# Agent-based Simulations in Quarter Deployment

### A theoretical construct

In Germany the last few years the problems of the social insurance system have been discussed in public discourse about “demographic change.” The question frequently raised asks how the system can be sustained when people age and the group of persons who should finance this system diminishes. This is just one aspect of change which will be the result of a declining population. The other is the fact that a declining population involves changes in their composition. In this context, the incremental shift of the transposition of the well known population pyramid will evidentially entail a change in the mixture of a district. The shifts in the age structure in favor of the elderly will risk the social integrity.

The challenge of the social integration can be divided in two sections. The first is the integration of migrants and the second is the intergenerational integration of all peer groups. Because of the demographic segmentation, social knowledge will decrease. This will endanger the social cohesion [nbcite author=”Berger, P. L. & Luckmann, T.” title=”Die gesellschaftliche Konstruktion der Wirklichkeit” year=”2007″ publisher=”Fischer” publisher_place=”Frankfurth a.M.” type=”book” ]. “Gated Communities” can be considered as first evidence of this problem. This phenomenon is not restricted to a single section of the population. A rudimental segmentation can also be observed in the immigrant population [nbcite author=”Krummacher, M., Kulbach, R., Waltz, V., & Wohlfahrt, N.” title=”Soziale Stadt – Sozialraumentwicklung – Quartiersmanagement” year=”2003″ publisher=”Leske+Budrich” publisher_place=”Opladen” type=”book” ].

For this reason we have to develop new individual and social aspects for an aging society. In this case, the public area, as a region for social interaction and communication, has a prominent impact.

The public area is one of the most important characteristics of the European enlightenment, where people can meet one another as equals. Streets, places and parks can be entered without any purpose. It is a place where political awareness is still founded.

The district is, especially for the elderly people and children, because of the limited mobility, the place of daily supply, living and social contacts. For them it is the place with the most important reference [nbcite author=”Thabe S.” title=”Alte Menschen im Stadtteil” year=”1997″ publisher=”ILS NRW” publisher_place=”Dortmund” type=”book” ].

Segmentation, as a multi-faceted distribution of population groups, is a normal process and will always happen. A population is never evenly distributed, but concentrated in diverse subareas depending on different parameters like economic potential. This situation becomes problematic when the disproportional concentration of people with the same characteristic values becomes static, or consolidated, and is unintended by people.

Against the background of this situation, the goal of local affairs should be the deployment of a district with a low fluctuation density. This can only be achieved when the district fits the requirements of the residents.

If politicians change the environment variables, this will affect not just one section of the population, but all others too. This is because the environment variables and each population group mutually affect each other.

The well known models of network analysis, e.g. Ucinet or Lisrel, are not appropriate to simulate the dynamics of such a system. They are not able to describe the trajectory of the system, however, exactly this is important when we want to predict the changes in a quarter.

The only way out of this dilemma is to build an agent-based simulation, therefore, a hybrid system with a stochastic cellular automat (ca) coupled with a genetic algorithm (ga) is the best choice. The ca is used to represent the public range and the ga to get an adaptive system. Based on the fitness of the correspondent groups, the simulation gives a forecast of how the district changes if some environment variables would be changed by policy, therefore, the sociological interaction rules have to be transformed into the formal model. A first idea of a model looks like the following.

We can define household $H$, which consists of one or more family members $FM$ as:

$H_i=(FM_i, ...,FM_m)$

These actors have one or multiple roles.

$FM_i=(R_i, ..., R_n)$

These roles are related to a corresponding set of requirements about the district.

$R_i=(P_1, ..., P_o)$

If the actors of a family have multiple roles, the preferences of the $FM$are weighed against each other. Based on the fact that a neighbourhood is better when more requirements about a district are fulfilled, a weighed average $A_i$ of the respective requirements i is formed by:

$\bar{A_i}=\frac{\sum f P}{\sum f}$

The requirement $A_i$ will be matched against the environment $U_i$ as a distance $d$ while a value $\geq{0}$ represents a perfect environment.

$d=U_i - A_i$

The overall evaluation of the living situation will be calculated from the totals of all distance $d$ divided by the number of requirements.

$W=\frac{\sum d}{n}$ $\textrm{while }d_i \geq{0} \rightarrow{d_i}=0$

The more negative the value of the evaluation, the higher the extrinsic motivation to change the location. In the case of more than one $FM$, the change probability $CP$ in percent for $H_i$ is given by the sum of all weighted $FM$ divided by the maximum of all preferences.

$CP = \frac{\sum fW}{f} / P_{max}$

In the case of a change, the whole environment will be searched for a better location which would be an improvement for the overall situation $W$ and not beyond the maximum lease cost $M_{PART}$. Therefore the household $H_i$ will be extended with a modifier of the change probability $CP_{MOD}$, the household income $H_{INC}$, the maximum lease costs $M_{PART}$, as well as the weighting of the family members $W_{FM}$.

$H_i = (FM_1, ..., FM_n, CP_{MOD}, H_{INC}, M_{PART}, W_{FM})$

Another possible extension would be a variable for the political motivation $POL_{MOT}$, for changing the environment of the district.

Every cell has two dimensions. The first is the infrastructural dimension which will describe attribute $E$ of a cell e.g. residential zone, traffic-reduction, etc.

$Z_i=(E_1, ..., E_q : H_1, ..., H_q)$

It must be considered that the infrastructural dimension cannot change the usage; only the other way around is feasible.

[nbcite print=”chicago” ]