The Throughput Flow Constraint Theorem and its Applications

The paper states and proves an important result related to the theory of flow networks with disturbed flows:“the throughput flow constraint in any network is always equal to the throughput flow constraint in its dual network”. After the failure or congestion of several edges in the network, the throughput flow constraint theorem provides the basis of a very efficient algorithm for determining the edge flows which correspond to the optimal throughput flow from sources to destinations which is the throughput flow achieved with the smallest amount of generation shedding from the sources. In the case where a failure of an edge causes a loss of the entire flow through the edge, the throughput flow constraint theorem permits the calculation of the new maximum throughput flow to be done in time, where m is the number of edges in the network.In this case, the new maximum throughput flow is calculated by inspecting the network only locally, in the vicinity of the failed edge, without inspecting the rest of the network. The superior average running time of the presented algorithm, makes it particularly suitable for decongesting overloaded transmission links of telecommunication networks, in real time.In the paper, it is also shown that the deliberate choking of flows along overloaded edges, leading to a generation of momentary excess and deficit flow, provides a very efficient mechanism for decongesting overloaded branches.

@article{Todinov2014,
  title     = {The Throughput Flow Constraint Theorem and its Applications},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {5},
  number    = {3},
  year      = {2014},
  publisher = {The Science and Information Organization},
  author    = {Michael T. Todinov},
  doi       = {10.14569/IJACSA.2014.050302},
  url       = {https://doi.org/10.14569/IJACSA.2014.050302}
}