A behavioral departure time choice model with latent arrival time preference and rewards for peak-hour avoidance

Departure time choice modeling has been part of main stream travel behavior research for more than three decades. Congestion management schemes are based on the assumption that travelers optimize their departure time choice. Ever since Vickrey, in the late 1960's and later updated by Small in the 1970's, the concept of schedule-delays (early and late) has been the focus of most modeling endeavors. The main idea is that travelers organize their departure time based on a preferred arrival time (PAT). The main challenge of departure time choice models is lack of sufficient and accurate data on travelers' departure and arrival times. Surveillance techniques to capture real departure and arrival times are less frequently adopted probably due to both high costs of the infrastructure and privacy issues. In this respect, Spitsmijden the Dutch peak-avoidance experiment provides researchers a remarkable dataset of revealed preference. In the course of 13 weeks, 340 individuals participated in a program whereby they were rewarded (either with money or credits to acquire a smartphone) for avoiding commuting during the morning peak (7:30-9:30). Participants car use was monitored by electronic vehicle identification, giving information about the time and location of detection. Car detection time is a good enough proxy of departure time given that the identification devices were located very close to the place of residence. Travel times are known from the traffic control systems. In addition, personal travel logs were filled out while socio-demographics and information about work conditions were also collected through surveys before and after the reward experiment. Initial analysis suggests that departure time is characterized by very high variability both across participants and over time. In previous research, discrete-choice models were estimated to find regularities between degree of peak avoidance and reward regimes, socio-demographics and work/household related constraints. They assert that peak avoidance is affected mainly by type and height of the reward. However, other factors also influence behavior, such as availability of alternatives, household and work constraints, access to real-time traffic information as well as certain socio-demographics like gender and education. In this paper we continue with this line of research with a focus on departure time choice behavior during the experiment. We apply the schedule-delay framework albeit in more flexible manner. The utility function has three main components: travel time, schedule delays and the rewards. Departure time is treated as discrete with a choice of ten intervals of 15 minutes from 6:00 to 11:00 AM. Since we do not know the real PAT it is regarded as a latent choice variable. As mentioned, PAT could well vary between participants according to personal characteristics (e.g. gender, education), habitual behavior (commuting frequency) and constraints/supports for changing behavior. This implies t