2020 № 3(48)

CONTENTS

1. Pagano M., Rodionov A., Sokolova 0., Tkachev K. Queuing Model of a Processing Node in Mobile Geo Monitoring Network             

2. Kuyantsev V. P. Development of a model and tools for network reliability analysis in conditions of using fuzzy data    

3. Vishnevsky V. M., Semenova О. V. Review on models of polling systems and their applications to telecommunication networks             

4. Khairetdinov M.S., Karavaev D.A., Yakimenko A. A., Morozov A. E. Reconstruction of Geophysical Models of Elastic Media Using Neural Nets            

M. Pagano, A. Rodionov*, O. Sokolova**, K. Tkachev**

University of Pisa, Italy
*Novosibirsk State University,630090, Novosibirsk, Russia
**Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

QUEUING MODEL OF A PROCESSING NODE IN MOBILE GEO MONITORING NETWORK

DOI: 10.24411/2073-0667-2020-10009

The article discusses a mathematical model of the data flow received by a processing center with a limited input buffer, receiving packets of the same type from a large number of independent sources. All sources send packets with the same frequency, and the initial moment (the moment when the first packet is sent) for each source is random in the first period. There is a probability of packet loss on the network, which is the same for all sources.

The model arose in connection with the task of collecting information on air pollution in cities using sensors located on city electric transport ears and serves to assess the parameters of the corresponding system: the volume of the receiving buffer depending on a given interval of sending packets or vice versa, determining such an interval with a known size of the receiving buffer. Both tasks arc solved based on the acceptable level of losses due to refusal to receive packets due to the lack of space in the receiving buffer.

The analytical model is built on the basis of LDT large deviation theory. The obtained analytical estimates were compared with the results of simulation experiments and showed good quality in terms of behavior when changing the model parameters.

Key words: queuing model, processing center, geomonitoring.

This research is supported by the grant of Novosibirsk State University.

Bibliographic reference:  Pagano M., Rodionov A., Sokolova 0., Tkachev K. Queuing Model of a Processing Node in Mobile Geo Monitoring Network //journal “Problems of informatics”. 2020, № 3. P.5-13. DOI: 10.24411/2073-0667-2020-10009

article

V. P. Kuyantsev

Novosibirsk State University, 630090, Novosibirsk, Russia

DEVELOPMENT OF A MODEL AND TOOLS FOR NETWORK RELIABILITY ANALYSIS IN CONDITIONS OF USING FUZZY DATA

DOI: 10.24411/2073-0667-2020-10010

The problem of calculation of network fuzzy reliability is discussed. The network is represented by a graph with absolutely reliable links and unreliable nodes. Obtaining of fuzzy network data and general approach to calculating reliability arc described. This paper proposes solution for the problem of calculating reliability of the single nodes and the whole network according to specified conditions.

Calculation of the network reliability is an important issue that often comes up during solving any problem that could appear in practice. Moreover, some information about the network often happens to be not quite clear or accurate. In this ease pure graph theory can not be applied for solving the problem. But the using of theory of fuzzy logic and its applications can help to describe such inaccurate data.

In current work the unreliable tree-structured graph is considered. It is assumed that the nodes of the graph arc unreliable and link arc absolutely reliable. The nodes of the graph represent some kind of devices which can be broken during their work. If the node is broken, it loses it’s electricity power supply and for some time it can still continue working using its own accumulator. The node becomes absolutely unreliable when it’s accumulator is discharged. The nodes arc connected by absolutely reliable wires which are used for power supply. Only the root node has power supply from the outer world. It is also assumed that except the root node all the rest nodes’ power supply depends on the state of their parent nodes: if the node is broken, it’s state from now depends on it’s accumulator, and the same is correct for all it’s child nodes.

It is assumed that if the node is broken, it will be repaired by some worker and there is approximate information about the time when repair is done. This information is assumed to be well dcscribable by triangle fuzzy number [1-2] since it is a convenient way to describe intervals with some one most feasible value. Also, the accumulator’s capacity is also considered as triangle fuzzy number since it can not be measured accurately in real life. Assuming that device need the same amount of energy at the every moment of time, we can represent the fuzzy time when accumulator is discharged. These factors are described in details in section 2.

Topology of the graph, fuzzy repair time and fuzzy discharge time is only information that used for calculating network reliability.

Since reliability of the node depends on its own state and the state of it’s parents, the calculation of the reliability consists of two parts: calculation of self-reliability of the node which based on information about repair time and accumulator discharge time and calculation of topologically dependent reliability which based on self-reliability of the current node and all the topological reliability of it’s all parent nodes.

The purpose of the current work is creating the mathematical model for calculating self reliability and the model that takes into account reliabilities of parent nodes. These models are described in sections 3 and 4. Described reliabilities are represented by triangle fuzzy numbers which possible values are bounded in [0,1]. Another purpose is calculating integral reliability for the whole network. Several approach for this issue are shown in section 5. Also current paper describes reducing the task of calculating reliability of a graph with unreliable nodes to the task with unreliable links which is more classic king of issue in reliability analysis [4-7].

Key words: reliability, network, fuzzy logic, fuzzy number, fuzzy reliability.

