# Modeling Activity-Time to Build Realistic Plannings in Population Synthesis in a Suburban Area
## 7 Urban Experiment
### Model Simulation  
After the best configuration \(c\) from the validation step is selected, two sets of activity-plans (for the whole population) are generated. The first set is generated using the proposed approach, which includes the defined time constraints, while the second set of plans is built without the constraints \(EVT\) and \(LLT\). To establish a fair comparison of time-constraint plan generation with simulation versus no-time-constraint plan generation with simulation, five different generated plans are used for each of these algorithms. The simulation process is applied with the same setting for both algorithms, and each simulation is run with eight iterations. The difference \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Conf** & **Static** & **Dynamic** & **Description** \\ \hline A & x & & Standard static coefficients \\ \hline B & x & & Double standard static coefficients \\ \hline C & & x & Maximum dynamic coefficients \\ \hline D & & & Null static coefficients \\ \hline E & & x & Random dynamic coefficients \\ \hline F & x & x & Standard static coefficients \\  & & & Random dynamic coefficients \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model validation: set of configurations. between generated plans of the same synthetic population is a result of the start-time random affectation steps. Once activity-plans for all agents are generated, transportation is simulated using MATSim [17], which is a mesoscopic traffic simulator. The simulation requires three files: the demand (plans) file, which contains the generated plans of the whole population (126,151 agents); the catchment area multimodal network (84,429 nodes and 330,464 links); and the configuration file, which contains the simulation settings. The output of the simulation is a multimodal dynamic traffic model; the simulation generates a set of files, for example, a plans file, which contains the simulated plans including their travel routes and the updated activity-setting, and an events file, which contains the trips of agents through the network at each time-step. To evaluate the quality of the agent-plans, a (dis)utility function (score) \(S\) measure is defined, which is composed of two functions: activity utility \(Ua\) and trip (dis)utility \(Ut\). The activity utility depends on the activity-setting (start-time, end-time, and duration), while the trip utility depends on its travel-mode. The score is calculated as the sum of all activity utilities \(Ua_{act}\) plus the sum of all trip utilities \(Ut_{trip}\). The score equation is defined in Equation (40). \[S_{plan}=\sum_{act\in plan}Ua_{act}+\sum_{trip\in plan}Ut_{trip} \tag{40}\]  
The activity utility \(Ua\) is defined as the sum of five (dis)utility terms: utility of performing activity (\(Ua_{tar,act}\)), disutility of waiting time to begin activity (\(Ua_{wait,act}\)), disutility of late arrival (\(Ua_{late,act}\)), disutility of early departure (\(Ua_{early,dp,act}\)), and disutility of too-short duration (\(Ua_{short,act}\)), which is the case when time spent by an agent is shorter than the minimum duration of the activity. The defined utility function is in Equation (41). \[Ua_{act}=Ua_{tar,act}+Ua_{wait,act}+Ua_{late,ar,act}+Ua_{early,dp,act}+Ua_{short,act} \tag{41}\]  
The trip disutility \(Ut\) is defined as the sum of the constant of the trip transport mode (\(C_{mode,trip}\)) and disutility of travel time (\(Ut_{trav,time,trip}\)), travel cost (\(Ut_{trav,cost,trip}\)), travel distance (\(Ut_{trav,dist,trip}\)), and public transport transfer (\(Ut_{transfer,trip}\)). The trip disutility function is then defined by Equation (42)  
\[Ut_{trip}=C_{mode,trip}+Ut_{trav,time,trip}+Ut_{trav,cost,trip}+Ut_{trav, dist,trip}+Ut_{transfer,trip} \tag{42}\]  
For more details about the above utility functions, we refer the reader to [17]. A good plan must perform an activity with its typical duration in order to start the activity within the window (opening-closing) to avoid the waiting time or the late arrival penalties.