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We discuss some of the concepts related to the flow problems in a discrete·continuous compound system, and propose an approximation method as well as a numerical algorithm for the maximum-flow problem in a network which is assumed to be locally uniform and sufficiently dense. The algorithm is derived by means of the fmite-element technique, and is tested by taking up as an example the maximum-flow problems on the road network of Tokyo Metropolitan Area. 1. Introducti on The theory of flows in networks is now well established from the standpoint of theory as well as of application, and many effective practical algori thms are being developed for dealing with problems of flows in networks. However, in general, applications of these algorithms to practical problems are limited due to the fact that they require prohibi ti vely large computation time and memory for considerably large networks. One of the 'ways to circumvent this difficulty would be to consider an approximate model. The model to be considered in this paper is based on the theory of flows in continua proposed by M. Iri in (5). Continuum models of flow problems have been considered by Monge (7), Appell (1) and Kantorovitch (6), and recently by R. E. Gomory and T. C. Hu (3) for the isotropic case, and the general anisotropic case was formulated by M. Iri in invariant tensorial terms to include the continuous counterparts of all the concepts appearing in the established formalisms of the theory of flows in networks. Each point of the continua concerned is endowed with characteristics of "capacity" and/or "distance", which are the eontinuous counterparts of branch

MAXIMUM-FLOW PROBLEM IN DISCRETE CONTINUOUS COMPOUND SYSTEM AND ITS NUMERICAL APPROACH