A.P. Shibanov – Dr.Sc.(Eng.), Professor, 

Department of Computer-Aided Design Systems, Ryazan State Radio Engineering University named after V.F. Utkin E-mail: apshibanov@yandex.ru

Anh Dung Nguyen – Post-graduate Student, 

Department of Computer-Aided Design Systems, Ryazan State Radio Engineering University named after V.F. Utkin E-mail: nguyendunganh1306@yandex.ru

Anh Minh Pham – Post-graduate Student, 

Department of Computer-Aided Design Systems, Ryazan State Radio Engineering University named after V.F. Utkin E-mail: phamanhminh231@gmail.com

The model of packet transmission over the telecommunication channel of communication with the implementation of control operations is considered. The execution time of control operations is set as a function of the random transmission time of the packet. To obtain the distribution of message transmission time, the theory of analytical functions of a complex variable is used. Estimates are given of the probabilitytime characteristics of systems with loss of value from information over time. An example of modeling of queuing systems M/G/1 is given.  The model describes the operations of packet transmission from the transmitter to the receiver and the random transmission time of short positive or negative receipts from the receiver to the transmitter. All control operations are functionally and linearly dependent on a random frame transmission time. Using the equivalent simplifying transformations method through the inversion formula, we find the distribution density of a random value of the message transmission time. The time taken to perform control, functionally related operations is taken into account. The transition to the analytic function in the left half-plane is performed. 

The probability density characterizes the transmission time of the packet stream over the communication channel. Among them there are packets for which a maximum permissible transmission time has been established and such packets can be discarded from the system. The distribution density is constructed provided that the packets do not exceed the maximum permissible value. If the random outcomes of interest to us fall into a given interval, then the ordinates of the conditional distribution density in this interval increase by the sum of the probabilities that a random variable falls into this interval. One can formulate the problem of constructing a conditional distribution density when only those outcomes are taken into account when the random variable exceeds the maximum permissible value. In practice, such a density can be used when the «late» packets are not destroyed, but processed according to special algorithms. The probability-time characteristics of mass service systems of the M/G/1 type are evaluated with a service device with operations depending on the functions of random variables. The quadratic coefficient of variation of the operating time of the serving device is found. After that, the average number of applications in the system, the average residence time of applications in the system, and the average time spent in the queue using functional dependencies between random variables are calculated. From the above material we can draw the following conclusions. The expressions obtained are convenient for further mathematical operations performed when analyzing the processes of information transfer taking into account the relationship of operations preceding, the work of channels in a group, researching systems with aging applications, taking into account actions to perform quality control of these operations.

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