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 Âûïóñê 49
- Gorelov M. Games with costly information transfer
We consider a principal-agent model with information transfer about the agent’s choice, where the principal chooses information volume and contents. Information transfer and processing incurs costs influencing the payoff of the principal. We calculate the guaranteed payoff of the principal and build her optimal strategy.
- Gusev S. Identification algorithm for static object: transition from space of inputs-outputs to space of parameters estimates
We suggest an algorithm to identify a static control object with restrictions. We start with the case when the output measurement error leads to some probability of parameter estimates to leave the admissible set for all n-dimensional blocks. We then consider the case of large errors, when this probability is equal to zero. We study the connection between errors and probabilities using the Cramer formula.
- Rudko I. Stochastic model of harmonic series
We develop mathematical models for discrete components and harmonic series in an energy spectrum of rotating equipment and machinery noise emission. Using the theory of random functions we build a stochastic model of harmonic series, which is more realistic than existing heuristic models. The proposed stochastic model can be used in modeling and designing of detection devices narrowband signals, as well as in studying, modeling, and designing vibration damping devices.
- Smirnova N. Student’s psychological state model based on logs of his/her activity in a model-tracing intelligent tutoring system: construction experience
We employ machine learning techniques to develop a mathematical model, which predictsstudent’s psychological state basing on logs of his/her problem-solving activity in an intelligent teaching system.The suggested model can be extended to predict the state of a user of any information system, which stores user activity logs.
- Zakharov V., Krylatov A. Competitive routing of traffic navigation systems
We study a game-theoretic model of traffic flow assignment with multiple customer groups and a BPR-delay function on a network of parallel links. We prove existence of a unique Nash equilibrium in the game of m > 2 traffic navigation systems and provide closed-form expressions for equilibrium strategies. Finally, we show that under navigation systems’ competitions the average travel time between origin-destination areas increases.
- Stetsyura G., Chernyavskiy A. Organization of switched direct connections of active objects in complex digital systems
We suggest a routine for designing direct switching connections between a large number of digital message sources and receivers. Conflicts on a receiver input are being quickly removed. Elimination of connection refusals is hardware-efficient. It is shown that the scheme of direct switching connections can be implemented by virtue of optoelectronic equipment.
- Enaleev A. Optimal coordinated mechanisms in active systems and contract theory
The principal-agent model is considered, where the principal’s payoff depends on the monetary incentive she provides to the agent. We seek an optimal incentive scheme and prove that the, so-called, coordinated mechanisms are optimal for the principal. We also establish connection between the considered model and the adverse selection model in contact theory.
- Losev A., Maria R. Processing method of cost accounting and model of enterprise management
We suggest a descriptive and optimization model of medium-term planning and decision-making at an industrial enterprise. This model is studied for an enterprise employing processing method of cost accountingwith combined scheme of cost distribution over intermediate products. In particular, we establishthat profit function is linear with respect to the product mix.
- Sandomirskaia M. Game-theoretical dynamic insider trading model with non-zero bid-ask spread
We consider the model of multistage insider trading between two market agents for one-type risky assets. One of the players (the insider) has private information about the liquidation value of the asset. At each step of the bidding each player simultaneously proposes bid and ask prices for one share with fixed non-zero spread. The uninformed player uses history of insider’s moves to update his beliefs. For the unlimited duration bidding we construct upper and lower bounds of the guaranteed insider’s gain and the strategies of both players insuring these bounds. We also calculate insider’s loses in the case of disclosure of his private information.
- Gatsenko S., Mirzoyan G., Novochadov V., Shemonaev V., Shkarin V. Mathematical models for healthcare demand in regional markets (case of dental services)
We suggest mathematical models of healthcare demand on a regional market under price and quality competition. The models are identified using the data on dental services market in an industrial megalopolis.
- R. Gonchar D., G. Furugyan M., Shcherbakov M., Quang Vinh T. Efficient scheduling algorithms in multiprocessor real time systems
We study a task scheduling problem for real-time multiprocessor systems and consider the cases when (a) – jobs are pre-emptive and allow for processor switch, (b) – jobs are not pre-emptive and processor switch are prohibited, (c) – only a part of tasks are pre-emptive and allow for processor switch. We suggest a number of approximate algorithms, provide simulation results, and carry out comparative analysis of the developed algorithms.
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