Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic Capacity

This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.

Modeling Departure Time Choice of Car Commuters in Dhaka, Bangladesh

Dhaka, one of the fastest-growing megacities in the world, faces severe traffic congestion leading to a loss of 3.2 million business hours per day. While peak-spreading policies hold the promise to reduce the traffic congestion levels, the absence of comprehensive data sources makes it extremely challenging to develop econometric models of departure time choices for Dhaka. This motivates this paper, which develops advanced discrete choice models of departure time choice of car commuters using secondary data sources and quantifies how level-of-service attributes (e.g., travel time), socio-demographic characteristics (e.g., type of job, income, etc.), and situational constraints (e.g., schedule delay) affect their choices. The trip diary data of commuters making home-to-work and work-to-home trips by personal car/ride-hailing services (957 and 934 respectively) have been used in this regard. Given the discrepancy between the stated travel times and those extracted using the Google Directions API, a sub-model is developed first to derive more reliable estimates of travel time throughout the day. A mixed multinomial logit model and a simple multinomial logit model are developed for outbound and return trip, respectively, to capture the heterogeneity associated with different departure time choice of car commuters. Estimation results indicate that the choices are significantly affected by travel time, schedule delay, and socio-demographic factors. The influence of type of job on preferred departure time (PDT) has been estimated using two different distributions of PDT for office employees and self-employed people (Johnson’s SB distribution and truncated normal respectively). The proposed framework could be useful in other developing countries with similar data issues.

Departure Time Choice in Schedule-Based Transit Assignment

This paper investigates existing departure time models for a schedule-based transit assignment and their parametrization. It analyzes the impact of the temporal resolution of travel demand and suggests functions for evaluating the adaptation time as part of the utility of a path. The adaptation time quantifies the time between the preferred and the scheduled departure times. The findings of the analysis suggested that travel demand should be discretized into intervals of 1 min, with interval borders right between the full minute, that is, ±0.5 min. It was shown that longer time intervals led to arbitrary run volumes, even for origin–destination pairs with just one transit line and a fixed headway. Although a linear relationship between adaptation time and adaptation disutility is a common assumption in several publications, it cannot represent certain types of passenger behavior. For some trip purposes, passengers may be insensitive to small adaptation times, but highly sensitive to large adaptations. This requires a nonlinear evaluation function.

Impact of Flextime on Departure Time Choice for Home-Based Commuting Trips in Austin, Texas

An increasing number of corporations and workplaces are providing flexible working hours or flextime for employees, which is expected to reduce congestion by redistributing the temporal pattern of commuters’ departure time. This study examines the impact of flextime on departure time choice using a Bayesian continuous-time hazard duration model. The model accommodates the time-varying effect of covariates and unobserved heterogeneity. Results from the Austin Household Travel Survey collected between 2017 and 2018 show that workers who have a flextime option choose to leave later, with a predominant effect deterring morning peak departures. Other trip and individual-specific variables, such as travelers’ job type, trip duration, number of trips during the travel day, and household income, are found to have significant impacts on departure time choice. The results also show that flextime is more effective in shifting the departure time for retail and service sector employees, for those whose journeys are longer, and for those who perform more daily activities. The findings of this study support the theory that implementing such policies may ease congestion by staggering the travel demand from peak to off-peak hours.

Exploration of Maximum-to-Minimum Shifts in Generic Methods for Departure Time Choice Models

Vickrey’s seminal departure time choice model is based on a penalty function which is a linear combination of travel time, earliness, and lateness. The original model depicts a single link from a single origin to a single destination, serving homogeneous travelers by a deterministic point-queue regime. Numerous variants of the basic model, relaxing one or more of these assumptions, have been used in a wide range of contexts. The equilibrium solution of the basic model can be computed directly by exact formula. Specific convergent methods have been proposed for certain variants. One of the troubling challenges in this model is the need for a generic iterative numeric approach, that may address complex models in which departure time choice is embedded. Natural candidates were shown to fail even on the basic model. In this paper we explore a fairly naive approach, where, in each iteration, demand is shifted from the maximum cost time interval to the minimum cost time interval. Results for the basic model are promising, demonstrating that, with a fixed shift, solutions converge to a deviation which is proportional to the shift size and that semi-adaptive or adaptive shift size may offer convergence to any desirable level of approximation of the exact equilibrium.