An Algebra for the Analysis and Design of Transportation Networks

A transportation network algebra is developed as a set of definitions and rules of logic needed to create a useful, integrated theory for systematic design and development of networks. A network is viewed as the output of the physical components of the transportation system. The algebra is based on the concept of a direct trip as a function, and an indirect trip as the result of the composition of these functions. Special forms of network addition are developed and theorems related to the properties of networks are proved. The algebraic operations and theorems permit the composition and decomposition of networks and the systematic, efficient, and sequential generation of networks and their evaluation. The theorems are on some of the properties to be used in their evaluation, such as: connectedness, coalescence, and the criticalness of stations and trips.