Mathematical models of structural connectivity for fixed and dynamic systems are considered. Ezary-Proshan and Polessky estimations are given for fixed systems while for dynamic systems these estimations are determined in the state space. Quality of state estimation under different connectivity of vector components of dynamic system nodes is analyzed. It is shown that Tchebotarev-Achaev basic model approaches the procedure of stochastic synchronization of states. The presence of connectivity in the network structures, such as infocommunication systems, provides the acquisition of properties for the reliability and survivability of networks. For fixed (invariable with time parameters) networks connection is displayed as connectivity matrix, which may have a binary structure or consist of quantitative data de-fining the level of the connection (probability, number of channels, distance, etc.). The co-efficient of connectivity or connectivity probability for such networks is found by the approximate methods of Ezary-Proschan, Polesski etc. For dynamic (with time-varying elements of connection) network connectivity values can be obtained through the current assessment of the state of connectivity for each node from all adjacent nodes. For real posteriori evaluation of connectivity it is appropriate to use the state-space model that allows us to characterize the dynamic systems as deterministic and stochastic. Practice has shown that the state of the process allows to use the methods of stochastic approximation under the condition of choosing the sampling rate. The analysis of multi-dimensional differential systems shows that the existence of connections between components of the system cannot have arbitrary values. A large number of connections leads to unstable regimes. In the other extreme case: under the absence of reciprocal connection the system loses its system properties (integrity, emergence). The connection between random processes improves accuracy (reduced values of a posterior variance) of the estimates of the components for these processes compared to that case when data of the process are independent.
Popovsky Vladimir Vladimirovich Models of structural coherence in telecommunication system // Проблеми телекомунікацій, Vol. 2013, Issue 2, 2013, pp. 3-11

The flow-based model of multicast routing in the telecommunications network is developed. The model is represented by a system of linear algebraic inequalities and equations of the network state. Model calculates a set of paths for multicast routing with a maximum bandwidth or a minimum number of hops. The model includes conditions to prevent a possible overload of network links.
Lemeshko, O.V. ; Arous, Kinan Mohamad. The flow-based model of multicast routing // Microwave and Telecommunication Technology (CriMiCo), 2013 23rd International Crimean Conference. - PP. 523-524.

A Design of flow-based model for MPLS Fast ReRoute is proposed in the paper. The model allows calculating two types of paths, i.e. primary and backup ones, for the same flow. Depending on the parameters of the model, different schemes of reservation such as link protection, node protection, or path protection, can be implemented. In the course of solving the problem of MPLS Fast Reroute the classical metric of primary and backup paths is minimized. The nonlinear restrictions, which are responsible for prevention of node, link or path intersection of primary and backup routes, are introduced in the structure of the model.
Lemeshko, O.V. ; Kozlova, H.V. ; Romanyuk, A.A. Flow-based model of fault-tolerant routing in MPLS-network // Microwave and Telecommunication Technology (CriMiCo), 2013 23rd International Crimean Conference. - PP. 509 - 510.

The paper describes a proposed flow model of load-balancing routing by two criteria for software defined network such as the coefficient of maximum link utilization, and the average multipath delay. The results of comparative analysis of solutions of the routing problem with proposed model against those of the previously known models have been presented.
Lemeshko, A.V.,; Vavenko, T.V. ; Goriunov, A.A. Design of model of load-balancing routing for software defined networks // Microwave and Telecommunication Technology (CriMiCo), 2013 23rd International Crimean Conference. - PP. 511 - 512.

Flow model for multipath routing with guaranteed the quality of service (QoS) is proposed. The model is based on the updated version of flow conservation law, which is taking into account the possible packet loss caused by buffer overflow at the network routers. The accounting such losses is related to revise conditions associated with the quality of service. By using tensor approach analytical boundary conditions were obtained. The conditions allow ensuring different parameters of the quality of service (rate, average delay and packet loss probability) at the same time. In addition, proposed model provides minimal value of average end-to-end packet delay where delays along all paths are same. As a result jitter caused by the multipath routing (difference between delays along different paths) is minimized. The developed conditions for QoS ensuring have invariant form which do not depend on the used at the interface. Changing the traffic models and/or packet servicing algorithm is related to a modification of the metric only within the same form of conditions.
Lemeshko O.V., Yevseyeva O.Yu., Garkusha S.V. A Tensor Model of Multipath Routing Based on Multiple QoS Metrics // 2013 International Siberian Conference on Control and Communications (SIBCON). Proceedings. – Krasnoyarsk: Siberian Federal University. Russia, Krasnoyarsk, September 12−13, 2013. IEEE Catalog Number: CFP13794-CDR. - P. 1-4.

Current approaches to slot allocation among data bursts in downlink of WiMAX technology were analyzed. As a result of the completed analysis drawbacks of known decisions were distinguished and basic requirements to the slot allocation problem among data bursts were formed. A mathematical model of slots allocation and data burst scheduling in the downlink of IEEE 802.16 standard is proposed. The proposed model is focused on the formation of one data packet in downlink for each subscriber station that minimizes the number of overhead information sent over the used frequency communication channel. The dependence of the amount of slots, forming one data packet from required transmission rate of a subscriber station and type of modulation and coding scheme were analyzed.
Lemeshko O., Garkusha S. Slot allocation model and data burst scheduling in downlink WiMax technology // Proceedings of IEEE XXXIII International Scientific Conference "Electronics and nanotechnology" (ELNANO), April 16-19, Kyiv, Ukraine, 2013. - PP. 455-459.

The article introduces a double index model of the distribution frequency channels in the multichannel multiradio wireless mesh-networking standard IEEE 802.11. The influence of stations territorial separation and technological characteristics of multiradio multichannel mesh networking upon the quality of the allocation of channels problem solution are analyzed.
Lemeshko, A. V.; Garkusha, S. V. ; Abed, Ahmed Hasan. Design and analysis of two-index model of frequency channels distribution in a multichannel mesh-network of IEEE 802.11 // Microwave and Telecommunication Technology (CriMiCo), 2012 22nd International Crimean Conference. - pp. 273 - 274.

The article introduces a two-index model of the distribution channels in the multiradio multichannel wireless mesh networking (MR-MC WMN) standard IEEE 802.11. The model describes the process of distribution channels in both homogeneous and in heterogeneous MR-MC WMN.
Lemeshko А., Garkusha S., Abed A.H. Two-index Mathematical Model of Channels Distribution in Multichannel Mesh Networks 802.11 // Modern Problems of Radio Engineering, Telecommunications and Computer Science. Proceedings of the international Conference TCSET’2012. – Lviv-Slavske, Ukraine, February 21-24, 2012: Publishing House of Lviv Polytechnic, 2012. – P. 279-280.

In this paper is offered the method of analysis of bifurcational properties of dynamic systems represented by differential equations on the example of model of TCP-session of data communication at the management by a length of queue with the use of mechanism of congestion avoidance the RED.
Lemeshko O.V., Starkova O.V., Merkulov М.V. Analysis of Bifurcational Properties of the Mechanism RED // Modern Problems of Radio Engineering, Telecommunications and Computer Science. Proceedings of the international Conference TCSET’2008. – Lviv-Slavsko: Publishing House of Lviv Polytechnic, 2008. – P. 513-514.