| This dissertation develops a stochastic programming approach to proactively consider a variety of uncertainties associated with signal timing optimization for fixed-time or actuated traffic signals. Representing the uncertain parameter of interest as a number of scenarios and the corresponding probabilities of occurrence, the stochastic programming approach optimizes signal timings with respect to a set of high-consequence or worst-case scenarios. The resulting signal timing plans produce smaller delays and less vehicular emissions under those scenarios, thereby leading to more reliable and sustainable mobility.;To illustrate the stochastic programming approach, below are three applications in traffic signal timing. The first application is to optimize the settings of fixed-time signals along arterials under day-to-day demand variations or uncertain future traffic growth. Based on a cell-transmission representation of traffic dynamics, an integrated stochastic programming model is formulated to determine cycle length, green splits, phase sequences and offsets that minimize the expected delay incurred by high-consequence scenarios of traffic demand. The stochastic programming model is simple in structure but contains a large number of binary variables. Existing algorithms, such as branch and bound, are not able to solve it efficiently. Consequently, a simulation-based genetic algorithm is developed to solve the model. The model and algorithm are validated and verified using two networks, under congested and uncongested traffic conditions.;The second application further considers traffic emissions, and develops a bi-objective optimization model to make an explicit tradeoff between traffic delays and roadside human emission exposure. Based on the cell-transmission representation of traffic dynamics, a modal sensitive emission approach is used to estimate the tailpipe emission rate for each cell of a signalized arterial. A cell-based Gaussian plume air dispersion model is then employed to capture the dispersion of air pollutants and compute the roadside pollutant concentrations. Given a stochastic distribution of the wind speed and direction of a corridor, a scenario-based stochastic program is formulated to optimize the cycle length, phase splits, offsets and phase sequences of signals along a corridor simultaneously. A genetic algorithm is further developed to solve the bi-objective optimization problem for a set of Pareto optimal solutions. The solutions form an efficient frontier that presents explicit tradeoffs between total delay of the corridor and the human emission exposure of the roadside area incurred by high-consequence scenarios.;The last application is to synchronize actuated signals along arterials for smooth and stable progression under uncertain traffic conditions, mainly addressing the issue of uncertain (not fixed) starts/ends of green of sync phases. The model developed is based on Little's mixed-integer linear programming (MIP) formulation, which determines, e.g., offsets and progression speed adjustment, to maximize the two-way bandwidth. By specifying scenarios as realizations of uncertain red times of sync phases, the regret associated with a coordination plan is defined with respect to each scenario, and then a robust counterpart of Little's model is formulated as another MIP to minimize the average regret incurred by a set of high-consequence scenarios. The numerical example shows that the resulting robust coordination plan is able to increase the worst-case and 90th percentile bandwidths by approximately 20% without compromising the average bandwidth.;In summary, these three applications demonstrate that the proposed stochastic programming approach is valid for signal timing optimization under uncertainty. The resulting timing plans are expected to perform more robustly and effectively in uncertain environments, thereby making the transportation system more reliable and sustainable. |
