# Ambulance Locations in a Tiered Emergency Medical System in a City
## 2 Materials and Methods
### Modelling Demand  
If the historical data on the locations of emergency incidents are not available, the spatial distribution of the demand for EMS must be predicted by a demand model. We investigated two different demand models. The first one is a grid model which takes data from the LandScan database ([[https://landscan.ornl.gov](https://landscan.ornl.gov)]([https://landscan.ornl.gov](https://landscan.ornl.gov)), accessed on 18 December 2021). LandScan data represents an ambient population distribution, meaning the average presence of people over 24 h. A grid cell corresponds to an area of 30\" \(\times\) 30\" (arc-seconds) in the WGS84 geographical coordinate system. The population distribution is derived from demographic and geographic data, including land cover, roads, slopes, urban areas, village locations, and high-resolution imagery analyses. Based upon the spatial data and the socioeconomic and cultural understanding of an area, cells are weighted for the possible occurrence of a population during a day. Therefore, the advantage of the ambient spatial model is that it accounts not only for permanent residents, but also for commuters who are not city inhabitants but may need emergency services while they are at work or at school.  
The territory of Presov is covered by 121 grid elements with the population count ranging from 1 to 7827 people, with a median of 79. The centroids of these grid cells are displayed in Figure 2. The nodes of the road networks that are the nearest to the centroids are regarded as demand points.  
We assume that the number of patients is proportional to the ambient population. To verify this assumption, we did a correlation analysis between the LandScan population distribution and the real EMS trips performed in 2019 in the city of Presov. The Spearman correlation is \(\rho\) = 0.847, suggesting a strong correlation.  
The alternative demand model uses only demographic data on permanent citizens aggregated at a high-resolution level. The local administration regularly updates the number of citizens in every street in the town, which enables us to identify the demand zones within the streets. In 2019, there were 344 streets in Presov. The number of residents ranged from 0 to 5246 people, with a median of 85. For modelling purposes, the street is represented by its center (Figure 3).  
Figure 2: LandScan grid.  
Again, we verified that the demand for EMS is proportional to the number of street residents, using the historical data on EMS trips. The Spearman correlation is \(\rho=0.813\), still quite strong, although slightly weaker than in the case of the LandScan population.  
To calculate the center of the street, first we need to determine the centroid (geometric center) of the street. The centroid of the street is the centroid of the envelope enclosing the street. The coordinates of its corners are defined by the extreme points of the polylines that form the street in a digital map. The center of the street is, therefore, the point within the polylines that is nearest to the centroid (Figure 4).  
Figure 4: Centroid and center of the Hviezdna street.  
Figure 3: Street centers.