Addition and Removal of Agents

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The previous simulations have highlighted how the system evolves under different assumptions. This section will further this exploration through the addition and removal of agents. The ability to add and remove agents allows one to explore how an area’s land-uses might change through adding and removing agents, especially how new agents affect the composition of the area. Two separate experiments were carried out. The first sees agents being added and removed (once an agent’s age is greater than 65, it has a 10% probability of being removed). In the second experiment agents were only added. In both cases at the end of each iteration, 200 of type resident and 20 of type employer agents are added to the system. The same area, parameters, and model were used as in (see Figure 1 on the Effects of Space and Income page). The following section will present the results of these two experiments, starting with experiment one.

Figure 1 illustrates the average number of agents of different types for 100 iterations of the model where agents are both added and removed. After the initial growth of the residential population, the population stabilises around 60 iterations as there are nearly equal number of residents being added and removed from the system. This can be seen in the number of agents that died over time (Figure 1). While the absolute number of agents searching of both type resident and employer varies over time, on average 39% and 24% respectively are classed as searching as the system evolves.

Table 1 presents the average number of agents in different zones over 100 iterations. As more agents are added to the system the high income employers (commerce and services) focus on the more accessible areas and over time the commerce employer group effectively exclude all other groups from zones 1 and 2. For residents who desire more space, this growth in employers forces them to more peripheral locations as can be seen with the growing number commerce residents in zones 6 and 8 over time. Figure 2 highlights this process taking place, which has close similarities to that of invasion and succession proposed by Burgess (see below for a typical model run). The outward migration of commerce and service residents from the centre of the city leads to empty spaces left by these residents which are then filled by the new residents, mainly the industrial residents.

Figure 1: The number of different types of agents over time when agents are being added and removed.

Table 1: Average number of agents in different zones over the course of multiple simulations where agents are both added and removed.

Figure 2: Typical configurations of agents during the course of a simulation where agents are both added and removed.

In the second experiment, agents were only added to the system. This was carried out to speed up the process of outward migration. Over time, the populations of residents and employers increased to such an extent that all zones were occupied by agents as highlighted in Table 2. Different groups of agents have their own spatial niches. For example, service employers are predominantly in zones 3 and 4 by 100 iterations. Once all the zones were occupied, resident agents of type commerce are being removed from the system as they cannot find a suitable area to locate. For example, at iteration 90, there were 6196 commerce residents but by iteration 100 this was 6093 (Table 2). Similarly some industrial workers were also removed from the system. If the simulation had continued, all commerce residents and industrial employers would have been removed. Figure 3 illustrates this process taking place, with residents moving to more peripheral locations and employers focusing on more central areas (see below for a typical model run). However, within the different zones, clusters of one group of agent can be seen.

Table 2: Average number of agents in different zones over the course of multiple simulations where agents are only added.

The addition and removal of agents presented in this section is quite a simplistic view of how a city grows, for example, employers are not removed as it is presumed that when the city grows, there will be an increase in employment as the population grows. This growth in employment attracts more residents, but the relationship between population and employment type is not explored in detail. This could be an avenue for future work. Notwithstanding this simplistic assumption, this section has demonstrated how agents being added and removed from the system causes the spatial distribution of land-uses to change over time, specifically as those agents who desire the most space are forced further and further away from the centre and eventually are excluded from the system as the population of agents increase. Additionally, it has highlighted how ideas postulated by Burgess about invasion and succession, i.e. agents are entering an area forcing other agents to move, can be seen in a dynamic model based on Alonso’s (1964) bid-rent theory. Employers can out bid residents for land, and residents with greater space requirements are forced to more peripheral locations.

Figure 3: Typical configurations of agents during the course of a simulation where agents are only added.

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Examples of runs where agents are both added and removed

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Reference

Alonso, W. (1964), Location and Land Use: Toward a General Theory of Land Rent, Harvard University Press, Cambridge, MA.