Multi-Commodity F N Reliability Evaluation with Multiple Constraints

Capacitated stochastic flow networks have applications in telecommunications, transportation, and supply chain management. They are designed to manage uncertain demand and supply, making them suitable for volatile environments. Evaluating their reliability involves understanding probability theory and network dynamics, assessing the probability of successful transmission from source to destination. Advanced mathematical models and simulations are used to estimate performance and reliability. The primary purpose of this paper is to evaluate multi-commodity flow network reliability with multiple constraints. I.e. Calculate the probability that the required amount of multiple commodities can be transported simultaneously through a stochastic flow network under budget and tolerable error rate constraints. Based on minimal paths the proposed formulation is used to identify all lower boundary points necessary for the requirements. Subsequently, system reliability can be computed using these lower boundary points. To show its validity and efficiency, the proposed formulation has been used to evaluate the reliability of multi-commodity four-node network with six arcs under error rate constraint. Then, evaluate the reliability of multi-commodity four-node, five-node, and six-node networks with budget and error rate constraints.