3.1. Facilities and SRs

In this section, we briefly describe the type of emergency vehicles (for roads and air) currently available in the SEM. Also, we summarize the main features and purpose of each kind of vehicle.

4.1. SEM Dataset Overview

The SEM provided us with records of 12,977 incidents that occurred in TE from January 1st 2018 to December 31st 2019. For each one of those incidents, at least one ALS was assigned (notice that severe incidents might have more than one ALS assigned). In our work, we have considered incidents with origin in TE and also incidents with destination in TE (we have also considered the border regions that belong to Lleida and Camp de Tarragona). Additionally, we have also considered cases with destinations in the SEM hospitals assigned to TE, see Table 1. After selecting those cases from the SEM dataset, we have 6780 incidents.

It is important to note that the AT is not influenced by ambulance distribution nor base location (which are the focus of this study), but rather by the severity of the incident. Besides, TT depends on the incident location and, consequently, on the distance to the assigned hospital. Therefore, among the three values, only the RT is affected by the ambulance distribution or the base location, which are the focus of our work. We included the AT and TT description in the paper to provide a complete overview of the total time an ambulance is occupied, which includes RT, AT, and TT, as shown in equation (1).

Nonetheless, both AT and TT values in the SEM dataset have been useful in helping us clean the dataset of incidents. The raw EMS incident dataset contains several errors, primarily due to the stress faced by operators handling emergency calls. In some cases, incidents are logged but ultimately do not require a response, and the operator may forget to close them, leaving these entries in the dataset. As a result, the first step was to clean the dataset. This process is summarized in the next subsection.

4.2. Data Cleaning and Filtering

4.3. Coordinates of the Ambulance Bases

Currently, there are four bases in the TE SR, see Figure 2. Ambulances return to their designated base after completing the incident they have responded to. Each vehicle’s code name and its respective location coordinates are shown in Table 2.

For each new incident/event that occurs (either an incident or a hospital-to-hospital transportation), SEMSIM needs to keep track of all the available ambulances mentioned in Table 2 to assign the best possible ambulance to each incident, i.e., the one that arrives sooner.

In the case of A and C rows, notice that we have two different ambulance code names for the same vehicle. This variation occurs because the ambulance code name changes depending on the personnel it transports.

For instance, when the ambulance stationed at Base A is staffed with a doctor, its code is E605 (and it will be an ALS); however, when it only transports a nursing technician, the code changes to E405 (and it will be a BLS).

4.4. Dataset Features

In the code of our SUMO-based simulator SEMSIM, we input the dataset containing incidents that occurred in 2018 and 2019, provided by the SEM. Subsequently, we simulate the performance of ambulances responding to the temporal sequence of accidents, testing various combinations of ambulance locations at available bases.

In this section, we will provide an overview of the types of incidents and their main statistical features. This will enhance our understanding of the SEM dataset regarding the specific characteristics of the incidents.

5.1. Use of SUMO to Generate the Ambulances’ Trips

First of all, SEMSIM needs to simulate the entire journey of ALS ambulances whenever they are assigned to any incident that occurs over time. This will allow us to optimize the assignment of ambulances to incidents by selecting the most suitable ambulance available, ensuring it arrives first at the scene by traversing the real map on actual roads. Notice that severe incidents might require more than one ALS.

To know which available ambulance is the fastest for a given incident, we need to develop a model that fulfills our objectives. We want simulation results to be as close as possible to the real-life scenario. This is why we decided to include a mobility simulator to carry out the ALS trips in our SEMSIM simulator. SEMSIM includes real maps taken from OSM [10] so that SEMSIM makes ambulances travel over realistic roads.

Notice that roads in OSM have different speed limits assigned. Nonetheless, notice also that, of course in real life, activated EMS vehicles (e.g., with the siren on) will travel at the highest possible speed that the EMS driver can achieve, even crossing red traffic lights if required, although always avoiding dangerous situations for others. In our SEMSIM simulator, we have currently not included normal vehicles, and there are only EMS vehicles. The reason is that in this work, we are interested only in comparing which is the best ambulance configuration (i.e., where to deploy the available ambulance fleet to improve the EMS service). Therefore, to simplify the analysis and decrease simulation time, it was sufficient to compare the available alternatives under the same circumstances (i.e., only ambulances are traveling on the map). In future work, we will also include normal vehicles in the simulations, which will, of course, have to give way to passing EMS ambulances attending a service.

