Method for deriving the probability function and probability density of the duration of processing requests by an infocommunication system with parallel sequential uniformly distributed random durations of actions

Background. Improving the adequacy of mathematical models used in the design of infotelecommunication systems is due to the increased requirements for theoretical methods for designing modern automation tools. The object of the study is an analytical method for calculating the execution time of actions in the PERT stochastic network. The subject of the study is the method of analytical calculation of the duration of parallelsequential processing of a request by system elements with independent uniformly distributed random durations of actions. The purpose of the work is to improve the methods for calculating the probabilistic-temporal characteristics of infocommunication systems. Materials and methods. When deriving the probability distribution functions and the probability density of temporal characteristics, methods of probability theory were applied. Results. A scheme for deriving formulas for a small number of parallel and sequential actions for processing requests, as well as formulas for the probability and probability density functions of three parallel-sequential independent uniformly distributed random variables are given. Conclusions. The obtained analytical expressions for the duration values of parallelsequentially performed actions for data processing by the infocommunication system increase the adequacy of the assessment of its probabilistic-temporal characteristics