Time–space transformations of geographic space for exploring, analyzing and visualizing transportation systems

Transportation systems exist within at least two types of space. One is the apparent geographic space, but equally important is the time–space implied by the travel time relations created by the system. Differences between the geographic and time–spaces are properties induced by the transportation system. Methods for time–space transformations of geographic space to explore, visualize and analyze transportation systems were initially developed in the 1960s and 1970s. However, these methods have not been pursued beyond this initial flurry of research activity, most likely due to the difficulties associated with handling and processing digital geographic data. The rise of geographic information systems (GIS), as well as continued development and wider availability of transformation techniques such as multidimensional scaling (MDS) and spatial analytical techniques such as bidimensional regression can allow the potential of time–space transformation techniques to be realized. This paper presents a general methodological framework that exploits recent advances in GIS, MDS and spatial analytical techniques. Results from applying these techniques to the Salt Lake City metropolitan area illustrate the power of these techniques to reveal spatial patterns in the travel time relationships induced by a transportation system. The application also addresses fundamental issues in time–space transformations, such as two-dimensional versus three-dimensional solutions, Euclidean versus non-Euclidean solutions and symmetric and asymmetric solutions.