MATHEMATICAL MODEL OF THE LOAD BALANCING SYSTEM OF DPC SERVER CLUSTERS UNDER FRACTAL LOAD CONDITIONS - V. P. Mochalov; N. Yu. Bratchenko; I. S. Palkanov; E. V. Aliev (Современная наука и инновации, 2023)
A mathematical model of the system for distributing and balancing the load of servers of clusters of data processing centers (DPC) is proposed, which provides a solution to the problem of assessing its performance, taking into account the degree of workload. The performance of the proposed model and the verification of the results obtained were carried out by simulation. The characteristics of the average queue length, average delay, and packet loss probability were used as the main quality indicators. The mathematical apparatus for evaluating these quality indicators is the queuing theory. The load distribution and balancing system is presented as a multi-channel system with a limit on the length of the queue, which includes an unlimited buffer (disk memory) for all servers in the cluster, as well as input buffers of limited capacity for each server. The model is built taking into account the features of the network traffic of modern infocommunication networks, characterized by self-similarity properties, and each type of traffic (HTTP/TCP, HTTPS. SMTP/TCP, VoIP, FTP/TCP, IP, Ethernet, ATM) is described only by its characteristic distribution law as packet arrival intervals and protocol block lengths. To take into account the features of the self-similar network traffic entering the system, it is described by the fractal Brownian motion fBM/M/1/N and a special function that depends on the self-similarity coefficient H (Hurst coefficient). The presented model can also be used to study the characteristics of network traffic in order to prevent network congestion and minimize losses.