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The flows and levels of service in a transport network are determined by constructing demand and supply functions so as to incorporate the equilibrium approach more explicitly. The graph theoretic system theory models used in the paper provide a "custom tailored" fit to each individual transportation system as opposed to the formula-oriented models widely prevalent in the transportation literature. The physical system theory approach suggested here can be potentially used for modeling real-world transportation systems for the purposes of prediction, evaluation of alternatives, and sensitivity and optimal design studies. Certain illustrative examples and a highly simplified empirical application are included with a view to establishing the feasibility of the approach.