# Modeling Activity-Time to Build Realistic Plannings in Population Synthesis in a Suburban Area
## 7 Urban Experiment
### Model Validation  
The validation model compares the distribution of the generated activity-plans, for both duration and end-time attributes, with the distributions extracted from \(ENTD\). It is composed of four steps: (1) the configurations are defined based on the approach parameters, (2) the population-plans are generated for each configuration, (3) the configurations outputs are compared with \(ENTD\) distributions, and (4) the best configurations with its population are selected for the simulation. The validation is applied to a set of activities \(X\), which contains: work, education, leisure, shopping, and restaurant.  
Firstly, if the configuration \(c\) (the tolerance coefficients) is varied, a set of activity-plans are generated; they are compared to the referent distributions. Six configurations {A, B, C, D, E, F} are proposed to validate the proposed approach. The configurations (A) and (B) use only static coefficients, (A) uses the standard coefficients defined in Section 5.3, (B) and uses a double value of configuration (A). With the aim of studying the impact of static coefficients on the activity-plan times, the objective of these configurations is to test the output distribution independently of the selected duration. To avoid selecting  
Figure 24: Trips’ predicted travel time: the green arrow is a walking trip, the gray arrows are car trips, and the orange arrow is a public transportation trip.  
Figure 25: The region of interest is a suburban area 10 km from Paris, France. Its population amounts to 126k agents over five municipalities. Blue dots are Home-locations of the agents (cartography MapData ©2021 Google).  
a non-feasible duration, the maximum value of dynamic coefficient is used to keep the selected duration within the distribution range. The configurations (C) and (E) use only the dynamic coefficients. (C) uses the maximum dynamic coefficient value and generates the largest end-time (duration) range with the selected duration as a center, while (E) uses a random dynamic coefficient. The configuration (D) does not use the tolerance coefficients; as a result, the selected duration is used immediately to calculate end-time value. The last configuration (F) is a combination of (A) and (C) and references the defined configuration are presented in the process described in Section 6.1, and the different configurations are presented in Table 1.  
Secondly, by using the configuration settings (tolerance parameters), the next step is to generate the activity-plans for the whole population. Once the activity-plans are generated, by basing on the \(ENTD\) proportions (time-ranges), the end-time and duration distributions are extracted for each activity from the set \(X\). This step is applied for each configuration separately.  
Thirdly, to evaluate the different configurations \(c\), a validation error measure \(error_{c}\) is defined for both duration and end-time. For each activity \(x\) from \(X\), an activity-error gap \(error_{c}^{x}\) (not to be confused with the activity-gap \(Gap\)) is calculated between the configuration \(c\) output distributions and the reference distribution \(ENTD\), which refers to the difference between each time-proportion \(p\) and \(P_{x}\) (\(P\) refers to both duration and end-time distributions) between the reference rate \(r_{p}^{x}\) and the configuration rate \(c_{p}^{x}\) (see Equation (38)). Finally, the \(error_{c}\) is equal to the average of all \(error_{c}^{x}\) (see Equation (39)).  
\[error_{c}^{x}=\frac{1}{|P_{x}|}\times\sum_{p\in P_{x}}|c_{p}^{x}-r_{p}^{x}| \tag{38}\]  
\[error_{c}=\frac{1}{|X|}\times\sum_{x\in X}error_{c}^{x} \tag{39}\]  
Finally, after the duration and end-time average error for each configuration are calculated, the next step is to select the best configuration. By comparing the average error of both duration and end-time error of each configuration, with a priority to the end-time. The best configuration is saved also as its activity-plans, they will be used in the simulation step.