Model of a distributed information system solving tasks with the required probability

Abstract

Introduction: Distributed in space-time Networks: IIoT and IoT, fog and edge computing tend to penetrate into all spheres of human activity. Enterprises, government, law enforcement agencies, etc. depend on the quality of those technologies. Purpose: To determine the composition of the Network that provides the required uptime probability. Methods: According to the concept of structural and functional synthesis, a distributed Network is presented as an unstable queuing system in which servicing devices are connected and disconnected at an arbitrary point in time. A simulation model of the Network has been built. Results: The state of the Network depends on the number of devices and tasks, their performance and lifetimes. The model does not use these quantities themselves, but their ratios. The values of the uptime probability of the Network are calculated for all possible combinations of ratios. The confidence interval has been calculated with a confidence level of 0.95. From the data obtained, it is clear: 1) what should be the minimum composition of the Network in order to provide the required probability; 2) what probability the current composition of the Network can provide; 3) what flow of tasks is admissible in order to solve tasks with the required probability. It is shown that the dependence of the mean tasks residence time on the Network on the composition of the Network has two inflection points. Using information about these points, the Network Management System forms pools of devices or increases the number of devices. Discussion: It is assumed that the Net has a fully connected structure. Consequently, for practical application, it is necessary: to expand the model with an adjacency matrix describing the connections between nodes, and hence the paths of propagation of tasks over the Network or consider that each node is a relay and is capable of transmitting the task to any other node on the Network. Overhead costs arising from this are taken into account by adjusting the original data. Practical relevance: The results allow minimizing costs in the design and operation of distributed systems, maximizing the likelihood of system uptime under given constraints for resource.