A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph - Bo Xu; Xiaodong Ji; Zhengrong Cheng (Mathematics)
The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%.