Departure time choices and a modeling framework for a guidance system

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.