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A complex problem of communication network interconnected elements topology optimization

A topology of interconnected elements of communication network fragment (central and remote elements with distance from central element in certain interval) and justification of optimal interposition are the subject of the article. The optimal interposition of non-cetnral elements relatively to central element is that when the possible area of central element placement has the maximum square. This allows to maximize the indeterminacy of central element placement. As a fragment of the communication network, there are considered at first the radio center as a part of the receiving center (the Central element) and at second the transmitting radiocommunication means operating in different frequency ranges (the Other elements) taken from Central element to the given interval distances. Placing off the transmitting radio means outside the receiving center is performed in order to ensure electromagnetic compatibility at the receiving center. A theoretical approach to the problem of optimization of topology of interconnected elements of the communication network fragment is considered in order to increase the uncertainty of the location of the Central element at given intervals of distances of other elements from the Central. The direct and the reverse positioning of the Central and other elements within the topology of the network fragment is considered, taking into account the specified interval of change of their distances from the Central element. The methodology of the research is based on the application of the means of Set theory, Euclidean and Analytical geometry. From the points of placement of the Other elements, circles of two radii corresponding to the minimum and maximum of the predetermined values of their distances from the Central element are drawn, resulting in a total of the intersected rings, which the Central element of the communication network can be located within. The square of intersection area of the rings formed by positioning the Central element relative to other elements distanced from the Central is calculated. The analysis of the mutual arrangement of the circles on the plane formed in the process of mutual positioning of1the network elements, when calculating the area of their intersection, universal algorithms for the typical calculation of the area of intersection by the example of the three rings on the plane are presented. On this basis, the calculation and justified proposals for the optimal relative arrangement of the elements relative to the Central element in the network topology. Provisions and conclusions may be applied in planning of radio Center and Other elements placement on terrain.