Route Choice in Stochastic Time-Dependent Networks

For angling may be said to be so like the Mathematics, that it can never be fully learnt; at least not so fully, but that there will still be more new experiments left for the trial of other men that succeeds us. The main field of my research has been directed hypergraphs and how they can be used to model problems in stochastic time-dependent networks (STD networks). Other areas such as logical inference and logic-based methods for optimization have also gained some interest, but will not be covered by this thesis. As the title suggests, the thesis focuses on STD networks which are an extension of more " traditional " networks where the travel time or cost between two nodes (towns, telephone switches etc.) are deterministic and time-independent. In STD networks the travel time between two nodes are time-dependent, i.e. the travel time depends on the leaving time from a node. Furthermore, it is assumed that, for each leaving time, the travel time may not be fully known and hence a probability function is used to express possible travel times. This gives in many cases a better framework for modelling real world problems. We consider route choice problems in STD networks which may be regarded as extensions of traditional shortest path problems in directed graphs. The problem of finding a shortest path in a directed graph may be considered as two problems in an STD network, depending on whether the entire route, denoted a strategy, must be specified a priori, i.e. before travel begins (a priori route choice) or whether the driver is allowed to react while travelling on the revealed/actual arrival times at intermediate nodes (time-adaptive route choice). The problem of finding the best route/strategy under a priori or time-adaptive route choice consists in finding a strategy which is minimal with respect to a specific objective, e.g. expected travel time. The thesis focuses on two route choice problems in STD networks. In Chapter 4 we consider the problem of finding the K best strategies under a priori and time-adaptive route choice while Chapter 5 considers bicriterion route choice under a priori and time-adaptive route choice. Here we assume that two criteria are given, e.g. minimizing expected travel time and cost. The goal is now to find efficient strategies, i.e. strategies for which it is not possible to find a different strategy such that expected travel time or cost is …