Decentralized Flow Routing: A 4.0 Approach for Complex Operational Systems

Stochastic operational systems of high complexity frequently challenge the analytical and computational limits of static control approaches, especially in dynamic environments subject to constant demand fluctuations and resource degradation. This article proposes an investigative mathematical modeling for the heuristic control and optimization of entity flow, conceptually motivated by statistical thermodynamics and complex network theory. By mapping transient entities as discrete particles and processing capacities as discretized states at the edge, a directed acyclic graph representation is suggested to describe the system's occupation and transfer dynamics. The proposition of a local energetic cost operator (analogous to an operational Hamiltonian) is formulated, associated with the monitoring of Operational Entropy as an auxiliary indicator of uncertainty and the minimization of compound queue and physical risk costs—operationally translated as the mitigation of congestion and preventive bottleneck deviations. To enable adaptive decision-making, it is proposed that cost and transition equations be processed in a distributed manner by edge computing algorithms subject to hard admissibility constraints and atomic capacity reservation. It is suggested that this decentralized architecture can mitigate the impact of local perturbations before they cascade through the network, establishing a methodological proposition applicable from advanced manufacturing to flow management in highly complex services.