Vol 78, No 8 (2017)

We give a brief survey of literature devoted to studying queueing systems with Markovian and batch Markovian arrival processes and their application to modeling telecommunication networks.

Consideration was given to the numerical solution of the problem of parametric identification of the processes obeying the parabolic equations using an example of the processes of underground oil filtration. The identified parameters belong to the given functional classes such as the piecewise constant and piecewise linear functions. In the problem, needed is not only to determine the values of the coefficients, but also to identify the constancy boundaries of the coefficients. For numerical solution of the problem, an approach was suggested based on reduction of the initial problem to that of finite-dimensional optimization with a special structure of constraints. Obtained were the formulas for the gradient of the objective functional in the discretized problem allowing one to apply the efficient methods of first-order optimization. The results of numerical experiments on the model problems were presented.

In control of diffusion processes a very useful instrument is the equation for optimal strategy and cost. For the version of infinite time horizon with time averaging this equation is much more complicated than for the version of finite time horizon, and even than for the version of infinite time horizon with discounting. In particular, the equation solution may be non-unique. This problem of non-uniqueness is researched in book of A. Arapostathis et al., 2012, for special models—near-monotone. The result received in the book is extended in the article to an important general case—models with restrictions in control which guarantee ergodicity of the process. Besides we correct the proofs from the book.

Consideration was given to planning the optimal evasion trajectory of a moving object from the system of observers consisting of a sensor and initial and terminal points of the route. An optimization criterion was proposed. The optimal trajectory and the speed mode of the moving object were determined for sector and ring—the two zones of search for the maneuvering search means.

We show that if preferences can be defined with an additive utility function then decision making models based on the theory of criteria importance can be defined with imprecise probabilities. With this idea, we analyze new approaches to decision making in the theory of criteria importance.

The present author continued his work on the study of the control parametrization technique for solution of the distributed optimization problems. Proposed was a new method of control parametrization resembling that for information compression used in the JPEG format to reduce by the factor of several times the count of parameters describing the control without an appreciable deterioration in closeness to the optimum. Withdrawn were formulas required for application of the proposed approach to control parametrization in combination with the numerical methods of finite-dimensional optimization for solution of the mathematical programming problem approximating the original optimal control problem. The results of numerical experiments were described and analyzed in detail.

This paper considers a model of opinion dynamics in a social network with two principals, in which the members may affect the opinions of each other and their opinions evolve according to a time-homogeneous Markov chain. We study the existence of a consensus in this network for two types of influence models, namely, when the principals may or may not affect the opinions of each other directly. In addition, we find the values of social network parameters under which a consensus is reached. For the cases without a consensus in its standard definition, we introduce the notion of a consensus of the majority and find the parameter values under which it is reached. Two numerical examples illustrate the obtained theoretical results.

This paper proposes mathematical models for the biocommunity species composition preservation problem. We construct equilibrium for the dynamical model describing the self-regulation of populations in a patch. For the model with the varying food attractivity of the patch, we design specimen removal control that allows to preserve the species composition.

We consider an optimal portfolio selection problem to track a riskless reference portfolio. Portfolio management strategies are compared taking into account the investor’s temporal preferences. We investigate stochastic optimality of the strategy that minimizes the expected long-run cost, deriving an asymptotical upper (almost sure) estimate for the difference between the values of the objective functional corresponding to the optimal strategy and for any admissible control.

Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.