Time-distance Mapping: Visualization of Transportation Level of Service

Time-distance mapping is a method to obtain a spatial configuration of points, so that the Euclidean distances between points consist with the given time distances. The approaches are divided broadly into two categories. One deals with the time-distances between all pairs of points. Multidimensional scaling (MDS) is generally applied to the solution. Another deals with the limited number of time-distances given to some of pointpairs such as links of a transportation network. However, no mathematical solution has been proposed for this type of time-distance mapping. This paper proposes the generalized solution of the two types of time-distance mapping based on the non-linear least squares, which is mathematically clear and of practical use.