From rectangle to parallelogram: an area-weighted method to make time-space diagrams incorporate traffic waves

A time-space (TS) traffic diagram is one of the most important tools for traffic visualization and analysis. Recently, it has been empirically shown that using parallelogram cells to construct a TS diagram outperforms using rectangular cells due to its incorporation of traffic wave speed. However, it is not realistic to immediately change the fundamental method of TS diagram construction that has been well embedded in various systems. To quickly make the existing TS diagram incorporate traffic wave speed and exhibit more realistic traffic patterns, the paper proposes an area-weighted transformation method that directly transforms rectangular-cell-based TS (rTS) diagrams into parallelogram-cell-based TS (pTS) diagrams, avoiding tracing back the raw data of speed to make the transformation. Two five-hour trajectory datasets from Japanese highway segments are used to demonstrate the effectiveness of the proposed methods. The travel time-based comparison involves assessing the disparities between actual travel times and those computed using rTS diagrams, as well as travel times derived directly from pTS diagrams based on rTS diagrams. The results show that travel times calculated from pTS diagrams converted from rTS diagrams are closer to the actual values, especially in congested conditions, demonstrating superior performance in parallelogram representation. The proposed transformation method has promising prospects for practical applications, making the widely-existing TS diagrams show more realistic traffic patterns.