Departure time choice is a key component of travel behavior that directly influences the spatial and temporal distribution of travel demand. This paper tries to develop a modeling framework for choosing the departure time that minimizes travel costs. In this regard, a modeling framework for generating departure time recommendations is proposed and applied to real commuting trips. The methodology is an extension of the departure time choice model with unreliable travel time. Two cases are considered. The first calculates the optimal time of departure when the mean of the travel time varies by time of day but the variance is constant. An exact solution to the departure time choice problem is provided for this case. In the second case, both the mean and variance vary with the time of day. A numerical solution is proposed; it is proved that the sequence of the numerical solution is contractive with a unique fixed point obtainable for any initial guess. We apply both to the departure time planning problem for a transportation operator that offers repetitive mandatory trips on a dense network. The case study offers two insights into departure time choice analyses. First, the assumption that the travel time variance at peak hours is constant induces biases for the optimal departure time. However, this assumption provides plausible results for the off-peak period. Second, travelers relying on personal judgment may have significantly different costs of travel than passengers making their decisions based on the system's recommendations.

中文翻译：

---

出发时间选择和引导系统的建模框架

出发时间选择是出行行为的关键组成部分，直接影响出行需求的时空分布。本文试图开发一个建模框架来选择最小化旅行成本的出发时间。在这方面，提出了一种用于生成出发时间建议的建模框架，并将其应用于实际的通勤旅行。该方法是旅行时间不可靠的出发时间选择模型的延伸。考虑两种情况。第一个计算当行程时间的平均值随一天中的时间变化但方差恒定时的最佳出发时间。针对这种情况，给出了出发时间选择问题的精确解决方案。在第二种情况下，平均值和方差都随一天中的时间而变化。提出了数值解；证明了数值解的序列是收缩的，并且对于任何初始猜测都可以获得唯一的不动点。我们将这两种方法应用于在密集网络上提供重复强制行程的运输运营商的出发时间规划问题。该案例研究为出发时间选择分析提供了两个见解。首先，高峰时段出行时间方差恒定的假设会导致最佳出发时间的偏差。然而，这一假设为非高峰时段提供了合理的结果。其次，依赖个人判断的旅行者的旅行成本可能与根据系统建议做出决定的乘客的旅行成本显着不同。