This study employs an analytical approach to scrutinize the dynamics of network streaming phenomena, specifically the transfer processes of continuous and discrete traffic flows across n-dimensional network structures. Introducing an evolutionary differential system in a generalized framework, we establish a summable function as a generalized solution that satisfies a crucial integral identity. This reliance on generalized solutions enhances the precision in depicting the physical nature of transported flows and elucidates the study of dynamic processes within multidimensional network-like domains. Employing a mathematical model, we apply it to n-dimensional flows with distributed parameters in network models. Our approach leverages generalized solutions and the construction of a compact family of approximations within the chosen state space. The results shed light on fundamental challenges related to optimal control and stabilization of differential systems, encompassing those with delays. Furthermore, the study unveils optimal and sustainable energy delivery strategies for both short and long-term scenarios. Notably, utilizing a digital N-D logistics network with real-world data facilitates a thorough assessment of the environmental sustainability implications of energy resource transport operations. These findings underscore the system's efficacy in guiding policymakers toward formulating sustainable energy policies for a greener future.