Stochastic transport network model and optimization for reliability and vulnerability analysis

Abstract

This thesis aims to contribute to the rapidly growing research area of transport network reliability and vulnerability by introducing the concept of stochastic network (SN) into the reliability and vulnerability analyses. The thesis also aims to develop advanced methods for evaluating network reliability and vulnerability and solving network design problem (NDP) with reliability consideration. The thesis first derives closed-form expressions of SN flow and cost models. Three static SN traffic assignment models are also formulated, including user equilibrium (SN-UE), system optimum (SN-SO), and stochastic user equilibrium (SN-SUE). The SN-SUE model is then used to propose an evaluation and design model for network capacity reliability assessment/enhancement under travel demand variability. The implicit programming approach is applied to solve the proposed optimization problem. Sensitivity analysis (SA) is adopted to provide all necessary derivatives. For vulnerability analysis, the thesis proposes a SA-based approach to improve computational efficiency and allow for large-scale road networks. With the road networks of Sioux Falls City and Bangkok metropolitan area, the proposed method can significantly reduce computation time compared with the traditional approach. For integrated analysis, the thesis proposes an integrated scenario tree model for road network design under both recurrent day-to-day traffic congestion (evaluated by SN-SUE model) and non-recurrent events, e.g. disasters, (assessed by SN-SO model). Finally, the thesis focuses on developing a global optimization method for solving a mixed network design problem (MNDP). The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting-constraint algorithm (CCA) is developed for solving the MILP problem. The proposed method and algorithm is also applied to solve a discrete stochastic network design problem and to evaluate stochastic network vulnerability.