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GEOGRAPHICALLY PARTITIONING A TRANSPORT NETWORK* Patrick O'Sullivan One reason for seeking structure in transport systems is to reduce the computation involved in network investment planning. Either for evaluating individual projects or designing the best set of additions to a network, the interrelationships of parts of the system dictate an extensive tracing of costs and benefits. It may be possible to specify the structure of a transport network so that some geographically delimitable parts can be identified which operate in relative isolation from the rest of the system. If such structure can be discerned, then it may be exploited to reduce the arithmetic burden involved in making decisions. A more profound justification for seeking to partition parts of a whole is that of understanding and explaining the nature of the phenomenon . Distinguishing unique parts of a system and their connections is a major step in comprehension. In this paper, after examining the ways in which simple structure can be exploited in analyzing large systems, attention will be focussed on the difficulties which the geography of transport networks present to such an endeavor. Finally some empirical evidence on the geographical extent of the impact of improving a part of a network is presented. This holds out good prospects for the discernment of useful partitions of urban road networks. THE DECOMPOSITION OF LARGE SYSTEMS. The exploitation of structure plays a major role in the analysis of large systems. Be they military organizations, production processes, spatially separated suppliers and consumers, electrical circuits, or transport networks, complex , integrated systems become far more manageable if they can be decomposed into parts. The attempt to optimize system performance, * This work was supported by NSF Grant SOC76-16832. Dr. O'Sullivan is Professor and Chairman of the Department of Geography, The Florida State University, Tallahassee, FL 32306. 126Southeastern Geographer or the search for stability conditions for the system's operation, is often only possible if advantage is taken of its structure to separate the overall problem into elements whose solution is within the range of available computing machinery. The readiest example of this is the experience of dealing with Leontief input-output systems. The Leontief model of the economy postulates fixed-proportion, constant-returns production functions, so that the solution of the system for equilibrium outputs consists of the inversion of a matrix of fixed intersectoral, input-output coefficients. With a large number of industries specified, this presented a hefty computational task. Given the somewhat arbitrary assignment of position to industries , the coefficient matrices presented seemingly random patterns of interindustrial connections. Initially these matrices were manipulated to seek pattern purely for computational convenience. If they could be recast so that all the non-zero coefficients fell below the main diagonal (triangularized) , then great computational advantage would accrue. In the course of these manipulations it became clear that discernible coefficient structures implied structured interindustrial relationships . A homogeneously dense matrix reflected complete interdependence ; triangularity indicated an hierarchical structure; diagonal blocks represented fairly autonomous sectors connected by one or two industries while sparse, scattered coefficients showed complete specialization. This qualitative input-output analysis has been applied to international comparisons and to tracing the course of development. (1) Prior to this, in electrical engineering, Kron had formalized the notion of tearing integrated systems into pieces which could be solved individually but with system coordination. (2) He entitled this the art of diakoptics. For him the system parts were a series of electrical motors in some combination. In the same fashion, Dantzig and Wolfe devised a decomposition principle for solving large scale linear programs characterizing a system consisting of separate managerial units. (3) The system of equations describing such an operation can be arranged so that the coefficients form independent blocks linked by coupling equations. The solution algorithm works by iterating between solving the independent sub-problems and a "master" problem. This process lent itself to interpretation as an economy in which a central director coordinates the independent solution of local allocation problems to Vol. XVIII, No. 2 127 achieve overall optimality by setting prices on the common resources used. The identification of structure and means of using it to solve optimization problems has burgeoned in the last decade and a half...

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