Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

asymptotic analysis

Contact problem for functionally graded orthotropic strip

Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed.

Application of queueing network models in insurance

The purpose of this paper is to study the issues of the functioning of insurance companies using the methods of the queueing networks theory. The introduction provides a brief overview of scientific publications in this area. In particular, research based on the use of Markov stochastic processes and queueing systems are considered. In the first section of the article, a closed exponential queueing network is proposed as a model for the process of processing insurance claims. A detailed description of the corresponding network model is given.

Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed.

On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals

In this paper, we consider a resource system with an unlimited resources and servers number, with parallel customers servicing, arriving at the system according to the MMPP. Using a combination of multidimensional dynamic screening methods and asymptotic analysis, it is proved that the joint asymptotic probability distribution of the total resource amounts converges to a bi-dimensional Gaussian distribution under conditions of increasing intensity of MMPP. The parameters of the asymptotic probability distribution are found.