AbstractThe purpose of this paper is to find a control procedure which would efficiently unload the congestion in a queueing network. The congestion phenomenon is described by a dynamic deterministic model. The total waiting time of all entities in the overloaded region is assumed to be a performance index. The Pontryagin maximum principle is applied to show that for the optimal flow pattern cycles cannot exist and all routes leading from the given node to the outside of the overloaded region have to have the same length. These two properties are the basis for a construction of the algorithm. A topological optimization algorithm is used, since the solution must be a tree. The existence and uniqueness of the optimal solution are investigated.
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