Bibliographic reference: Kuyantsev V. P. Development of a model and tools for network reliability analysis in conditions of using fuzzy data  //journal “Problems of informatics”. 2020, № 3. P.14-28. DOI: 10.24411/2073-0667-2020-10010

article

V. M. Vishnevsky, O.V. Semenova

Institute of Control Sciences of Russian Academy of Sciences 117997, Moscow, Russia

REVIEW ON MODELS OF POLLING SYSTEMS AND THEIR APPLICATIONS TO TELECOMMUNICATION NETWORKS

DOI: 10.24411/2073-0667-2020-10011

The paper provides an overview of studies on stochastic polling systems published in 2007 2019. Due to the applicability of the stochastic polling models, the researchers face new and more complicated polling models. Stochastic polling models arc effectively used for performance evaluation, design and optimization of the telecommunication systems and networks, transport systems and road management systems, traffic, production systems and inventory management systems. Polling systems arc queuing systems with multiple queues and a common server (or a multiple servers). Each queue has its own input of customers. Following to a certain rule, the server visits the queues and serves the customers. In the review, we separately discuss the results for two-queue systems as a special ease of polling systems. Then we discuss new and already known methods for polling system analysis including the mean value analysis and its application to the systems with heavy load to approximate the performance characteristics. We also present the results concerning the specifics in polling models: a polling order, service disciplines, methods to queue or to group arriving customers, and a feedback in polling systems. The new direction in the polling system models is investigation of how the customer service order within a queue affects the performance characteristics. The results on polling systems with correlated arrivals (MAP, BMAP, and the group Poisson arrivals simultaneously to all queues) arc also considered. Then we briefly present the results on multi-server and non-discrete polling systems (the continuous systems where the number of waiting places arc nondenumerable and the fluid polling models) arc briefly presented.

Key words: polling systems, polling order, queue service discipline, mean value analysis, probability generating function method, broadband wireless networks.

The research is supported by the Russian Foundation for Basic Research, project N 19-29-06043.

 

Bibliographic reference:  Vishnevsky V. M., Semenova О. V. Review on models of polling systems and their applications to telecommunication networks //journal “Problems of informatics”. 2020, № 3. P.29-59. DOI: 10.24411/2073-0667-2020-10011

article

M.S. Khairetdinov*’**, D. A. Karavaev*, A. A. Yakimenko*’**, A. E. Morozov**

*Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
**Novosibirsk State Technical University, 630073, Novosibirsk, Russia

RECONSTRUCTION OF GEOPHYSICAL MODELS OF ELASTIC MEDIA USING NEURAL NETS

DOI: 10.24411/2073-0667-2020-10012

The work is related to questions of the methodology of using neural networks for the restoration of inhomogeneities in elastic media, which arc primarily considered underground cavities. Such problems arise when detecting underground caverns in places of underground explosions, searching for various underground natural voids (grottoes, eaves, etc.), man-made underground structures. This also includes on-site inspection tasks related to locating hidden underground explosions at test sites in the interests of the Treaty on the General Prohibition of Nuclear Tests (CTBT).

Such studies arc relevant from an environmental point of view. In particular, this is due to the need to monitor the migration paths of environmentally harmful products of radioactive decay in places of underground nuclear tests.

The proposed work is a comprehensive study on the development of neural network architectures for solving the problems of reconstructing heterogeneities in a host geophysical environment based on the results of theoretical and field experiments. Variants of two different architectures of neural networks and their training on the series of results of numerical modeling were developed and investigated. Thus, the work shows the applicability of neural networks to solving the inverse problem of geophysics associated with restoring the geometry of cavernous objects in an clastic medium. In this paper, the cavity is considered as an oval-shaped object with its clastic parameters different from the surrounding medium. The architecture of the neural network was faced with the task of analyzing the sequence of two-dimensional images and their segmentation to restore the position and size of the cavity. Corresponding images of wave fields were obtained as a result of numerical calculations using the developed program for modeling seismic field on computing clusters of the Siberian Supercomputer Center SB RAS. In the result of simulation performed we obtain set of models and set of snapshots for different time intervals showing evolution of seismic waves generated from point source in presence of cavity inclusion. Such material serves as input data for neural network train process. We developed neural networks based on LSTM layer and U-Net architecture. To realize the model based on the LSTM layer, it was necessary develop a unit to encode information from each snapshot into a numerical vector. Such a vector can be transferred to the input of the recurrent layer. The learning process of such a model consists of two stages. First is to train image encoder. Second is to train model restorer from a sequence of numerical vectors obtained by encoder. To obtain encoder with high quality it was trained on the principle of auto-encoder. The structure of the simplest auto-encoder is presented in the paper. After autocoder is trained, its part can be used to encode the input data into a vector of smaller

dimension. Such part of the autocoder is called the encoder. The auto-encoder was assembled from convolution and pulling operations (encoder, first part), sweep and anpuling (decoder, second part). When working with U-Net architecture based neural net there is a problem of storing data in time from all input images. This was solved applying one encoder for all images. In the paper we perform a study to compare results and performance (working time) of neural networks work on models. We perform tests for a single model and ensemble of models on CPU and GPU computing devices. Experimental results shows that neural network based on LSMT-layer works faster than U-net based. However, neural network based on U-net showed results that are more accurate in reconstruction of shape of cavity inclusion.

Key words: parallel algorithm, neural net, elastic media, LSTM layer, U-Net architecture, geophysical model, model reconstruction.

The reported study was funded by RFBR according to the research project N 19-07-00170, 20-07-00861, project 0315-2019-0003 of ICM&MG SB RAS.

 

Bibliographic reference: Khairetdinov M.S., Karavaev D.A., Yakimenko A. A., Morozov A. E. Reconstruction of Geophysical Models of Elastic Media Using Neural Nets  //journal “Problems of informatics”. 2020, № 3. P.60-69. DOI: 10.24411/2073-0667-2020-10012

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