Using Dual Graph and Wavelet Transform for Evaluation and Planning Transportation systems

Geographic Information Systems have many capabilities for transportation systems management. The network capabilities of GIS such as shortest path computations are very useful for transportation management. Graph theory is the base of network analysis in GIS. The current method for conversion of a transportation network to a graph is modeling the stations as nodes and the paths between stations as edges. In this paper we have proposed a new method for translation of a transportation network to a graph by dual graph concepts. Dual graphs are presented for simplifying and solving of the original graph problems. In dual aspect the transportation lines are modeled by nodes and their relations are modeled by edges. The implemented case study showed that a bus transportation network with 5 bus lines could be translated to a graph with 5 nodes and 5 edges that could be very useful in many cases، specially in evaluation of transportation system. In continuous، we have explained the wavelet transform and its applications in evaluating and planning of transportation systems. Wavelet is a mathematical transform that could extract much useful information from a signal. For instance in an innovative task، we used the wavelet transform for extracting the moment precise number of needed vehicles in every transportation lines. The implemented case study illustrates the direct relation between number of required vehicles and the rate of traffic in a bus line.