The mobility simulator we used to develop SEMSIM is the widely known SUMO [23] simulator. SUMO allows for intermodal simulation including pedestrians and it comes with a great set of tools to create scenarios. Even though the SUMO framework facilitates the traffic generation with its build-in tools (e.g., OD2Trips, RandomTrips, DUArouter, DUAIterate, and MARouter), the overall traffic demand generation may result in a complex and time-consuming process. To build route traces, SUMO tools require several input files to be configured. Moreover, in order to enable rerouting functionality, additional configurations are required. Rerouting is needed when an ALS ambulance that finishes its service assisting an incident and is now on its way back to the base is assigned to a new incoming incident. In such a case, we need to change during the SUMO simulation the ambulance’s destination to the new incident location.

In this regard, we have used the SUMO Traffic Generation (STG) tool to generate the traffic demand. STG was developed by Barbecho, and it is available in [24]. STG facilitates the traffic demand generation based on SUMO tools. It allows researchers to quickly execute the different SUMO tools to select the appropriate traffic generation tool for a given scenario (e.g., urban and highway). For this, the STG tool automatically generates the required files to execute the different SUMO tools. Additionally, STG uses real traffic statistics to create route traces as realistic as possible.

The main features of the SUMO simulation logic are detailed in the following subsection.

5.2. Requirements to Develop the SEMSIM Simulator

In this section, we highlight the essential requirements of our research, establishing the foundation for the development of our SEMSIM simulator. Additionally, we offer deeper insights into the implemented code.

5.2.1. SEMSIM Objectives

To start with, in this work, we have considered the SR of TE, although we plan to extend our work to the rest of SRs in Catalonia, see Figure 1. In TE, there are four bases for the ALS ambulances and four ALS ambulances, see Figure 2. The first base will be referenced as Base A, the second base as Base B, the third as Base C, and the fourth as Base D. Currently, each ambulance is stationed in a different base, i.e., they follow configuration 1111 meaning that there is one ambulance per base. The goal of our research is to optimize the ambulance location (i.e., how to optimally distribute ambulances at bases) and to find the configuration that results in the smallest average ambulance RT, i.e., the smallest trip time required from the ambulance coordinates to the location of the assigned incident. Notice that the ambulance location has an impact on the time elapsed from the moment when the ambulance is assigned to an incident to the moment that the ambulance arrives to the incident location (i.e., RT). The other times of equation (1) (AT and TT) are independent of that configuration, and rather depend on the severity of the incident and on the distance to the assigned hospital, respectively. That is, the only parameter from equation (1) that we measure in our simulations is the RT, and we do not measure AT nor TT.

In TE, there are 35 ways to distribute the 4 ALS ambulances in the 4 current bases (combination with repetition m = 4 bases, n = 4 ambulances). Therefore, we have CR_5,4 = 35 possible ambulance configurations, among which we have these examples, see Figure 3:

• •

  1111: One ambulance at each of the bases. This is the current configuration.

• •

  0112: One ambulance at Base B, one ambulance at Base C, and two ambulances at Base D.

• •

  1030: One ambulance at Base A and three ambulances at Base C.

After simulating the 35 different configurations, we will find which is the configuration that produces the smallest average RT ($$). That configuration would be the optimal ambulance configuration. The simulation run time was 2 h per each configuration (server DELL R752, GPU, 12 RAM 64 GB), so that the whole simulation time was 70 h. Note that the simulation is performed only once, and all the results of the 35 configurations can then be visually analyzed using our public Power BI-based SEMSIM tool [25]. Notice that while 2 h of simulation time may seem long to test various ambulance distributions and base locations, doing so in real life would be nearly impossible. SEMSIM enables EMS decision makers to simulate 2 years of real incidents in just 2 h, allowing them to evaluate the impact of different configurations, such as adding new bases or adjusting ambulance assignments.

To fulfill our objectives, we have designed three algorithms in the SEMSIM simulator using Python code to mimic the SEM operation: (i) Algorithm 1 to assign ALS ambulances to incidents; (ii) Algorithm 2 to find out if the ambulances are busy or free; and (iii) Algorithm 3 to find out the location of the free ambulances. In the following, we explain those algorithms.

