Headway control schemes to resist bus bunching
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Bus bunching occurs when two or more buses travel head to tail. It is an annoying problem in public transportation because it increases passengers' average waiting time and traveling time, wastes bus capacity, reduces the frequency of bus service and increases the pressure on bus drivers. So eliminating bus bunching is important in public transportation. Eliminating bus bunching is highly challenging due to the complexity and variability of the bus dynamics. Bus bunching results from a positive feedback mechanism of headway evolution, which is a flaw born with the bus system. In this thesis, we quantify the intensity of the tendency to bus bunching and propose a headway control modeling framework to reverse tendency. Our framework subsumes many headway control schemes to coordinate buses and so enables batch analysis. Given different headway information, our framework produces different control schemes under which headways self-equalize. The stability of the bus system under control is characterized by a single measure and it can be optimized. Besides, the bus system under control is robust against traffic conditions and the level of ridership. The framework is based on a snapshot model capturing the bus dynamics including the tendency to bunch by taking traffic conditions and the level of ridership into account. It is linear and time-invariant, which makes the bus dynamics tractable. This model considers a single control point and constant bus velocity in a deterministic manner, but it can be extended to handle many control points, inhomogeneous velocity along the route, and randomness. Using our framework, we further study two simple control schemes---Threshold control and ``Prefol". Threshold control drives headways to self-equalize the fastest but the corresponding bus system needs large slack time for robustness. "Prefol" needs small slack time but headways self-equalize slower. We hybridize them and find the hybrid control scheme balances robustness and fast headway equalization. We also show that it outperforms several state-of-the-art control schemes in tests on a simulated bus route in Chicago.