Classical and Contemporary Shortest Path Problems in Road Networks: Implementation and Experimental Analysis of the TRANSIMS Router

We describe and analyze empirically an implementation of some generalizations of Dijkstra's algorithm for shortest paths in graphs. The implementation formed a part of the TRANSIMS project at the Los Alamos National Laboratory. Besides offering the first implementation of the shortest path algorithm with regular language constraints, our code also solves problems with time-dependent edge delays in a quite general first-in-first-out model. We describe some details of our implementation and then analyze the behavior of the algorithm on real but extremely large transportation networks. Even though the questions we consider in our experiments are fundamental and natural, it appears that they have not been carefully examined before. A methodological contribution of the present work is the use of formal statistical methods to analyze the behaviour of our algorithms. Although the statistical methods employed are simple, they provide a possibly novel approach to the experimental analysis of algorithms. Our results provide evidence for our claims of efficiency of the algorithms described in a very practical setting.