ASSESSMENT OF THE STABILITY OF THE SERVICE CHARACTERISTICS IN THE INCREASE OF THE NUMBER OF DEVICES IN THE CONDITIONS OF A SELF-SIMULAR INPUT FLOW

Abstract

. This study investigates the performance of telecommunication systems operating under self-similar traffic conditions, which are characteristic of modern 4G/5G networks, cloud services, and Internet of Things (IoT) technologies. Unlike the traditional Poisson arrival process, real network traffic exhibits long-range dependence, resulting in correlated traffic bursts, significant increases in queue lengths, and service delays. The Hurst parameter (H) is employed to quantitatively characterize the degree of self-similarity and to evaluate the impact of the input traffic structure on the main Quality of Service (QoS) metrics. A comparative analysis of the M/M/n and Wb/M/n queuing models is performed for systems with different numbers of service channels (n = 1, 2, 3), where self-similar traffic is approximated using the Weibull distribution. Numerical simulations are conducted to evaluate the average queue length, average waiting time, average system residence time, and the average number of requests in the system for different values of the Hurst parameter and system utilization factor. The results demonstrate that increasing the Hurst parameter from 0.5 to 0.8 leads to an almost sixfold increase in the average residence time in a single-channel system, indicating its high sensitivity to self-similar traffic. It is shown that transitioning to multi-channel configurations significantly improves the stability of service characteristics and substantially mitigates the adverse effects of long-range dependence. In particular, for the three-channel system, the average waiting time is reduced by 53.7 times compared with the single-channel configuration under heavy traffic conditions, while the QoS metrics become practically invariant to changes in the traffic structure. The obtained results confirm that increasing the number of service channels is a more effective approach to ensuring the stability of telecommunication systems than improving the performance of individual service devices. The practical significance of the proposed approach lies in its applicability to the design, optimization, and adaptive resource management of modern telecommunication networks operating under self-similar traffic conditions.

Keywords: Queuing Systems, self-similar traffic, Hurst parameter, Weibull distribution, QoS, multi-channel systems.