Question about Network Flow + Calculus
A research data center needs to transfer data to a remote backup facility during a 4‑hour maintenance window. The data transfer process is modeled as a directed network, where nodes represent logical components (functional stages) of the data transfer pipeline, and edges represent logical communication channels, with limited capacity. In this model, node A represents the point where data is generated in the primary data center. The intermediate nodes (B, C, D) represent functional stages of the transfer process, such as internal processing, aggregation, or interfaces to external networks. And the node E represents the logical destination where data is finally stored at the backup site. All edges have constant transmission capacity, except for one critical link, whose capacity varies over time due to shared usage with other services. The network is described as follows, with capacities measured in GB/hour: \( A→B: Capacity = 8 \) \( B→C: Capacity = 4 + 2sin(\frac{πt}{4}) \) \( C...