5.2.3. Proposed Algorithm in SEMSIM to Find Out the State of the ALS Ambulances

Upon the event of a new incoming incident, the SEM assigns the best free ALS ambulance, i.e., the ALS ambulance that will arrive first to the incident location. This is precisely what our SEMSIM simulator must do. Recall that in this work, for the sake of simplicity, we are only considering incidents that require an ALS due to their higher level of severity. To fulfill this goal, we have designed an algorithm to be used by SEMSIM to find out the state (i.e., free or busy) of all the ALS ambulances available in the SR, see Figure 4.

Algorithm 1: Assign ALS ambulances to incoming incidents following the SEM policy.
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  Input:

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   • SEM dataset of incidents from 2018 to 2019 in Terres de l’Ebre.

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   • Incident details:

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    1. Location: Longitude, latitude.

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    2. Time (t): Moment when the incident occurs.

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    3. Number of ALS ambulances (N_ALS) in the Sanitary Region: Four in Terres de l’Ebre.

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    4. State of each ALS (ALS_state_i,t): Free or busy, determined using Algorithm 2. Find out the state of each ALS ambulance i at moment t, i € (1 … N_ALS).

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    5. Type of incident (Type): One of:

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     ⁃ IHT (interhospital transfer).

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     ⁃ EmIn with hospital transport.

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     ⁃ EmIn without hospital transport.

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  Output:

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   Assigned ambulance to the new incoming incident.

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  while not at the end of the list of incidents do:

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   Step 1. New incident detected:

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    o Check the states of all ALS ambulances.

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    o Determine locations of all free ALS ambulances using Algorithm 3.

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   Step 2. Response time calculation:

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    o Compute the response times (RTs) for each free ALS ambulance to the incident location using SUMO functions.

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   Step 3. Assign the ALS that will arrive first:

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    o The ALS ambulance with the smallest RT is assigned to respond to the incident.

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   Step 4. Update ambulance state:

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    o The assigned ALS will remain busy for the duration: OT = RT + AT + TT, see equation (1), where:

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     ⁃ RT = Response time to the incident location (simulated with SEMSIM).

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     ⁃ AT = Assistance time (retrieved from the SEM dataset).

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     ⁃ TT = Trip time to the hospital (if transport is needed, simulated with SEMSIM).

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    o If transport to the hospital is required, the ambulance will travel to the designated hospital and change to “free” state upon arrival.

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   Step 5. Return to base:

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    o After the busy period (OT seconds), the ambulance’s state changes back to “free,” and it returns to its base location.

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  end

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  Description: This algorithm assigns ALS ambulances in real time based on SEM operational policies, minimizing response times and efficiently managing the availability of resources.

To know the state of an ambulance (i.e., if it is busy assisting another incident or available to be chosen to assist the new incident), we compute the time elapsed from the activation moment of the last incident to which that ambulance was assigned to the current moment (T_elapsed), see Algorithm 2. If the time elapsed is higher than the last OT, using equation (1), obtained for that ambulance (T_elapsed > OT), it means that the ambulance has already finished assisting its last incident assigned, so that now the ambulance is free (ALS_st = free). Thus, the ambulance will be included in the set of available ambulances to be chosen for the new incoming incident, according to Algorithm 1. Otherwise, the ambulance is still busy (ALS_st = busy) and therefore cannot be considered to attend the new incoming incident.

Notice that SEMSIM (and the EMS in real life) could also know the state of the ambulances (free, busy) once they change their state and communicate it to the EMS. However, for the sake of accurate and up-to-date knowledge of the state of the ambulance fleet, Algorithm 2 tracks the current locations of the ambulances and updates their OTs as soon as they arrive to destination (e.g., incident location, hospital, and base). To achieve this, we assume that the ambulances use a geolocation device and that the EMS tracks the location of the ambulance fleet. This is a reasonable assumption and we certainly know that the SEM applies it. In this way, once the ALS arrives at destination (e.g., the hospital), it updates its OT and becomes available.

Algorithm 2: Find out the state of the ALS ambulances.
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  Input:

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   • SEM dataset of incidents from 2018 to 2019 in Terres de l’Ebre.

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   • Ambulance details:

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    1. Number of ALS ambulances (N_ALS) in the Sanitary Region: Four in Terres de l’Ebre.

