Optimizing the fleet of emergency medical service vehicles

Figures & data

Table 1. Probability distribution and the average on-scene time for different types of ambulances.

	Condition	Chest pain	Severe trauma	Stroke	Other severe diagnoses (e.g., cardiac arrest)	Other diagnoses
ALS	Average on-scene time (min)	25.6	22.2	25.9	28.7	24.7
	Variance on-scene time (min)	117.1	152.4	82.5	149.3	138.2
	Probability distribution	Erlang (λ = 4.27, k = 6)	Gamma (θ =6.6, k = 3.37)	Erlang (λ = 3.23, k = 8)	Gamma (θ =5.23, k = 5.49)	Gamma (θ =5.79, k = 4.27)
BLS	Average on-scene time (min)	27.7	23.9	29.2	30.5	25.5
	Variance on-scene time (min)	109.7	136.9	111.9	146.0	159.3
	Probability distribution	Erlang (λ = 3.96, k = 7)	Gamma (θ =5.6, k = 4.27)	Erlang (λ = 3.65, k = 8)	Erlang (λ = 5.09, k = 6)	Erlang (λ = 6.37, k = 4)

Table 2. Actual and simulated average response times (ART) in Slovakia.

Patient’s priority	Actual ART mean (min)	Actual ART variance (min)	Actual ART standard deviation (min)	Simulated ART mean (min)	Simulated ART variance (min)	Simulated ART standard deviation (min)
high	10.0	44.9	6.7	10.1	39.7	6.3
medium	11.2	46.2	6.8	10.6	43.6	6.6
low	13.5	65.6	8.1	13.3	68.9	8.3

Table 3. Theoretical average response times for the optimal network of ALS and BLS stations.

Patient’s priority	Theoretical ART (min)
high	5.87
medium	5.80
low	5.81

Table 4. Simulation results for Slovakia.

		Current locations (Feb 2023)	Optimal deployment of ALS and BLS stations	Optimal deployment of ALS, BLS and RV stations	Optimal deployment of ALS, BLS and PTS stations
Average response time (min)	high priority	10.1	8.9	8.9	8.7
	medium priority	10.6	9.3	9.5	9.1
	low priority	13.3	12.0	12.2	15.8
Proportion of high priority calls responded to within 8 min (%)		43.2	52.9	52.7	54.1
Proportion of high and medium priority calls responded to within 15 min (%)		80.5	85.8	84.9	86.7
Proportion of low priority calls responded to within 15 min (%)		65.1	72.8	71.8	63.1

Table 5. Simulation results for urban areas.

		Current locations (Feb 2023)	Optimal deployment of ALS and BLS stations	Optimal deployment of ALS, BLS and RV stations	Optimal deployment of ALS, BLS and PTS stations
Average response time (min)	high priority	8.3	7.2	7.2	7.1
	medium priority	8.7	7.5	7.8	7.4
	low priority	11.7	10.6	10.9	14.9
Proportion of high priority calls responded to within 8 min (%)		59.6	68.3	68.6	69.6
Proportion of high and medium priority calls responded to within 15 min (%)		87.7	91.4	90.5	92.0
Proportion of low priority calls responded to within 15 min (%)		72.5	78.9	77.8	67.9

Table 6. Simulation results for rural areas.

		Current locations (Feb 2023)	Optimal deployment of ALS and BLS stations	Optimal deployment of ALS, BLS and RV stations	Optimal deployment of ALS, BLS and PTS stations
Average response time (min)	high priority	11.8	10.4	10.4	10.2
	medium priority	12.3	10.9	11.1	10.7
	low priority	14.9	13.2	13.4	16.6
Proportion of high priority calls responded to within 8 min (%)		28.1	38.6	38.1	39.9
Proportion of high and medium priority calls responded to within 15 min (%)		73.8	80.7	79.8	81.8
Proportion of low priority calls responded to within 15 min (%)		58.3	67.3	66.3	58.7

Figure 1. High and medium priority call handling.

Figure 2. Low priority call handling.

Figure 3. (a) The ratio of the number of trips on individual days to the daily average; (b) The ratio of the number of trips in individual months to the monthly average; (c) The average number of trips per hour.

Figure 4. Proportion of high priority calls responded to within 8 min against the average response time. Error bars are 95% confidence intervals. (a) Slovakia; (b) urban areas; (c) rural areas.

Figure 5. Number of calls responded to within a time threshold. (a) High priority; (b) Medium priority; (c) Low priority.

Figure 6. Distribution of demand from the simulation model over thirty months in the city of Banská Bystrica, showcasing both current and optimal positions of stations.