“Informatics and Applications” scientific journal

Volume 3, Issue 3, 2009

Content   Abstract and Keywords   About Authors

MULTICHANNEL QUEUEING SYSTEM WITH REFUSALS OF SERVERS GROUPS.

• A. Pechinkin    IPI RAN. apechinkin@ipiran.ru
• I. Sokolov    IPI RAN. isokolov@ipiran.ru
• V. Chaplygin    IPI RAN. VasilyChaplygin@mail.ru

Abstract:    The multichannel queueing system SM/PH/n/r with unreliable servers and their group refusals is under consideration. The refusals and the restorations of servers groups occur with a constant intensity, the number of servers refusing simultaneously is a stochastic value, and customers with the interrupted servicing begin its servicing anew after server restoration. The methods are offered to calculate the stationary distribution of the number of the customers in the system under different variants of the functioning of the system.

Keywords:    multichannel queueing systems; unreliable servers; refusals and restorations of servers groups

ON THE LIMITING CHARACTERISTICS FOR M(t)/M(t)/S QUEUE WITH CATASTROPHES.

• A. I. Zeifman   Vologda State Pedagogical University, a_zeifman@mail.ru
• Ya.A. Satin   Vologda State Pedagogical University, yacovi@mail.ru
• A. V. Korotysheva   Vologda State Pedagogical University, a_korotysheva@mail.ru
• N.A. Tereshina   Vologda State Pedagogical University, nataliya_tereshi@mail.ru

Abstract:    An M(t)/M(t)/S queue with catastrophes is considered and it is supposed that the catastrophes rates depend on the length of the queue. Sufficient conditions for weak ergodicity of the respective queue-length process and the respective bounds are obtained. Some examples are also considered.

Keywords:    nonstationary Markovian queueing system; birth and death process with catastrophes; weak ergodicity; bounds; limiting characteristics; approximation

LARGE DEVIATION ASYMPTOTICS OF STATIONARY QUEUES.

• E. V.Morozov    Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences, emorozov@krc.karelia.ru

Abstract:    The paper is a survey of main asymptotic results playing an important role in the quality of service estimation (QoS) of stationary systems. The asymptotics of the probability that the workload/queue-size process with heavy tail exceeds an increasing level is considered. Similar results for the systems with Levy input process and light-tailed service time are given. The proofs are based on the methods of large deviations theory and illustrated in detail by theM/M/1 system. The asymptotics of the overflow probability within regeneration cycle is considered, including the multiserver systems. An asymptotic analysis of system with the long-range dependent input is discussed, with focus on fractional Brownian process. The ties between the long-range dependence of a queue-size process and the moment properties of the embedded process of the regenerations are discussed.

Keywords:    stationary queue; large deviation probabilities; asymptotic analysis; light-tailed distributions; fractional Brownian process; long-range dependent process; regeneration

TRAFFIC-LEVEL PROBABILITY MODEL FOR THE NETWORK CENTRIC SYSTEM

• V. Y. Borodakiy    National Research Nuclear University “MEPHI”, vladbor@inbox.ru

Abstract:      A network centric system model with datacenters serving subscribers’ requests for a data transfer is considered. Data flows, so called elastic traffic, are characterized by a class independent bandwidth requirement and have exponentially distributed size. Flow request arriving is modeled by a Poisson process and data flows are served in accordance with the processor sharing discipline. A single link probability model analysis is presented and the exact expression of the flow blocking probability is derived.

Keywords:    network centric system; elastic traffic; blocking probability; single link

AN APPROACH TO ACTUARIAL MODELING WITH QUASI-MONTE CARLO: SIMULATION OF RANDOM SUMS DEPENDING ON STOCHASTIC FACTORS.

• G. Temnov    Edgeworth Centre for Financial Mathematics, University College Cork, Ireland, g.temnov@ucc.ie
• S. Kucherenko    CPSE, Imperial College, London, UK, s.kucherenko@ic.ac.uk

Abstract:    The problem of estimating the characteristics of a random sum, when the number of summands is also random, is addressed. The considered case includes an additional stochastic factor: although the summed random variables come from a distribution of a known form, the parameters of this distribution are stochastic and can themselves be viewed as random variables (with known distributions). The Quasi-Monte-Carlo techniques are used to handle this problem and to analyze its efficiency relative to the regular Monte-Carlo simulation methods. The typical area of the application of the investigations is actuarial practice which often deals with random sums of financial losses. Besides actuarial applications, the proposed method may be useful in application to certain problems in informatics, related to the aggregation of heavy-tailed data.

Keywords:   actuarial modeling; quasi-Monte-Carlo simulation; random sums

ON STABILITY OF IMAGE RECONSTRUCTION IN THE PROBLEMS OF EMISSION TOMOGRAPHY.

• O. V. Shestakov    Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. LomonosovMoscow State University, oshestakov@cs.msu.su

Abstract:    This paper deals with the problem of reconstructing images from projections in emission tomography settings. Within the frames of given mathematical model, the closeness estimates are derived for reconstructed images when using finite number of projections.

Keywords:    emission tomography; Radon transform; projections; closeness estimates

ON PROBABILISTIC ASPECTS OF ERROR CORRECTION CODES WHEN THE NUMBER OF ERRORS IS A RANDOM SET.

• A.N. Chuprunov    Research Institute of Mathematics and Mechanics, Kazan State University, achuprunov@mail.ru
• B. I. Khamdeyev    Research Institute of Mathematics and Mechanics, Kazan State University, Khamdeyevbi@mail.ru

Abstract:    In the paper, n messages each containing N blocks are considered. Each block is encoded with some antinoise coding method, which can correct not more than q mistakes. Here, it is assumed that the number of mistakes lies

Keywords:    generalized allocation scheme; convergence almost sure; Hamming code

ON THE DISTRIBUTION OF PARTICLE SIZE UNDER FRACTURING.

• V.Y. Korolev    Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University; Institute of Informatics Problems, Russian Academy of Sciences

Abstract:    A new model for the distribution of particle size under fracturing with the account of nonconstant or random character of the intensity of the flow of impacts.Within the framework of thismodel, a criterion of the log-normality of the distribution under consideration is formulated and the class of possible distributions of particle size under fracturing is described. Along with many known models, this class contains scale mixtures of log-normal laws.

Keywords:    log-normal distribution; mixtures of normal distributions; compound Cox process

SOME ESTIMATES FOR CHARACTERISTIC FUNCTIONS WITH AN APPLICATION TO SHARPENING THE MISES INEQUALITY.

• I.G. Shevtsova   Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, ishevtsova@cs.msu.su

Abstract:   New estimates are constructed for characteristic functions of distributions with finite absolute moments of order 2 + b, 0 < b < 1. TheMises moment inequality for lattice distributions is also improved.

Keywords:    Fourier transform; characteristic function; symmetrization; convolution; lattice distribution; arithmetic distribution; span

ON THE POWER OF THE TESTS IN THE CASE OF GENERALIZED LAPLACE DISTRIBUTION.

• V.E. Bening    Faculty of Computational Mathematics and Cybernetics, M. V. LomonosovMoscow State University, bening@yandex.ru
• O.O. Lyamin    Faculty of Computational Mathematics and Cybernetics, M. V. LomonosovMoscow State University

Abstract:    In the paper, the formula for the normalized limit difference between the power of asymptotically most powerful test and that of a locally most powerful test in the case of the generalized Laplace distribution is obtained.

Keywords:    generalized Laplace or generalized double exponential distribution; power function; deficiency; asymptotic expansion