117 Transportation Research Record: Journal of the Transportation Research Board, No. 2345, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp. 117–125. DOI: 10.3141/2345-15 Department of Civil and Environmental Engineering, University of Maryland, 1173 Glenn Martin Hall, College Park, MD 20742. Corresponding author: L. Zhang, lei@umd.edu. dynamic traffic assignment models, and activity- and agent-based travel demand models. The remainder of the paper is organized as follows. A brief review of previous studies on departure time choice modeling and behav- ior theories is provided in the next section. Following that is a presentation on the positive theoretical framework and quantita- tive modeling components for departure time and peak spreading analysis under uncertainty. Then is a section that demonstrates the model in a numerical example in which the heterogeneous behavior under various supply- and demand-side uncertainties is studied. Conclusions and discussions on future research are offered in the final section. LITERATURE REVIEW Rational behavior theory assumes that individuals can identify all feasible alternatives, measure all of their attributes, and choose the alternative that maximizes their utility (3, 4). There have been extensive research efforts applying this approach to departure time choice analysis. In particular, some earlier studies have adopted the following utility function V(t) with respect to departure time t: Vt Tt t Tt t Tt ( ) ( ) ( ) ( ) () () () () =α +β - - +γ + - max 0, PAT max 0, PAT (1 ) where T(t) = travel time associated with departure at time t, PAT = preferred arrival time at destination, and α, β, and γ = parameters to be estimated. The second and third terms on the right-hand side of Equation 1 are thus formulated as the deviation from one’s preferred schedule. In other words, they measure the disutility of schedule delays (i.e., being either too early or too late). Preferred arrival time and schedule delays have been studied by many researchers (5, 6). The main line of research based on rational behavior theory focuses on discrete departure time choice modeling. Small’s paper adopted the multinomial logit approach to model departure time decision making (7). However, the underlying assumption of inde- pendence from irrelevant alternatives in multinomial logit does not hold for departure time choice analysis because adjacent departure time options tend to exhibit correlated unobservable factors. Nested logit models have been used to identify and address the correlated departure time intervals (8–10). Cross-nested logit models, which allow more flexible substitution patterns than nested logit does, were also explored (11–13). Steady-state transportation system per- formance is often assumed in most previous studies, wherein users Positive Model of Departure Time Choice Under Road Pricing and Uncertainty Chenfeng Xiong and Lei Zhang A novel positive model was developed for departure time choice under road pricing and uncertainty at individual levels, and the consequent system-level dynamic properties were also analyzed. The proposed modeling framework avoided assumptions of substantial rationality and focused on how individuals actually make decisions. Bayesian learning, knowledge updating, search, and decision making under uncertainty were modeled in the framework. Then time-dependent departure pat- terns along with other system performance were investigated in a series of agent-based simulation experiments. The way in which individuals actually chose departure time under various supply- and demand-side uncertainty scenarios was explored for the effect of the scenarios on system performance and its dynamic properties. An important dimension of the decision-making process available to trip makers is that of the time at which to depart from their ori- gins. Nowadays, as commuting corridors are getting increasingly congested, more than half of which can be attributed to random incidents such as traffic accidents, severe weather conditions, travel demand fluctuation, and so on, travelers’ departure time choice under uncertainty draws growing research attention. Understanding the factors and behavioral mechanisms that determine travelers’ depar- ture time choices under uncertainty is a prerequisite to designing and evaluating policies aimed at mitigating congestion and improving system reliability. Existing models either do not give adequate attention to the dynamic aspects or only consider risk-avoiding behavior in a ran- dom utility maximization manner. In a previous work, a novel posi- tive approach to departure time choice modeling considering the steady-state traffic conditions is specified, estimated, and validated (1). It has also been demonstrated on a real-world network (2). This approach theorizes the role of search, information, learning, and knowledge in decision making, and it focuses on modeling how departure time decisions are actually made. The main research objective of this paper is to extend the fully operational positive departure time model, to understand individuals’ actual choice under various supply- and demand-side uncertainty lev- els, and to analyze the day-to-day system performance. The proposed positive model tracks the departure time changes of each individual in the transportation system, and therefore is especially suitable for integration with microscopic traffic simulators, simulation-based