# Ambulance Locations in a Tiered Emergency Medical System in a City
## 3 Results
### Results for the Street Demand Model  
In this section we evaluate the mathematical models where the demand is derived from the permanent residents. The same methodology as in the previous section is applied. As it shows in the static criteria (Table 4), the results correspond to the theoretical assumptions. The models with response time objectives result in better average response times, while the MEXCLP model is better at the expected coverage within the tighter time limit. The expected 15 min coverage is the same for all models. The results of the simulation study are in Tables 5 and 6 for the city and district, respectively. As for the average response time to all patients, the binary MEXCLP model is the best in the city, as well as at the district level, while the ERTM outperforms other models regarding the accessibility to the most critical patients. The distribution of ambulances proposed by two of the most successful binary MEXCLP and ERTM models are in Figures 7 and 8, respectively. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Criterion** & \(p\)**MP** & \
\begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} &
\begin{tabular}{c} **MEXCLP** \\ **Integer** \\ \end{tabular} & **ERTM** & **MCLP** \\ \hline Average response time (min) & 2.40 & 3.57 & 3.71 & 2.54 & 2.43 \\ Average expected response time (min) & 3.40 & 4.07 & 4.18 & 3.30 & 3.38 \\ Expected coverage within 15 min (\%) & 99.37 & 99.37 & 99.37 & 99.37 & 99.37 \\ Expected coverage within 8 min (\%) & 95.96 & 99.07 & 99.08 & 97.61 & 96.01 \\ Computing time (s) & 19.39 & 2.28 & 2.33 & 4252.16 & 138.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Static evaluation of the location models, street model of demand. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Indicator** & \begin{tabular}{c} **Current** \\ **Locations** \\ \end{tabular} & \(p\)**MP** & \
\begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} &
\begin{tabular}{c} **MEXCLP** \\ **Integer** \\ \end{tabular} & **ERTM** & **MCLP** \\ \hline Average response time & 9.60 & **8.75** & 8.89 & 9.04 & 8.94 & 8.81 \\ to all patients (min) & (9.51; 9.69) & (8.70; 8.80) & (8.76; 9.02) & (8.98; 9.11) & (8.88; 9.00) & (8.72; 8.90) \\ \hline \% of calls responded to & 83.37 & **85.87** & 85.17 & 85.02 & 84.78 & 85.83 \\ within 15 min & & & & & \\ \hline Average response time & 9.43 & **8.38** & 8.70 & 8.86 & 8.60 & 8.40 \\ patients (min) & (9.31; 9.55) & (8.33; 8.43) & (8.53; 8.88) & (8.74; 8.99) & (8.44; 8.75) & (8.28; 8.53) \\ \hline \% of high-priority calls & & & & & & \\ responded to within & & & & & & \\
8 min & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance indicators for different distributions of the EMS stations in the district of Presov, LandScan model of demand. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Indicator** & \begin{tabular}{c} **Current** \\ **Locations** \\ \end{tabular} & \(p\)**MP** & \
\begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} &
\begin{tabular}{c} **MEXCLP** \\ **Integer** \\ \end{tabular} & **ERTM** & **MCLP** \\ \hline Average response time & 6.12 & 5.41 & **5.06** & 5.26 & 5.41 & 5.56 \\ to all patients (min) & (6.07; 6.17) & (5.32; 5.49) & (4.95; 5.16) & (5.17; 5.34) & (5.32; 5.50) & (5.45; 5.67) \\ \hline \% of calls responded to & 95.21 & 95.05 & **95.66** & 95.45 & 95.07 & 94.53 \\ \hline Average response time & & & & & & \\ to high-priority & 5.86 & 5.02 & 4.83 & 5.04 & **4.73** & 4.93 \\ patients (min) & (5.78; 5.93) & (4.80; 5.25) & (4.71; 4.95) & (4.93; 5.15) & (4.59; 4.88) & (4.74; 5.13) \\ \hline \% of high-priority calls & & & & & & \\ responded to within & & & & & \\
8 min & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance indicators for different distributions of the EMS stations in the city of Presov, street model of demand. Figure 8: Ambulance locations using the BETM model with the street demand model.