# B. Huseynov, Kh. Babazadeh ABOUT ONE PROBLEM OF OPTIMAL CHANNEL DISTRIBUTION

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## B. Huseynov, Kh. Babazadeh ABOUT ONE PROBLEM OF OPTIMAL CHANNEL DISTRIBUTION

In the paper the following task was studied.

Channel number ki N , i{1,…,n} of stations A i , xi N is given, is channel request number on A i, ri N is reject number on A i

Distribute K=ki channels between A i so that  ri rjmin, rimin

A program solving the problem in case when time and dynamics are not considered was worked out and is presented. Furthermore it was tried to expand it onto case which includes time consideration. Here period of time T was divided to s time intervals T =j

xij) is defined as channel request number on A i during interval j, rij) as reject number on A i during interval j, bi j) as busy channel number on A i at the beginning of j

xi = xij) - total channel request number on A i

ri = rij) - total reject number on A i

x i = xij)+ bij) total channel request number on A i during interval j

i =max{ xij)| j=1,…,s}

i = max{ rij) | j=1,…,s}

Note that if a channel was busy just a part of interval j and then was released in this case we consider the channel busy during all interval j

Remark: In reality data which is known are xi , ri , ki but xij), rij), bi j) are not given. Instead of this average channel busy time i is given for each station and load li of each station during time T. So it is nesessary to find relation between the data we use and the data given in reality.

## M. K. Hasanov, N. E. Huseynov, M. A. Mammadov, J. M. Rasulov CHANNELS CONTROL SETTING IN TRANSFERRING SYSTEMS

It’s well known that for transferring, receiving and reprocession of different kind of increasing information in the network link, link setting – photon technology, which is one of the modern technologies, is used.

The photon technology is already applied to the different spheres of network link, link lines, settings of receiving and transferring, switch equipment and other settings.

In such settings for the photon flux control (optical rays) – direction choosing, switching, subscribes dispatching, channels transferring, different methods and elements are used. One of these elements are piezoelectromechanotron – optic conductors.

In the current work piezoelectromechanotron – optic channels control, analysis of other setting advantages and the method of investigation were shown. Basing on the method of work of piezoelectromechanotron – optic channel control, which was founded by us, piezoeffect and optic laws, the optimal variant of optical link channel control was chosen. On the basis of dynamic analogy methods and equivalent circuit, the mathematical model of piezoelectromechanotron – optic setting was assigned and installed. Besides it, the phsycomechanical characteristics of piezoelectromechanotron – optic settings were installed and the analysis of difference between the held experiment and the above-mentioned characteristics was done.

This newest setting may be widely used in the optical link system, computing systems and optical channels control system.

## M.A.Kokurina, Y.S.Fedosenko, A.V.Sheyanov ON BICRITERIAL OPTIMIZATION ALGORITHMS FOR INTERACTIVE MODELS OF PLANNING THE SERVICING OF OBJECTS FLOWS

Some problems in operative control of transport-technological processes in adequate mathematical production lead to extremal models of scheduling theory.

As example we can state empty tonnage dispatching for large-scale cargo processing device in regions of mass riverbed mining non-ore building materials on the rivers Kama, Belaya and upper Volga.

It is important that in the number of cases estimation of quality of management requires to model two criterions, taking into account accordingly such economic factors as working expenses and loss of potential profits. These criteria are independent and have linear form.

This report is devoted to consideration computing problems arising and to discussing the possible approaches to their solving.

1. Given flow Z = {z(1), z(2), …, z(n)} of objects to be serviced by processor P (single-stage processing). The objects servicing order is defined by schedule R nominated by decision-maker (DM). Processor can not service more one object simultaneously; service of each object is realized without interruptions.

The Object z(i) is characterized by integer parameters: – duration of service; – moment of arrival for servicing; ; , – linear coefficients of binary penalty Ш(R) = {ш1(R), ш2(R)} per time unit (servicing or waiting).

If on schedule R servicing the object z(i) is terminated at moment t+(R, i), then penalty Ш(R) components are equal to ш1(R) = a(i)(t+(R, i) - t(i)), ш2(R) = b(i)(t-(R, i) - t(i)) respectively.

Basing on the general philosophy of bicriterial problems stating, there is possible several approaches to minimization of penalty Ш(R), among them are following.

1. Building in criterion plane {ш1(R), ш2(R)} full totality of efficient points with the possibility of syntheses corresponding Pareto-optimal schedule for any efficient point.

2. Reducing of bicriterial problem to unicriterial one with different variants of decision synthesis.

In case 1. solution can be received as a result of applying recurrence correlations, built on base of bicriterial analogue of dynamic programming principle, or by generalized to bicriterial case branch and bound method .

In case 2. there are such approaches: a) dedication of main criterion and solving problem of its minimization provided that values of other criterions do not exceed threshold values; b) lexicographic ordering of the criterions; second criterion minimization is possible only after solving of extremal problem on first criterion; c) realization procedures of consequent concessions as modification of method of lexicographic sequencing; g) convolution of vector criterion.

With all stated approaches computational difficulty of solving algorithms is exponential on n, because it is known that problem of optimum schedule synthesis is NP-hard even in unicriterial case.

The report presents results of analysis of representative collection of numeric experiments on solving stated extremal problem. The solution process uses an interactive technology as primary mode. Also we should notice that for number of transport applications considered model could lead to multycriterial generalizations.