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    2. Activation time (t_i) of the last incident to which ambulance ALS_i was assigned, i € (1 … N_ALS).

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    3. Occupation time OT_i regarding the last incident to which ambulance ALS_i was assigned, i € (1 … N_ALS). Calculated in Algorithm 1.

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  Output:

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   • ALS-state_i,t: Free or busy. State of each ALS ambulance i at moment t, i € (1 … N_ALS).

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  i = 1;

•  

  whilei ≤ N_ALSdo

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   Compute T_elapsed, i = Time elapsed from the activation moment t_i of the last incident to which ambulance i was assigned, to the current moment:

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   ifT_elapsed,i > OT_ithen

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    ALS_st, i, t = free; ambulance ALS_i already finished its last assigned service and it is free.

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   else

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    ALS_st,i,t = busy; ambulance ALS_i is still busy with its last assigned service.

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   end

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   i = i + 1;

•  

  end

•  

  Description: This algorithm finds out the state (free or busy) of each one of the ALS ambulances of the Sanitary Region.

6.1. Results of 4 Ambulances in 4 Bases

Our dataset consists of all 4001 incidents that occurred in TE during 2018 and 2019. Table 6 shows the results of the simulations for all the scenarios with n = 4 ambulances combined with r = 4 bases. There is a total of 35 possible configurations, i.e., combination with repetition C_4,4 = 35. The goal is to explore if there is a better alternative configuration than the current 1111 (i.e., 1 ambulance per base), after carrying out all the 35 simulation scenarios with SEMSIM. We have arranged the configurations in the table in descending order of the average RT ($$) obtained with SEMSIM. This enables us to promptly identify the top configurations that yielded the lowest $$, providing the most efficient service as ambulances arrived faster compared to other configurations.

As observed in Table 10, configuration 1111, representing one ambulance at each base, yields the lowest average RT $$. This configuration is the current ambulance deployment in TE. To sum up, the SEMSIM results reveal that the current configuration of ambulances is the best possible among all the possible configurations that arrange 4 ambulances in the 4 bases following a fixed policy. Nonetheless, maybe there are other better dynamic configurations that could further reduce the RT, as we will see in the next sections.

Results also show us that the second-best configuration is configuration 1021, which means moving one ambulance from Base B to Base C. That configuration has a RT which is 1 min 30 s higher than the best configuration 1111. Similarly, the third best option is configuration 1120, which means moving one ambulance from Base D to Base C. That configuration has an RT 1 min 38 s higher than the best configuration 1111. These results could be useful for instance in case Bases B or D should be annulled temporary (e.g., due to some kind of works in the street), and then their ambulances could be reassigned to Base C as the best option.

7.1. Geographical Distribution of Incidents and Ambulance Base Location in TE

Looking at the geographical distribution of incidents shown in Figure 11, we can see that as expected, incidents are quite concentrated near the coast and near the largest villages (Tortosa, Amposta, Sant Carles de la Ràpita, Deltebre, Alcanar, and Ametlla de Mar). However, we anticipate that this geographical distribution could change throughout the year, as we will see in the next section.

7.2. Temporal Distribution of Incidents in TE

In this section, we will analyze which times of the day and which seasons of the year have a greater concentration of incidents throughout the territory. Also, we will analyze which temporary intervals suffer the longest ambulance RTs. In Table 10, we see that configuration 1111 shows the best performance with minimum $$ that equals 8.28 min. Note that this RT is averaged for the whole 2018-2019 period.

However, during the summer, there is an increase in tourism and recreational activities, leading to a higher number of incidents, particularly in tourist zones. This influx can result in elevated $$. Another case of interest is weekend nights, when there is more nightlife (especially in summer) which causes more incidents that affect the RT. These factors contribute to an overall increase in the RT, and the EMS could implement some measures to reduce it. However, it would be advisable to identify those specific moments of the day and of the year that have a significant increase in RT throughout the different areas and then reinforce the system during those specific intervals in the SR. By doing so, we could minimize the $$ and manage the available resources much more efficiently, which also saves money, compared to blindly trying to improve it overall. That is, we want to examine in depth the temporal and geographical distribution of incidents that affect RT in order to act accordingly.

