Backward Dijkstra Algorithms for Finding the Departure Time Based on the Specified Arrival Time for Real-Life Time-Dependent Networks

Abstract

A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piecewise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large-scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.