The formulations of problems of analysis and synthesis in multipolar communication networks with variable flow rates on the arcs of the network are considered. In contrast to traditional formulations, the concepts of flow density, flow rate, and flow intensity are introduced, and the temporal characteristics of the movement of the given volumes through the network are analyzed. Similar problems arise in various spheres of human activity, for example, when studying traffic flows in models of evacuation of large cities or in problems of planning and managing transportation in problems of urban logistics. Mathematical formulations and algorithms for solving problems of transportation in a multipole network with variable flow rates are presented, which, under certain conditions, make it possible to avoid solving complex nonlinear problems of mathematical programming of large dimensions.
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