This article examines the complex interaction between random processes in developing communication systems. As wired and wireless networks undergo radical changes and smart spaces become an integral part of our daily environment, under-standing processes' stochastic nature is paramount. The study examines the theoretical foundations of random processes, which link mathematical science and the unpredictable phenomena inherent in the development of modern networks. It ex-amines the fundamental characteristics, models, and representations of random processes and highlights their impact on the performance, adaptability, and effectiveness of IP-based wireless networks and smart spaces. Methodologically, the study uses mathematical models and analytical tools to determine the dynamics of random processes in each context. Understand-ing stochastic complexities, this study aims to provide practical recommendations to operators and stakeholders navigating an evolving communication system. In conclusion, the detailed study of random processes, offering a roadmap for the effi-cient operation of next-generation wired/wireless networks and smart spaces. The acquired knowledge contributes to the ongoing dialogue about adaptability and resilience necessary to meet the requirements of the modern communication envi-ronment.