Table 7 shows the percentage of incidents in each temporal division. We can see that in general in TE: (i) there are more incidents during the day (6.31 incidents/day) than during the night (3.57 incidents/night); (ii) there are more incidents during weekend (6.03 incidents/day) days than during working days (5.26 incidents/day); and (iii) there are slightly more incidents in summer (5.59 incidents/day) than in winter (5.36 incidents/day).

To complement Table 7, Figure 5 depicts the average RT for each of the 7 time intervals presented in the list above. There is a slight 10 s increase in the $$ during summer compared to winter (see blue columns). This is due to the summer holidays and the increase in activity in beach and other touristic areas, which increases the number of incidents (5.59 incidents/day). Additionally, there is a slight increase in $$ (9 s) on weekends (6.03 incidents/day) compared to weekdays (5.26 incidents/day), see purple columns, for similar reasons. Figures show confidence intervals (CIs) of 90%.

In terms of time divisions throughout the day (see orange columns in Figure 5), we can see that there is a slightly higher $$ (of 10 s) during the morning compared to night hours. The reason is that there are more trips during the morning (6.31 incidents/day) than at night (3.57 incidents/night). Although the number of incidents was similar in the morning and the afternoon, the RT is 21 s lower in the afternoon, which may be due to higher traffic conditions in the morning. Additionally, note that although the number of incidents at night (3.57 incidents/night) is around half of those in the afternoon (6.56 incidents/night), the $$ is approximately 10 s higher, likely due to the slightly slower RT of the EMS personnel to activate the vehicle at night and also reduced staffing at night.

Figure 6 displays the $$ of the 12 temporal subintervals defined in the list above. The figure is divided into four types of temporal intervals represented by four different colors: (i) Winter-Weekday in blue color; (ii) Winter-Weekend in purple color; (iii) Summer-Weekday in yellow color; and (iv) Summer-Weekend in green color. Each of these four intervals has three bars representing morning, afternoon, and night. The maximum RT was 9 min during summer weekend mornings (green column S/E/M).

Observing the data, we can see a clear correlation between people’s outdoor activities and an increase in ambulance RTs. This correlation is expected, as higher levels of activity lead to more incidents during those time intervals. Consequently, ambulances face increased demand during these periods, inevitably resulting in longer RTs.

Having examined Figure 6 and pinpointed time intervals with elevated ambulance RTs, our attention can now be directed toward optimizing support during these periods to mitigate RTs. This optimization may involve the strategic relocation of specific ambulances or the incorporation of additional support units during intervals with extended RTs. Subsequent sections will delve into addressing and implementing these enhancements.

7.3. Results for 5 Ambulances in 4 Bases

In this section, we consider a scenario where the EMS receives government funding to improve RTs in the TE SR and acquires a new ALS resource.

The question now rises: In which of the four bases in this SR should the new ambulance be assigned to achieve best reduction in the RT? Our tool SEMSIM can help the EMS to conduct some easy simulations to quickly obtain statistical results and analyze which would be the best option.

This way, we have successfully conducted simulations of the incidents using 5 ambulances distributed among the 4 bases in TE, resulting in a total of 56 different possible configurations, i.e., combination with repetition n = 5 ALS, m = 4 bases, CR_5,4 = 56. These configurations are presented in Table 11, arranged in descending order of RT, so we can see the best options at the top highlighted in bold.

Analyzing the 56 configurations in Table 11, we first observe that the top 4 configurations only differ in around 18 s. This indicates that the EMS would have flexibility and could select the base that aligns most effectively with their requirements, considering factors beyond just the $$, given the marginal difference between them. Those 4 configurations maintain one ambulance at each base and add the additional ambulance at one of the four bases.

These 4 configurations achieve a reduction in $$ of more than 1 min compared to all the other 52 cases, where we can see that at least one base has no ambulance.

Furthermore, we can see that with 5 ambulances and 4 bases, the $$ has decreased by just 37 s compared to the current configuration 1111, see Table 10. Thus, this option does not seem very beneficial.

7.4. Results for 5 Ambulances in 4 Bases, With a Mobile Support Ambulance (MSA) Shared Among the Bases

Based on the results from the previous section, we pose the following question: Why must the new additional ambulance be permanently assigned to a specific base throughout the entire year? This question is particularly relevant after analyzing Figure 6. Alternatively, we suggest deploying the additional ambulance as a reinforcement to support all bases.

