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 network. Differences between the geographic and time-spaces can be regarded as the properties induced by the transportation system. This paper examines the spatial representation of travel-time relations that exists in a transportation network in a cartographically useful way. The objective is to find whether any meaningful spatial pattern exists and, if so, determine the nature of that pattern. This paper improves on previous attempts to generate time-space cartographic transformations through more general and robust hybrid procedures. This includes: (i) a multidimensional scaling analyses that utilizes four different data models---ratio, interval, ordinal and spline---to yield the best configuration of points representing the time distances; (ii) an iterative majorization algorithm that greatly increases the probability of obtaining a unique solution; (iii) a set of custom routines in ArcGISRTM to map the data for spatial analysis; (iv) a design that repeats runs with different starting configurations to verify the uniqueness of the result. This paper applies the general procedure to data from the Salt Lake City, UT metropolitan area. The overall time-space map of Salt Lake County shows a smooth warping except in some localities. Detailed time-maps reveal the reasons for high distortions in these locations. In some areas three-dimensional spaces give the best-fit of data. Time-maps with asymmetric data model and non-Euclidean distance model do not vary from maps with symmetric data in Euclidean model for Salt Lake City.