In this paper we study the problem of optimal controlling in a processor sharing (PS) M/M/2 queueing system with heterogeneous servers. The servers differ in the service intensities, operating and usage costs. The objective is to find the optimal policy to allocate the customers either to an idle or partially loaded server, or to the queue at each arrival and service completion epoch to minimize the long-run average cost per unit of time. We handle this optimization problem as Markov decision problem and study numerically structural properties of the optimal control policy. Using a policy-iteration algorithm we show that this policy for the current model is of threshold type. In this case the faster server handles customers with maximum capacity, while the number of simultaneously serviced customers at the slower server can be increased only when the number of waiting customers exceeds a certain threshold level. The data-sets generated by classic methodology of analyzing the controlled queues are used to explore predictions for optimal thresholds through artificial neural networks. The presented theoretical results are accompanied by heuristic solution and numerical examples.

One-dimensional problems of two-phase filtration of liquids (water and oil) in porous media are described by the Buckley–Leverett equations, the Darcy law, and the law of conservation of energy under certain initial and boundary conditions. In this paper, we propose an asymptotic method of constructing a solution of the problem and methods for resolution of singularities associated with shock waves that arise in the process. The method proposed is implemented numerically by using the Maple software.

Эта статья дает утвердительный ответ на известный вопрос нелинейного анализа о существовании непрерывного однозначного локального правого обратного к локально липшицеву отображению. Более того, мы получили гораздо больше общий результат, дающий условия существования непрерывного полулокального и глобального однозначного правого обратного отображения.

The development and application of smart technologies in various fields is increasing every year. Different monitoring systems and sensors generate a large amount of data sets which allows to solve various tasks on data prediction and classification. This paper deals with data sets generated by a new tree monitoring system Open image in new window which evaluates in particular the sap flow density flux describing water transport in trees. The main task consists in prediction of the values of this characteristic which reflects the tree life state based only on observable air temperature during the predictable time interval and subsequent classification of trees according to some prespecified classes. The Fourier series based model is used to fit the data sets with periodic patterns. The multivariate regression model defines the functional dependencies between sap flow density and temperature time series. The paper shows that Fourier coefficients can be successfully used as elements of the feature vectors required to solve different classification problems. Artificial multilayer neural networks are used as classifiers. The quality of the developed model for prediction and classification is verified by numerous numerical examples.

Energy saving and energy efficiency are one of the most important factors determining the effectiveness of activities in any industry. Raising their level requires the introduction of innovative projects in these areas. The article gives a brief description of the technology for creating a development management system created at ICS of RAS together with leading specialists in strategic management and considers the task of adapting this technology to a system for managing innovative activities in the field of energy efficiency and energy conservation. Six mathematical models are proposed that increase the efficiency of its application. The first three models describe methods for comprehensive assessment of the state of the program for the development of energy conservation and energy efficiency, taking into account the presence of multi-purpose and interdependent projects. The last three describe the methods of risk management, adjustments to the program and the formation of calendar plans for its implementation.