# Spatiotemporal Modeling of the Smart City Residents' Activity with Multi-Agent Systems
## 4 Model City  
To validate the devised model of actant interaction, the authors developed a \"model city\" comprising seven hexagonal districts with a dominating type of function and structure (Table 1 and Figure 2). One million residents inhabit the city, as illustrated by the dot distribution map (Figure 3). Each of dots, representing 1000 inhabitants, was implemented into the system as an agent with specific characteristics such as age, education, wealth, marital status, number of children, identity (level of identification with the city), trust in people, and trust in institutions. The variations (standard deviation) of the agent characteristics in each district was assumed at 20% for model data. The parameters for agents were drawn according to the normal distribution. The ArcGIS ESRI (ArcGIS is the name of software developed by Environmental Systems Research Institute; GIS is abbreviation of Geographic Information System) application was used to develop the source spatial database, enabling the preparation of a set of thematic layers (land cover, buildings, communication routes, districts borders, distribution of residents) as shapefiles. These layers were used to build a multi-agent system in the GAMA simulation platform (see [49, 50]). GAMA is a modeling and simulation-development environment for building spatially explicit agent-based simulations (see [50]). It is a multiple-application domain platform using a high-level and intuitive agent-based language. With GAMA, users can undertake most of the activities related to modeling, visualizing, and exploring of the simulations using dedicated tools. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No** & **Name** & **Population** & **Trust to People (\%)** & **Trust to Institutions (\%)** & **Altruism (\%)** & **Education (\%)** & **Happiness (\%)** & **Wealth (\%)** & **Identity** & **Age** \\ \hline
1 & Greenland & 50,000 & 90 & 80 & 70 & 90 & 100 & 90 & 100 & 60 \\
2 & City Center & 250,000 & 40 & 60 & 30 & 60 & 60 & 60 & 90 & 50 \\
3 & Bedronup Suburb & 400,000 & 40 & 50 & 30 & 70 & 50 & 50 & 20 & 40 \\
4 & Old Town & 50,000 & 80 & 60 & 80 & 80 & 80 & 80 & 100 & 70 \\
5 & Business District & 100,000 & 50 & 60 & 20 & 70 & 50 & 60 & 20 & 30 \\
6 & Old Factory District & 150,000 & 30 & 20 & 20 & 20 & 10 & 10 & 40 & 60 \\
7 & Unspecified Space & 0 & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model city districts (mean values, in percent); standard deviation is equal to 20%. Figure 1: Linear (y = x), reinforcing (y = tan(x)), and diminishing (y = tanh(x)) functions. Thanks to the simulations carried out for the model city, it was possible to calibrate the multi-agent system properly, i.e., to determine the value of individual parameters, which then enabled the use of the devised model for a real urban agglomeration area. For example, 3650 iterations used by the authors correspond to a period of 10 years, during which the level of trust of residents changes significantly (and in a measurable way). The authors repeatedly modified the numerical values of particular factors (e.g., changing the level of trust of individual actants resulting from their mutual interactions) so that the parameterization of the model corresponds to the changes observed in the real cities. Because of the iterative calibration of the system, it was possible to determine the parameters of the model adequate for the research of real metropolises. The analyses made it possible to check the spatial distribution of changes in the level of trust of the residents of particular districts (Figures 2 and 3) in a long-term (decades-long) process. Thanks to the  
Figure 3: Dot distribution map (each dot represents 1000 inhabitants of the model city). Figure 2: Model city. use of a multi-agent system, it was possible to simulate many years of social processes in computational cycles lasting from several dozen minutes to several hours.