This section focuses on testing the AxS model’s accessibility outputs. In the model, accessibility is directly affected by two parameters: the time budget, which represents the amount of time individuals have available for travelling and par- ticipating in discretionary activities; and the movement speed, which depends on the agent’s transport mode and affects the time spent travelling. Environmental factors, such as travel distance and the spatial distribution of opportunities in the city, also affect the model’s accessibility results. The simulation scenarios used in this section were designed to test the effects of those parameters and environmental factors on accessibility.
Simulations were carried out in the abstract environment shown in figure 5.10. The commuting population is represented by three agents (A, B, and C), whose trips’ origins and destinations are illustrated in figure 5.10a. This scenario was designed so that agents have clear straight paths to their destinations, which are indicated by the black arrows in figure 5.10a, thus removing the effects of stochasticity in pathfinding from the test results. Places of activity were randomly distributed in the study area, following a normal distribution from the central cell of the grid with standard deviation of 50 cells (figure 5.10b).
Spatial and temporal scales were not set in real world units (such as metres and minutes) for this exercise. Abstract units were used instead, thus time
Figure 5.10: Abstract scenario for accessibility output tests: (a) origin and des- tination of the agents’ trips; (b) spatial distribution of activity locations (oppor- tunities) in the study area, with brighter colours representing higher density of opportunities.
was measured by the number of iterations elapsed since the start of the agent’s trip, and speed was measured by the number of cells an agent can traverse during one time step (cells per iteration)
The effects of movement speed and time budget on agents’ potential path area (PPA) are discussed in section 5.2.1, while section 5.2.2 compares the results of the geometric and cardinal accessibility metrics.
5.2.1
Potential Path Area
The sensitivity analysis exercise discussed here consists of 1083 model runs in total. The time budget parameter values tested range between 30 and 120 iter- ations, at intervals of 5 iterations. The agents’ movement speeds tested range between 1 and 10 cells per iteration, at intervals of 0.5. For each combination of parameters, a single trip was simulated corresponding to one of agents A, B, or C.
As discussed in chapter 4, the PPA is the area an individual can reach using their remaining time budget after travel time is discounted. A sample of the agents’ PPAs resulting from the parameter values discussed above is shown in figure 5.11. The figure shows the PPA’s of agents A (left-hand side column), B (middle column), and C (right-hand side column) in different model runs. The rows in the figure show results for different movement speeds, ranging from 1 to 5 cells per iteration. The time budget was set to 60 iterations in all cases presented.
Figure 5.11: Sample of PPA results for agent’s speed (SP) ranging from 1 to 5 cells per iteration and time budget (TB) equals to 60 iterations.
It is noticeable, from figure 5.11, that the larger the original time budget and movement speeds, the larger the agent’s PPA. In this sense, when movement speeds are too slow relatively to the distance travelled (figures 5.11a, 5.11b, 5.11c, and 5.11e), there is no time budget left for agents to participate in any activity, thus their PPAs are empty. As movement speeds increase, so do the PPAs, until a limit is reached: either the PPAs around the origin and destination points merge together (e.g. figure 5.11j), or the PPA reaches the study area’s limits (e.g. figure 5.11o).
5.2.2
Geometric and Cardinal Accessibility
In the AxS model, the geometric accessibility measure is equal to the number of urban cells in each agent’s PPA. The variations in geometric accessibility accord- ing to movement speed and time budget can be seen in figures 5.12 and 5.13. Figure 5.12 shows movement speed on the x axis, with panels representing differ- ent time budgets (60, 75 and 90 iterations), while figure 5.13 shows time budgets on the x axis, with panels representing movement speeds (3, 5, and 8 cells per iteration). The similarity between the patterns shown in both graphs is striking. The main difference between them is the curve in figure 5.13 (time budget in the x axis) is slightly smother than the curve in figure 5.12 (speed in the x axis). This means both parameters have the same effect on geometric accessibility: faster speeds and longer time budgets allow agents to access larger areas.
Figure 5.12: Geometric accessibility results for agents A, B, and C, with move- ment speed ranging from 1 to 10 cells per iteration and time budgets of 60, 75, and 90 iterations.
Figure 5.13: Geometric accessibility results for agents A, B, and C, with time budget ranging from 50 to 120 iterations and movement speeds of 3, 5, and 8 cells per iteration.
There are two more patterns worth discussing regarding the geometric accessibility results shown in figures 5.12 and 5.13. The first concerns agents A and C accessibility curves. When slower speeds and smaller time budgets are considered, agents A (red line) and C (green line), who travel the same distance in the simulation, have the same geometric accessibility. As speed and time budget are increased, agent C’s accessibility curve changes slope and increases more slowly than agent A’s. This happens because agent C’s PPA reaches the study area’s limits earlier than agent A’s, as shown in figure 5.11. The second pattern concerns the accessibility curves of agents B (blue line) and C (green line). Agent B’s accessibility curve starts lower than agent C’s, but the situation quickly inverts. This is an effect of agent B’s longer travel distance, which is a liability with slow movement speed and short time budgets. However, when those parameter values are increased, the larger PPAs around agent B’s origin and destination points (figure 5.11n) compensate the extra distance the agent has to travel. Conversely, agent C’s shorter travel distance causes the PPAs around agent C’s origin and destination points to merge (figure 5.11l), thus cancelling accessibility gains obtained from faster speeds and longer time budgets.
While geometric accessibility simply measures the size of an individ- ual’s PPA, cardinal accessibility measures the number of opportunities available within and individual’s PPA. The importance of the cardinal accessibility mea- sure stems from the unequal spatial distribution of opportunities in cities. Hence, an individual with low geometric accessibility may actually have access to more opportunities than an individual with high geometric accessibility, depending on the locations they live, work, and visit. The origins and destinations of agents A, B, and C (figure 5.10a) were chosen to test the model’s sensitivity to the spa- tial distribution of opportunities (figure 5.10b) in the abstract study area of this exercise.
The plots of figure 5.14 show the comparison between agents A, B, and C geometric (5.14a) and cardinal (5.14b) accessibilities at different movement speeds, at a constant time budget of 60 iterations. It is noticeable agent A’s cardinal accessibility is higher than agent C’s from the start, since agent A is located in an area with more opportunities than agent C. It is also noticeable agent B also has higher cardinal accessibility than C, despite agent B’s longer travel distance and lower geometric accessibility. Cardinal accessibility values of agents A and B also increases much faster than agent C’s.
Figure 5.14: Geometric (a) and cardinal (b) accessibility results for agents A, B, and C, with movement speed ranging from 1 to 10 cells per iteration, and time budget of 60 iterations.
This test summarises the range of possibilities and trade-offs in people’s residential, workplace, and other activity locations, movement speed (as a proxy for mode of transport), and free time available for carrying out discretionary activities. For example, agent A reaches a level of cardinal accessibility at a speed of 3 cells per iteration that is only reached by agent C when moving at 6 cells per iteration. In this example, agent A could represent an individual who lives and works near the city centre while the individual represented by agent C lives in the suburbs, so agent C needs to use a faster (and probably more expensive) means of transportation and travel longer distances to enjoy the same level of accessibility as agent A. Such level of flexibility and detail is impossible to achieve with traditional place-based accessibility measures.