Multiterminal Network Flows with Inverse Linear Constraints in Engineering Networks*

The necessity of using and studying models that are similar to reality leads to the development of new network flows, generalizing the already known network structures. The multiterminal network flow is a natural development of the classical flow with one source and one sink and fixed upper limits of the flow function on each arc [1, 2]. There exists a number of engineering and economic problems, the solution of which implies the use of more universal multiterminal flows for the interpretation and modeling of real systems [1, 4]. The fluid supply networks and in particular the waterand gas supply networks, the telecommunication networks, the transport networks are similar systems. Network flows with inverse linear constraints are introduced and investigated in [3] when defining the lower bounds of the capacity on subsets of the network arcs (ILC-flows) for more exact and adequate modeling of real physical networks and for increase in their reliability and functionality. The multiterminal network flows with inverse linear constraints are a logical generalization of this class of flows with respect to the real practical problems. The main difference between the classical flow and the ILC-flow determines the principal difference in the corresponding multiterminal flows and the necessity for independent study of the multirerminal network flows with inverse linear constraints.