int...

more 16:20 - 16:40 311 1. Stochastic Modeling and ApplicationsEstimation of MEMS Sensors Parameters Variations by the Batch

#### presented by Roman Voronov

Inertial MEMS sensors (accelerometers, gyroscopes, magnetometers) are used for real time motion analysis, orientation and trajectory estimation. Commercial-off-the-shelf sensors are cheap enough, however, not accurate. The main sources of errors are short term noises, bias instability and temperature dependence. In order to produce an industrial grade inertial measurement unit, MEMS senso...

more 16:40 - 17:00 311 1. Stochastic Modeling and ApplicationsSocial cost of deviation: new and old results on optimal customer behavior in queues

(Skype talk)

#### presented by Binyamin Oz

We revisit some of the classic optimization problems in single- and multi-server queueing systems. We look at these problems as strategic games, using the concept of social cost of deviation (SCoD), which is the extra cost associated with a customer who deviates from the socially prescribed strategy. In particular, we show that a necessary condition for a symmetric profile to be socially optima...

more 09:00 - 10:00 311 2. Game Theory in QueueingCognitive Wireless Radio Networks

#### presented by Garimella Rama Murthy

Cognitve Radio and Wireless Sensor Networks are proposed as technologies that will enable the deployment of Internet of Things ( IoT ). In this talk we will discuss Energy Efficient protocols utilized in such networks.

10:00 - 10:30 311 2. Game Theory in QueueingExistence of Nash Equilibrium of an M/M/1 queueing-inventory system

(Skype talk)

#### presented by Manikandan Rangaswamy

In this talk, we will be discuss about the behavior of customers in a single server queueing-inventory system for unobservable case, were the arrival process is according to a Poisson process; the service time is exponentially distributed and we restrict ourselves that the items in the inventory are homogeneous. We assume that customers individually decide on the issues such as "whether to queu...

more 10:30 - 11:00 311 2. Game Theory in QueueingThe advantages of different types of regenerations for multiserver systems simulation

#### presented by Irina Peshkova

TBA

13:30 - 13:50 311 2. Game Theory in QueueingThe problem of determining a rating level in the educational team

#### presented by Julia Dorofeeva

The report will consider a model of the dynamics of opinions in the team, among the participants of which there are two principals of influence. Team members can influence each other's opinions. The existence of consensus in the collective for several models of influence will be considered: when the collective is composed of several groups of participants with the same rating within each group,...

more 13:50 - 14:10 311 2. Game Theory in QueueingMatrix-analytical performance analysis of multiclass mixed orbit-queue

#### presented by Alexander Rumyantsev

In this paper we focus on a generalization of the so-called orbit-queue with constant retrial rate. We see a suitable generalization of the system structure which allows to obtain the solution for stationary system state probabilities explicitly.

14:10 - 14:30 311 2. Game Theory in QueueingTBA

#### presented by Oleg Lukashenko

TBA

14:30 - 14:50 311 2. Game Theory in Queueing