This way, the ambulance can be dynamically allocated among the four bases according to where it is most needed during each time interval. This approach may effectively minimize $$. Of course, there might be other interesting schemes for dynamic ambulance location, e.g., the possibility of placing 4 ambulances (without adding a 5th ambulance) dynamically on the 4 bases. If an EMS deems this alternative appropriate, it could easily be explored. However, after discussion with the SEM team, they suggested exploring the benefit of a single dynamic ambulance, considering EMS staff contracts and schedules.

This objective is in line with the fact that incidents do not occur with the same geographical or temporal distribution throughout the year, but rather, for example, they are more concentrated at certain times of the day, on weekends, and in tourist areas during the summer.

To explore this idea, we have used the 12 temporal subintervals as we did in Section 7.2. To display the $$ results obtained after simulating these 12 temporal subintervals, we have divided them into 4 figures representing the following time intervals: (i) Winter-Weekday; (ii) Winter-Weekend; (iii) Summer-Weekday; and (iv) Summer-Weekend.

Next, we show four figures that represent the $$ per base comparing the current 1111 configuration to a new configuration that includes a MSA in one of the bases for each one of the 12 temporal subintervals of the year, see Section 7.2. Each of the four graphs comprises three divisions corresponding to temporal intervals categorized into the following hourly day segments: Morning, Afternoon, and Night. Inside of each one of these temporal intervals there are 4 colored bars representing the $$ that we obtained per base by adding an extra ambulance to each one of the bases. Colored bars represent the RT of the ambulances assigned to each base: (i) for the current configuration 1111; (ii) for the MSA cases where the extra ambulance was added to each base.

In Figure 7, we can note two cases that notably improve compared to the current configuration (1111) thanks to the MSA scheme: (i) during the mornings, Base A would reduce its RT in 6 min thanks to the MSA, which represents a 49% of improvement (see purple bars during mornings); and (ii) during the nights, Base B would reduce its RT in more than 1 min, which represents a 10% of improvement (see green bars during nights). In the rest of periods, there is no significant improvement due to the MSA support.

Figure 8 shows the same results for winter weekends. During this temporal period, the MSA is useful for the 3-day segments: (i) during mornings and afternoons, Base B would reduce its RT in more than 3 min thanks to the MSA, equivalent to 28% reduction (see green bars during mornings and afternoons); and (ii) during nights, Base D would reduce its RT in more than 1 min, equivalent to 24% reduction (see red bars during nights).

The benefits of adding a new MSA during summer weekdays are shown in Figure 9: (i) during mornings and afternoons, Bases C and D would experience a reduction around 30% in the RT thanks to the MSA, which equals to around 3 min for Base C and more than 1 min for Base D (see blue and red bars during mornings and afternoons); (ii) during nights, Base D would notably improve in 3 min, which represents a 61% reduction (see red bars during nights).

Finally, in Figure 11, we can analyze the RT reduction for the summer weekend cases thanks to the MSA support: (i) during mornings, Base B would reduce its RT in 5 min (38,6%) while Base D would reduce it in 2 min (29%); (ii) during afternoons, Base C would reduce its RT in 3 min (36%) while Base D would reduce it in 1 min (27%); and (iii) during nights, Base B would reduce its RT in 6 min (50%) while Base A would reduce it in 4 min (32%).

In Figures 7, 8, 9, and 10, we observe that Bases A and B typically show higher CI values, while Bases C and D usually present smaller ones. This is because Bases C and D, covering the southern area, are closer to each other and can provide mutual support if needed. In contrast, Bases A and B, covering the northern area, are farther apart, cover a larger area (see Figure 11), and handle fewer incidents (see Table 6). This variability in incident distribution and response distances (both close and far) contributes to the larger CI values for Bases A and B.

Of course, incidents during the transition between weekdays and weekends will be handled appropriately to ensure optimal service, assigning the best available ambulance at that time. Configuration changes for the fifth MSA will only be made when the other ambulance at the same base is not attending any service, to avoid impacting potential new incident victims.

Concluding, the SEMSIM tool helped us to see that the EMS could further reduce the $$ with the help of an MSA doing a dynamic assignment of the supporting ambulance to the four bases, throughout time along the day and the seasons of the year. The optimal assignment throughout the 12 temporal subintervals is shown in Table 8. The $$ using the dynamic MSA would be 6.49 min, which is 1.78 min lower than the $$ with the current 1111 configuration (see Table 10), and 1.16 min lower than the $$ with the best configuration with 5 fixed ambulances, see Table 11.

