To solve problems of demand management in terms of smart energy systems (Smart grid), we need a mathematical model of active consumer decision-making. Existing models either do not consider important aspects of consumer behavior, or are too complex for use in multi-agent simulation. A mathematical model of an active consumer is proposed, based on which we formulate and solve the problem of optimization of electrical appliances and consumer equipment, as well as determine the loading conditions of self-generation, under which the consumer problem allows simple and effective solution. The proposed approach is illustrated by equipment optimization of a single household.

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.

To improve the reliability of data delivery, in Wi-Fi networks stations can reserve for their transmissions periodic time intervals of the same duration in which they are allowed to transmit, while adjacent stations do not have that right. Here there arises the problem of choosing the parameters of reserved intervals that would ensure quality of service requirements for transmitted data in the smallest possible amount of reserved channel time. We consider the data transmission process in periodic intervals with the block acknowledgement policy that lets us reduce the costs by acknowledgement the set of packets with a single service message. We propose a method for mathematical modeling of such a transmission.

In this paper we consider the NP-hard 1|rj|ΣTj scheduling problem, suggesting a polynomial algorithm to find its approximate solution with the guaranteed absolute error. The algorithm employs a metric introduced in the parameter space. In addition, we study the possible application of such an approach to other scheduling problems.

A model of informational control in network structures is analyzed. The result of informational control depends on the principal’s awareness and the influence levels of network structure elements (agents). Finally, the issue of beneficial network structures (from the principal’s viewpoint) is studied.

We give a survey of approaches for analyzing the sensitivity of non-dominated alternatives to changes in the parameters of partial quasi-orderings that define preferences. Such parameters can include values of importance coefficients for different criteria or boundaries of interval estimates of the degrees of superiority in the importance of some criteria over others, boundaries of intervals of criteria value tradeoffs uncertainty, and others.

Для передачи по mesh-сети потоковых данных, предъявляющих высокие требования к качеству обслуживания, удобно использовать описанный в стандарте IEEE 802.11s механизм MCCA детерминированного доступа к среде. При использовании этого механизма станции резервируют для своих передач определенные периодически повторяющиеся интервалы времени, тем самым получая бесконкурентный доступ к каналу связи.  Однако, чтобы обеспечить успешную доставку данных в условиях помех, необходимо устанавливать  дополнительные резервирования под повторные попытки передачи. В работе построена аналитическая модель процесса передачи неординарного потока по многошаговым беспроводным сетям с помощью механизма MCCA. Модель позволяет определить наибольший период резервирований, при котором выполнены требования на время доставки и долю потерянных пакетов. 

After a series of publications of T.E. O’Neil et al. (e.g. in 2010), dynamic programming seems to be the most promising way to solve knapsack problems. Some techniques are known to make dynamic programming algorithms (DPA) faster. One of them is the graphical method that deals with piecewise linear Bellman functions. For some problems, it was previously shown that the graphical algorithm has a smaller running time in comparison with the classical DPA and also some other advantages. In this paper, an exact graphical algorithm (GrA) and a fully polynomial-time approximation scheme based on it are presented for an investment optimization problem having the best known running time. The algorithms are based on new Bellman functional equations and a new way of implementing the GrA.

This paper describes a modified version of an algorithm suggested earlier by the authors for optimizing of ads allocation in sponsored search on the main page of search results in response to user search queries to a web search engine. It is demonstrated that the modification of the algorithm reduces appreciably the searching procedure and the algorithm complexity. And finally, the new algorithm undergoes experimental testing on real data sets provided by Yandex. © 2015, Pleiades Publishing, Ltd.

В работе предлагается вычислительно эффективный метод синтеза суб- оптимального анизотропийного регулятора для дискретных дескриптор- ных систем на основе методов выпуклой оптимизации. Приводятся чис- ленные примеры.

Показывается, что если предпочтения могут быть описаны аддитивной функцией ценности, то модели принятия решений, основанные на теории важности критериев, могут быть описаны с помощью неточных вероятностей. На основе этого анализируются новые подходы к принятию решений в теории важности критериев. 

For the process of order (1,1) spatial autoregression, the consistency and asymptotic normality of the sign estimate were established. The relative asymptotic efficiency of the sign estimate relative to least- squares estimate was calculated, and its behavior under various distributions of the renewing field was considered.

Using computer simulation and a study of the asymptotic distribution, we consider the relative efficiency of M-estimates for the coefficients of the threshold autoregressive equation with respect to the least squares and least absolute deviation  estimates. We assume that the updating sequence of the autoregressive equation can have Student’s, logistic, double exponential, normal, or contaminated normal distributions. We prove asymptotic normality of M-estimates with a convex loss function.

For the model of autoregression with a random coefficient, the estimate by the least absolute deviations (LAD) method was proved to be consistent and asymptotically normal. For the asymptotic relative efficiency of the estimate by the LAD method as compared to the least squares method, an analytical expression was obtained. For the case where the innovative field of the autoregression process has the Tukey distribution, consideration was given to the behavior of the relative asymptotic efficiency.