# Ambulance Locations in a Tiered Emergency Medical System in a City
## 2 Materials and Methods
### Setting Parameters in the Location Models  
In the \(p\)MP, MEXCLP, and ERTM models, the weight \(b_{j}\) of a demand point \(j\) corresponds to the ambient population in the grid cell \(j\) or the number of people living in the street \(j\), respectively. The MCLP model considers the expected number of patients. The expected numbers \(b_{j1}\) and \(b_{j2}\) of high-priority and low-priority patients, respectively, can be calculated using the age structure of the population in the city, and the emergency rates for the particular age categories [29]. Regardless of the demand model, in this study we suppose that candidate locations coincide with demand points. The travel time \(t_{ij}\) is the length (in time units) of the shortest path from node \(i\) to node \(j\) on the road network. The time an ambulance takes to travel along a road segment depends on the kilometer length of the segment, its quality, its location inside or outside a built-up area, and the average speed of ambulances. The digital street network was downloaded from the OpenStreetMap database ([[https://www.openstreetmap.org](https://www.openstreetmap.org)]([https://www.openstreetmap.org](https://www.openstreetmap.org)), accessed on 16 April 2019), which is a freely available source of geographical data. All directional, turn, and speed regulations are included in the road network model. For roads without a speed limit, the average travel speed of ambulances, with respect to a given road category, was applied [30]. When an ambulance is driving back to its base station, it rides at a lower speed and respects all traffic regulations. By applying regular speeds, the matrix of longer travel times \(\overline{t}_{ij}\) can be calculated. We have the population data valid for the year 2019 at our disposal. Therefore, in the discussion, when talking about the current situation or the current state, we refer to this year. In 2019, there were five stations located at two addresses (e.g., Figure 5). There was one ALS ambulance at each address. The remaining three stations were of a BLS type. Thus, the parameters that specify the number of ambulances in the models are set as follows: \(p=5\), \(p_{1}=2\), \(p_{2}=3\). If the optimization model does not specify the type of the located stations, we simply assume that the station is of the same type as the closest current station. The desired service standard \(T^{max}\) was set with regard to critical patients who are in a life-threatening condition, and every minute of delay in the response time worsens their chances to survive dramatically. These patients should be reached within 8 min, which is a widely accepted standard in most European countries [31]. Therefore, assuming a one-minute pre-trip delay, we set \(T^{max}\) to the value of 7 min. A BLS ambulance cannot be dispatched to priority 1 patients, therefore \(\gamma_{11}=\gamma_{12}=\gamma_{22}=1\), \(\gamma_{21}=0\). Figure 5: Ambulance locations using the MCLP model with the LandScan demand model. Most of the coefficients of the MCLP model were derived from an EMS trip sample provided to us by Falck Zachrana a.s., which was the largest EMS provider in Slovakia over the last decade. The Falck dataset contains depersonalized information on 149,474 EMS interventions performed in the year 2015. The age of the patient, their initial medical diagnosis, the type of the intervening ambulance, and the time stamps of the whole EMS trip (including the transport to hospital, if any) have been recorded. Using the data, the parameters were set as follow: \(\alpha_{1}=50.96\%\), \(\alpha_{2}=76.62\%\), \(\beta_{1}=2.51\%\), \(\beta_{2}=6.75\%\). In Presov, there is only one hospital. The average drop-off time is \(td=20.1\) min. The on-scene time depends on the patient's diagnosis and the crew's qualification: \(ts_{11}=26.5\) min, \(ts_{12}=24.4\) min, \(ts_{21}=24.9\) min, \(ts_{22}=23\) min. The probability \(q\) of an ambulance being unavailable was estimated using a detailed computer simulation model [30].