# Ambulance Locations in a Tiered Emergency Medical System in a City
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Area**} & \multirow{2}{*}{**Indicator**} & \multicolumn{8}{c}{**LandScan Model of Demand**} & \multicolumn{8}{c}{**Street Model of Demand**} \\ \cline{3-11}  & & **pMP** & \begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} & \begin{tabular}{c} **MEXCLP** \\ **Integer** \\ \end{tabular} & **ERTM** & **MCLP** & **pMP** & \begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} & **MEXCLP** & **ERTM** & **MCLP** \\ \hline \multirow{5}{*}{\begin{tabular}{c} \(\%\) \\ \end{tabular} } & Average response time & \multirow{5}{*}{6} & 3 & 5 & 2 & 7 & 8 & 1 & 4 & 8 & 9 \\  & to all patients (min) & & & & & & & & & & \\  & \% of calls responded & & & & & & & & & & \\  & to within 15 min & & & & & & & & & & \\  & Average response time & & & & & & & & & & \\  & to high-priority & & & & & & & & & & \\  & patients (min) & & & & & & & & & & \\  & \% of high-priority & & & & & & & & & & \\  & calls responded to & 8 & 1 & 2 & 4 & 3 & 10 & 6 & 5 & 7 & 9 \\  & within 8 min & & & & & & & & & & \\ \hline \multirow{5}{*}{\
\begin{tabular}{c} \(\%\) \\ \end{tabular} } & Average response time & \multirow{5}{*}{1} & 1 & 3 & 9 & 5 & 2 & 7 & 4 & 8 & 6 & 8 \\  & to all patients (min) & & & & & & & & & & \\  & \% of calls responded & & & & & & & & & \\  & to within 15 min & & & & & & & & & \\  & Average response time & & & & & & & & & \\  & to high-priority & & 1 & 5 & 9 & 3 & 2 & 7 & 6 & 8 & 3 & 4 \\  & patients (min) & & & & & & & & & & \\  & \% of high-priority & & & & & & & & & & \\  & calls responded to & & & & & & & & & & \\  & within 8 min & & & & & & & & & \\ \hline \multirow{5}{*}{
\begin{tabular}{c} \(\%\) \\ \end{tabular} } & Total score & 28 & 29 & 53 & 38 & **21** & 62 & 33 & 52 & 44 & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Rankings of the location models with regard to simulated performance. the ERTM outperformed the average response time model in most criteria. The MEXCLP performed better than the ERTM in terms of 15 min coverage. Of course, the previous studies do not contain our MCLP model that was proved superior by our experiments. Since this model also minimizes the average response time, our results are compatible with the cited works. The average response time seems to be the most important indicator of EMS access, especially from the most critical patients' point of view, because it strongly affects the probability of survival for those patients [17; 29; 33]. The outputs of our study are useful for healthcare providers. We recommend the optimal distribution of ambulances in the city that will increase the responsiveness of EMS. The weak point of our research was that there were no limits on the potential locations of the stations. We suppose that the station can be located at any central node of the LandScan grid, or at any centroid of the street. It was beyond our capabilities to investigate potential locations with all the aspects that have to be taken into account in practical station relocation (i.e., the existence of a proper building, the costs of its tenancy, etc.). Thus, our results should be interpreted in terms of the wards surrounding the calculated optimal station locations rather than stations' precise addresses. At present, such an interpretation is satisfactory for the decision-makers, as follows from the discussions with the EMS authorities. We note that in practice it may not be acceptable to relocate all stations operating in the city, mainly for economic reasons that are not incorporated into our study. However, the MCLP model, as well as other location models under consideration, can easily cope with such a limitation. It is enough to fix some stations in their current positions by setting corresponding location variables to 1, or by limiting the number of relocated stations by adding a simple constraint to the models.