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Continuum approximation to dense networks and its application to the analysis of urban road networks

1982; Springer Nature; Linguagem: Inglês

10.1007/bfb0121231

2364-8201

Azuma Taguchi, Masao Iri,

Evacuation and Crowd Dynamics

A continuum approximation is proposed for problems of flows in large and dense networks, where each point of the continuum is characterized by ‘capacity’ and/or ‘distance/cost’ which are convex sets in the tangent space. The problems of flows in continua corresponding to various problems of flows in networks are formulated in variational forms, of which mathematical properties are investigated and for which numerical algorithms are derived by means of the finite-element discretization technique. A practical procedure, based upon concepts from integral geometry, for constructing the continuum which approximates the original network is also proposed. The effectiveness of the continuum approximation is tested against flow problems on urban road networks of moderate size, to get satisfactory results. The continuum approximation has many advantages over the ordinary network model; e.g. (i) it is easier to build from the practical standpoint of data gathering; (ii) its solution helps us to intuitively understand the global characteristics of road networks; (iii) the amount of computation does not depend on the size of the original network.