Departure time choice behavior in commute problem with stochastic bottleneck capacity: experiments and modeling

ABSTRACT

The effect of environmental uncertainty on equilibrium patterns is of vital importance to understand travel choice behavior. This paper conducted a laboratory experiment to investigate the effects of stochastic bottleneck capacity on departure time choice behavior. In the experiment, the bottleneck capacity varied stochastically from round to round, and two different scenarios with different information feedback were investigated. Our experimental results showed that the relationship between the mean travel cost and the standard deviation of travel cost on each departure time was fitted approximately linearly with a positive slope ${\lambda }^{\ast }$, indicating subjects were more likely to minimize their travel cost budget rather than their mean travel cost. Also, we found that the feedback on costs of all departure times resulted in a smaller ${\lambda }^{\ast }$ than the feedback on the subjects’ own travel cost only. We propose a reinforcement learning model to reproduce the main experimental findings.

KEYWORDS:

• Departure time choice
• bottleneck model
• stochastic capacity
• laboratory experiment
• reinforcement learning model

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that in the discrete bottleneck model they proposed, Otsubo and Rapoport (2008) assumed that ties, which refer to the order in which commuters receive service, are broken randomly with equal probability among the commuters who arrive at the bottleneck simultaneously.

2 In some empirical studies, such as Small (1982), the three parameters were calibrated from the data collected from daily commuting behavior. However, in laboratory experiment studies concerning departure time choice, the travel cost function involving the values of the three parameters should be given in advance to guarantee the calculation of travel costs choosing different departure times. After the subjects in one group submitted their decisions in one round, the server would calculate the travel costs on different departure times and provided such information to these subjects in the next round.

3 Here we convert the cumulative score to payoffs to avoid the possible payoff fluctuations with random selections caused by environmental uncertainty. Another way of calculating payoffs is to randomly select several rounds and convert the score earned in these rounds to payoffs to avoid income effects. We would like to consider this alternative in the future work and compare with the present setup.

4 Note that in theoretical equilibrium patterns with continuous-time setting (mean value of parameter λ* in the experiment is used), no one departs before 7:30. The meaning of λ* will be introduced later in the main text.

5 It should be noted that in the second group of experiments in Scenario B, one subject misunderstood the travel cost shown in the interface as payoff. The subject mostly chose very early or very late departure time. Therefore, in the data analysis, the data of this subject were removed.

6 Our experiment does not exclude that commuters minimize $\overline{u}(t)=E(C(t))+\lambda \tilde{\sigma }(t)$. However, since both $\tilde{\sigma }(t)$ and $\sigma (C(t))$ reflect variability of travel cost, and $\sigma (C(t))$ is much more frequently used than $\tilde{\sigma }(t)$, we use travel cost budget in the modeling.

7 Note that there are several other equilibrium models based on "effective travel time/cost", including the percentile user equilibrium model, in which all travelers are assumed to choose routes to minimize their own percentile travel time (Nie 2011); the α-reliable mean excess traffic equilibrium model, in which all travelers are assumed to minimize their travel risk measured by the conditional expectation of the excess travel time for a certain travel time budget (Chen and Zhou 2010); and the traffic equilibrium model based on the quadratic disutility function (Yin, Lam, and Ieda 2004).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 71621001, 71631002, 71931002, 71890972, 71890970, 71801011].