Introduction: A microservice architecture, which allows applications to be built as a set of independent microservices that work together to fulfill a common client request, has recently become the basis or even the standard for deploying complex systems that affect multiple physical structures and devices. In addition, the introduction of parallel service scenarios into such systems, especially in the case of high-load systems, makes it possible to increase their efficiency and performance. Purpose: To develop a mathematical model of distributed transactional applications with a microservice architecture and parallel nodes and to evaluate such a performance indicator as the average response time. Results: We present a mathematical model of distributed transactional applications with a microservice architecture in the form of a queueing network with sequential nodes, one of which has a parallel structure with several subnodes, the number of those is more than two. Based on the decomposition method for analyzing queueing networks, an approach to estimating the average response time of the system under consideration is proposed. We use known results for assessing individual nodes of a G/G/1 type network, as well as nodes with division and with parallel service. The results of the computational experiments allow drawing conclusions about the admissibility of the proposed approach, and obtaining recommendations regarding the applicability of various formulas for different load levels, in particular, for those whose average approximation error does not exceed 10%. Practical relevance: The proposed model and the method of its research can be used for the initial assessment and prediction of the average response time of transactional applications with parallel nodes at different load levels and, as a result, can contribute to maintaining the required quality of service for users of transactional applications.

We consider a set consisting of an arbitrary number of conservative systems of arbitrary orders. It is assumed that each of the systems admits a nondegenerate family of single-frequency periodic motions and the whole set of systems considered as one conservative system has the same property. We assume that oscillations of one period in each system have individual phase shifts. The problem of aggregating a coupled system with an attracting cycle is solved. We choose a leader conservative system, which becomes a closed-loop system through van der Pol dissipation-type feedback in order to implement an attracting cycle. The next (follower) conservative system is connected to the leader one through a unidirectional coupling control. Van der Pol dissipation is applied in such a way that the coupled system also has an attracting cycle. Further, each subsequent system joins the previous system: a chain of weakly coupled conservative systems with an attracting cycle is aggregated. In the chain, the previous system, as the leader, acts on the subsequent system, as the follower, through a unidirectional coupling control. The selected coupling controls are universal and can be applied to any conservative systems that satisfy the stated assumptions. A numerical example of the formation of a chain of three identical mathematical pendulums, which are aggregated by the proposed method into a chain of weakly coupled systems with an attracting cycle, is given.

A principle for measurement of the vibration force of a downhole tool based on the use of magnetoelastic characteristics of ferromagnetic materials is proposed. The features of the construction of sensitive elements in the form of inductive and mutually inductive converters of a desired physical parameter are presented. The errors are estimated with respect to optimal cable transmission of information signal. An ultrahigh-frequency approach for calculation of the vibrational force based on varactor frequency tuning is proposed. Aiming at an increase in the efficiency of the measurement of vibration force, several widespread bridge measuring circuits are analyzed with a choice depending on the requirements for measurement accuracy and range of the desired parameter.

The paper is concerned with developing a methodology to analyze complex-structured systems of control indicators within decarbonization projects. The proposed methodology is based on a formal description of control scenarios using system dynamics models, combined with methods of representation and processing of expert knowledge of causal relationships.

The statement and solution of problem of estimating the state, parameters, and fractional order of fractional dynamical systems are given. Extended and unscented fractional Kalman filters are presented. Illustrative examples of using the extended and unscented fractional order Kalman filters are given.