Time-dependent networks : data representation techniques and shortest path algorithms with applications to transportation problems

Abstract

In this thesis, we develop methods for the following problems: the representation of discrete-time dynamic data, and the computation of fastest paths in continuous-time dynamic networks. We apply these methods for the following application problems: storage and communication of discrete-time dynamic transportation network data, and computation of fastest paths in traffic networks with signalized intersections. These problems are at the heart of realtime management of transportation networks equipped with information technologies. We propose a representation (called the bit-stream representation) method for nondecreasing discrete-time dynamic functions as a stream of 0 and 1 bits. We show that this representation is 12 times less memory consuming than the classical representation for such data, where the function value at each time-instant is stored as an L-bit integer. We exploit this representation to efficiently store and represent travel-time data in discrete-time dynamic transportation networks. Since the bit-stream representation requires lesser memory space, it also leads to lesser communication-time requirements for applications involving communication of such data. We adapt a classical dynamic one-to-all fastest path to work on bit-streams and show that this leads to savings of up to 16-times in over-all communication and computation times. This holds the potential to impact the development of efficient high performance computer implementations of dynamic shortest path algorithms in time-dependent networks. We model travel-times in dynamic networks using piece-wise linear functions. We consider the one-to-all fastest path problem in a class of continuous-time dynamic networks. We present two algorithms: Algorithm OR, that is based on a conceptual algorithm known in the literature; and Algorithm IOT-C, that is developed in this thesis. We implement the two algorithms, and show that Algorithm IOT-C outperforms Algorithm OR by a factor of two. We study the application problem of computing fastest paths in traffic networks with signalized intersections. We use a piece-wise linear link travel-time dynamic network model to address this problem, and demonstrate that this model is more accurate than discrete-time models proposed in the literature. Some of the implemented algorithms are applied to solve variants of the one-to-all fastest path problem in traffic networks with signalized intersections, and study the computational performance of these implementations.