Novel Path Counting-Based Method for Fractal Dimension Estimation of the Ultra-Dense Networks

Next-generation networks, including the Internet of Things (IoT), fifth-generation cellular systems (5G), and sixth-generation cellular systems (6G), suffer from the dramatic increase of the number of deployed devices. This puts high constraints and challenges on the design of such networks. Structural changing of the network is one of such challenges that affect the network performance, including the required quality of service (QoS). The fractal dimension (FD) is considered one of the main indicators used to represent the structure of the communication network. To this end, this work analyzes the FD of the network and its use for telecommunication networks investigation and planning. The cluster growing method for assessing the FD is introduced and analyzed. The article proposes a novel method for estimating the FD of a communication network, based on assessing the network's connectivity, by searching for the shortest routes Unlike the cluster growing method, the proposed method does not require multiple iterations, which reduces the number of calculations, and increases the stability of the results obtained. Thus, the proposed method requires less computational cost than the cluster growing method and achieves higher stability. The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks. The developed method is evaluated for two different network structures and compared with the cluster growing method. Results validate the developed method.