In this thesis we formulate three new models to discuss the bi-modal traffic assignment problem through a day-to-day dynamical system approach. Travelers’ knowledge on the network was represented by their perceived route and mode costs which is updated daily after absorbing new information (the actual route and mode costs). Equilibrium is obtained when a stationary pattern of knowledge is attained and is locally attractive when it is stable. The impact of the information provision on the stability of the dynamical system and travelers’ departure time choice is also investigated. The effectiveness of these three models can be assured.

In the first model, we investigate travelers’ day-to-day modal choice in a bi-modal transportation system with responsive transit services under va...[ Read more ]

In this thesis we formulate three new models to discuss the bi-modal traffic assignment problem through a day-to-day dynamical system approach. Travelers’ knowledge on the network was represented by their perceived route and mode costs which is updated daily after absorbing new information (the actual route and mode costs). Equilibrium is obtained when a stationary pattern of knowledge is attained and is locally attractive when it is stable. The impact of the information provision on the stability of the dynamical system and travelers’ departure time choice is also investigated. The effectiveness of these three models can be assured.

In the first model, we investigate travelers’ day-to-day modal choice in a bi-modal transportation system with responsive transit services under various economic objectives. A group of travelers with heterogeneous preferences adjust their modal choice each day based on their perceived travel cost of each mode, aiming to minimize their travel cost. Meanwhile, the transit operator sets frequency each period according to the realized transit demand and previous frequency, trying to achieve different profit targets. For a given profit target, the fixed point of equilibrium may not be unique. We establish the condition for existence of multiple fixed points and examine the stability of the fixed points in each case. Furthermore, in view of a socially desirable mode choice, we also investigate the impacts of total travel demand and bus size on the convergence of the system to various fixed points associated with different targeted mode split.

Next, based on the first model, we consider travelers’ dynamical route choice and the impact of the information provision. Particularly, we consider that on each day both travelers’ past travel experiences and the predicted travel cost (based on information provision) can affect travelers perceptions of different modes and routes, and thus affect their mode choice and/or route choice accordingly. This evolution process from day-to-day is formulated by a discrete dynamical model. Most importantly, we show that the predicted travel cost based on information provision may help stabilize the dynamical system even if it is not fully accurate. Given the day-to-day traffic evolution, we then model an adaptive transit operator who can adjust frequency and fare for public transit from period to period (each period contains a certain number of days) to achieve a (locally) maximum transit profit.

The joint evolution (over calendar time) of travelers' departure time and mode choices, and the resulting traffic dynamics in a bi-modal transportation system is analyzed in the third model. Specifically, we consider that, when adjusting their departure time and mode choices, travelers can learn from their past travel experiences as well as the traffic forecasts offered by the smart transport information provider/agency. At the same time, the transport agency can learn from historical data in updating traffic forecast from day to day. In other words, this study explicitly models and analyzes the dynamic interactions between transport users and traffic information provider. Besides, the impact of user inertia is taken into account in modeling the traffic dynamics. When exploring the convergence of the proposed model to a dynamic bi-modal commuting equilibrium, we find that appropriate traffic forecast can help the system converge to the user equilibrium. It is also found that user inertia might slow down the convergence speed of the day-to-day evolution model. Extensive sensitivity analysis is conducted to account for the impacts of inaccurate parameters adopted by the transport agency.