The article presents a diffusion approximation model of a G/G/N/N station – N parallel servers without queueing. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is very rare in classical queueing models. Then we may consider input streams with general intera...

In this paper new error estimates for an explicit finite element method for numerically solving the so-called zero-diffusion unipolar model (a one-dimensional simplified version of the drift-diffusion semiconductor device equations) are obtained. The method, studied in a previous paper, combines a mixed finite element method using a continuous piecewise-linear approximation of the electric fiel...

Flexible stationary diffusion-type models are developed that can fit both the marginal distribution and the correlation structure found in many time series from e.g. finance and turbulence. Diffusion models with linear drift and a known and prespecified marginal distribution are studied, and the diffusion coefficients corresponding a large number of common probability distributions are found ex...

We explore the effects of element diffusion due to gravitational settling and thermal and chemical diffusion on the pulsational properties of DA white dwarfs. To this end, we employ an updated evolutionary code coupled with a pulsational, finite difference code for computing the linear, non-radial g-modes in the adiabatic approximation. We follow the evolution of a 0.55 M⊙ white dwarf model in ...

A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems. This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types h?/G/i/w.r (multidimensional Poisson input flow, one server with general service times, retrial system) a...

We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the Wasserstein Diffusion [27], assuming that Markov uniqueness holds for the generating Wasserstein Dirichlet form. The proof is based on the variational convergence of an associated sequence of Dirichlet forms in the generalized Mosco sense o...

The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the normalized difference between solutions of the original and the homogenized problems. The asymptotic behaviour of this difference depends crucially on the r...

Motivated by cascade effects arising in network technology upgrade processes in the Internet, Goldberg and Liu [SODA, 2013] recently introduced the following natural technology diffusion problem. Given a graph G = (V,E), and thresholds θ(v), for all v ∈ V . A vertex u activates if it is adjacent to a connected component of active nodes of size at least θ(v). The goal is to find a seed set A who...

Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an e...

In this paper we consider the solution of the fractional differential equations. In particular, we consider the numerical solution of the fractional one dimensional diffusion-wave equation. Some improvements of computational algorithms are suggested. The considerations have been illustrated by examples.