Introduction: The amount of digital data is constantly growing as well as the need for its storage and processing for various purposes. To conduct data analysis, high-performance computing environments associated with parallelization methods, and, accordingly, dataintensive applications are used. The lack of quality tools for evaluating the effectiveness of the process of parallel data processing or tasks leads to excessive allocation of resources. Purpose: To develop mathematical models of data-intensive computing environments and methods for their performance analysis, i.e., for estimating the average system response time based on the data on system performance at the level of subtask solving. Results: We present a mathematical model of a parallel computing system in the form of a queueing system with parallel query processing on various architectures, including non-Poisson input flow and non-exponential service times. As a method for analyzing the average response time, we use a combination of simulation modeling with one of the machine learning methods (artificial neural networks). The effectiveness of the method is confirmed by numerical experiments and depends neither on the type of input flow, nor on the type of distribution of query service times, nor on the number of servers in the nodes of the system. The approximation error of the average response time does not exceed 10%, which makes it possible to optimize the generally accepted resource allocation, significantly reducing the amount of the resources. Practical relevance: The presented models and the method of their analysis can be used for efficient planning and allocation of resources for data-intensive systems.

The paper discusses estimation of the potential accuracy of navigation systems using various parameters of the Earth's magnetic field with the help of the Cramer-Rao bound. For a simple measurement error model, a formula that relates the navigation accuracy and the spatial derivatives of the magnetic field is derived. A spectral method for the continuation of the magnetic field to a higher altitude is described. Using the data of geophysical surveys, the potential accuracy of navigation is estimated at various altitudes and for both field-based and gradient-based navigation systems.

The article is devoted to algorithms developed for solving the problem of placement orthogonal polyhedrons of arbitrary dimension into a container. To describe all free areas of a container of complex geometric shape is applied the developed model of potential containers. Algorithms for constructing orthogonal polyhedrons and their subsequent placement are presented. The decomposition algorithm intended to reduce the number of orthogonal objects forming an orthogonal polyhedron is described in detail. The proposed placement algorithm is based on the application of intersection operations to obtain the areas of permissible placement of each considered object of complex geometric shape. Examples of packing sets of orthogonal polyhedrons and voxelized objects into containers of various geometric shapes are given. The effectiveness of application of all proposed algorithms is presented on an example of solving practical problems of rational placement of objects produced by 3D printing technology. The achieved layouts exceed the results obtained by the Sinter module of the software Materialise Magics both in speed and density.

The statement of the problem of adaptive estimation of the processes having disorders is presented in the paper. The traditional approach and the neural network approach are used to solve the task. In the first of them, a multi-alternative method based on the Kalman filter bank is used to solve the estimation problems. The alternative approach uses a bank of neural network algorithms. The example of adaptive estimation of processes with disorders is considered in relation to trajectory tracking of a maneuvering object.

The paper proposes a method for the synthesis of nonlinear systems invariant to the output variable, under the conditions of parametric and external perturbations, taking into account the constraints on phase variables and control. To solve the problem, the ideology of the block method using sat-functions as local feedback, and the disturbances observer on the sliding modes are applied.