UDC 004.724
MATHEMATICAL MODELS OF PLANNING AN ORDERED SET
OF OPERATIONS FOR DISTRIBUTION OF HETEROGENEOUS
RESOURCES IN INDUSTRIAL TELECOMMUNICATION NETWORKS
D. A. Perepelkin, Dr. Sc. (Tech.), associate professor, Dean of FCE RSREU, Ryazan, Russia;
orcid.org/0000-0003-4775-5745, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. M. Pham, post-graduate student, RSREU, Ryazan, Russia;
orcid.org/0000-0002-3055-3568, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Currently, an urgent problem is the task of planning and distributing resources in industrial systems and
networks. The aim of the work is to develop mathematical models of planning an ordered set of operations
for distribution heterogeneous resources in industrial telecommunication networks. Several cases of connection
between operations and processes in industrial network are considered. Mathematical models to find the
probability of determining a pair of operations performed by one resource unit are proposed. A technique
for determining the probability of two operations using mathematical expectation value and the variance
of random variables according to the Chebyshev inequality has been developed. To calculate the number
of ordered sets of operations, the paper proposes to use the method of solving maximum flow problem. To
confirm the effectiveness of the proposed approaches, experiments were carried out in an industrial network
based on the GERT network model with several parallel processes. The results of the experiments performed
allow us to optimize the amount of allocated resources with a certain probability of process completion.
Key words: industrial telecommunications networks, heterogeneous resources, ordered set of operations,
distribution law, random variable, Chebyshev's inequality, maximum flow, GERT-network model.