Leusmann C, 1975, "Über eine einfachen Gleichgewichtsfluß in Netzwerken" Environment and Planning A 7(2) 127 – 140
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Über eine einfachen Gleichgewichtsfluß in Netzwerken
Received 30 October 1973, in revised form 4 December 1974
Abstract. A simple equilibrium model of network flow, based on the topological properties of a given system, is derived with the aid of matrix algebra. This model is then used to characterise the vertices and edges of a network and to analyse real deviations. It is shown that the equilibrium characteristics are independent of the nature of the flow parameters, and are determined solely by the overall structure of the network. Three examples relating to West German railway systems are given as an illustration of the ease with which the networks can be topologically characterised. An extension of the analysis to take account of transport flow beyond boundaries of a region is suggested, which, however, involves appreciable computation work. The model provides a means of carrying out dynamic transport flow analyses relevant to planning, and is an extension of conventional analyses based on Markov chains.
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