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 Выпуск 98
- Nazarov A., Rindin A., Pakulova E., Turenova I., Moiseeva S. Scalar-vector recurrent algorithm for stationary probabilities in a heterogeneous system M/(M1, M2)/(N1,N2)/Inf/FIFO
This article proposes a generalized Erlang model with queue, the peculiarity of which is that two heterogeneous channels of finite volume and different service intensity are provided for data processing and transmission. When a message arrives, it first turns to a "faster" channel, if it has a sufficient number of channel resource units, then the message gets serviced. Otherwise, if there is not enough free service resource, the message is sent to the second "slow" channel. If it has a sufficient amount of free servise resource, then the message gets serviced. In the opposite case, the message gets into the queue. Messages in the queue have a lifetime, after which it makes no sense to transmit them. An original scalar-vector algorithm for calculating stationary probabilities of system states is proposed. The analysis of the characteristics of the quality of service is carried out. Namely, channel loading, average time spent in the system, the probability of instant service, the characteristics of service delays and the average number of service failures.
- Agasandyan G. Continuous VaR-Criterion and investor's optimal portfolio
The work continues studying problems of using the continuous VaR-criterion (CC?VaR) in financial markets. The application of CC?VaR in a collection of one two-dimensional and two one-dimensional theoretical markets that are partly mutually connected by their underliers is concerned. The construction of the combined portfolio that is founded on misbalance in returns relative between markets with maintaining optimality on CC?VaR is submitted. The optimal combined portfolio with three components is constructed from basis instruments of all markets. The feasibility of the solution obtained is based on ideas of randomizing portfolio composition. The complication of the object investigated motivates applying a special econometric approach that allows the full analytical description of the object convenient for computations is used. Unlike former authors works that solved the problem CB very fruitful for theoretical investigations, here the more ordinary problem CG with the given initial investment amount and risk preferences functions depended on scale parameter is solved. The parameter value and the regular combined portfolio that achieves the maximum of the average income with fulfilling the CC-VaR need to be found. The constructions suggested are tested by an example with beta-distributed characteristics of the problem. Also an idealistic version of the combine portfolio that allows plotting two-dimension diagram for incarnating an idea of combining portfolios of different dimensions is constructed.
- Morozov N. Generation of tasks for intelligent tutoring system based on abductive and deduction methods
With the rapid development of technology, computer learning is increasingly being integrated with artificial intelligence methods in order to develop more personalized educational systems. These systems are known as Intelligent Learning Systems (ITS). The possibility of using logical methods to expand the ITS functionality is considered. A method of automatic generation of exercises by means of deduction of the L language is proposed. A method of automatic generation of exercises according to a given specification by means of abduction of the L language is proposed.
- Sycheva A., Tolok A. Functional-voxel modeling of robot collision areas
The problem of avoiding collision between agents in motion constantly arises in multi-agent systems with decentralized control. As the number of moving agents increases, the amount of computation increases, which makes it difficult to adapt these algorithms for implementation on mobile platforms. The solution of this problem requires using simpler computational schemes and suitable models. The classical collision avoidance algorithm ORCA is based on mutual computation of half-planes of possible collision for each pair of agents, which is the most computationally expensive stage of the algorithm. The functional-voxel modelling will make it possible to store in graphical images the required local geometrical characteristics of the required geometrical region, as well as to perform most of the calculations in advance, thus simplifying the calculations and speeding up the algorithm. The paper presents a functional-voxel model of geometric region of possible collisions of agents by interpolation of the region's contour using Bezier curves. The local geometric modeling of B?zier curves is performed via a zero segment on the positive domain. A four-dimensional graphical model is proposed to simulate the dynamic case of the developed model. This model carries out the distribution of the results of static case modeling in space-time characteristics.
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