A maximum flow problem with intermediate node requirements

The conventional Maximum flow problem is modified to take account of possible requirements at intermediate nodes across which flow takes place. This is achieved by incorporating pseudo or priority arcs to act as thresholds controlling out-flow from the nodes and modifying the Ford and Fulkerson algorithm to take account of these thresholds. Effect of introducing these threshold-requirements at intermediate nodes on the final flow into the sink in the network is examined by some numerical examples.