7.5. Results of 5 Ambulances in 5 Bases

After analyzing the previous two sections, we see that the reduction in the $$ thanks to the addition of an extra ambulance, either fixed assignation in Section 7.3 or dynamic assignation in Section 7.4, is of around 1 min. It is true that every second counts when it comes to saving lives and improving by 1 min is significant, but maybe we could further optimize the use of this additional ambulance. This is another example demonstrating how our SEMSIM tool can effectively assist EMS in exploring alternative solutions within realistic scenarios, enabling informed decision making aimed at optimizing the utilization of available resources.

The approach outlined in this section to optimize the utilization of the additional ambulance is as follows: Instead of assigning the new ambulance to assist one of the existing four bases, potentially leading to instances with two ambulances stationed at the same base, we propose assigning this extra ambulance to a new base.

This configuration ensures that the five ambulances are distributed across five distinct bases, thereby enhancing territorial coverage. As anticipated and validated by our simulation results, a more dispersed distribution of ambulances correlates with a more significant reduction in the average RT.

To implement this, we first studied where it would be optimal to build a new ambulance base. The SEM provided us with a list of possible locations for a new base in TE. The list was made up of the 22 primary health centers (PHCs) of this RS, whose locations are shown in the location icons of Figure 12: (i) four of the PHCs are the current ambulance bases (Móra d’Ebre, L’Ametlla de Mar, L’Aldea, and Roquetes) located in the red icons; and (ii) the remaining 18 PHCs, located in the green icons, are candidate locations for the new ambulance base.

In the next study, we simulated in SEMSIM the same 4001 incidents that happened in TE during 2017-2018, but now with five ambulances located each one in one of the five different bases: the four current ambulances in their respective current bases and the new extra ambulance located at one of the 18 possible new locations. That is, in each of the 18 simulations’ configurations, we assigned the additional ambulance to each of the 18 new candidate locations, while keeping the other 4 ambulances at their current bases.

Table 9 shows the results of the 18 simulated configurations. The configuration name corresponds to the location of the 5th new base. As in previous sections, the table shows the average RT and average OT of the ambulances in descending order of RT to visualize the best configurations at the top of the table. The best options are marked in Figure 12 with green circles, while the worst options are marked with red circles.

Table 9 indicates that the best new base to add our extra ambulance is Amposta (1st in the list). By including an ambulance at that location, we achieve an average RT of 7.10 min, which represents an improvement of 71 s compared to the current 1111 configuration (see Table 10) and of 52 s compared to assigning the 5th ambulance at Base A (configuration 2111), see Table 11.

Surprisingly, the RT obtained with 5 ambulances and 5 bases ($$ = 7.10 min) is barely the same (1 s worst) than the RT with 4 bases and the extra dynamic MSA ($$ = 7.08 min), see Section 7.4. In Appendix 1 we add a discussion of the costs associated to each alternative, which would help the EMS to decide between both similar solutions.

Figure 13 highlights (red circle) the Amposta base where the new 5th ambulance would be assigned, constituting the 11111 configuration. We can observe a higher density of incidents (blue icons) occurring around larger populations and coastal areas, logically indicating the need for optimal base locations in these regions as well. The results obtained from these simulations offer valuable insights by quantifying the need for reinforcement in the southern region of TE. Clearly, the SEMSIM tool proves instrumental in enabling the EMS to assess the impact of alternative options, providing them with objective data and results essential for making informed decisions.

All these examples are case studies that can be easily explored with SEMSIM. Other interesting cases, which we do not include due to space constraints, could be analyzed, such as the scenario with 5 bases and 5 ambulances, considering demand variations (winter/summer; weekdays/weekends; morning/afternoon/evening) in the ambulance location.

7.6. Results of 3 Ambulances in 4 Bases

The final study conducted in this work involves analyzing the potential consequences hypothetically reducing the number of ALS ambulances from four to three. Would such a reduction have a significant impact on the $$? If such a measure were to be considered, perhaps due to budget cuts in the health service, determining which base should be removed to minimize the impact on the population and achieve the lowest $$ with the remaining ambulances poses a complex challenge for the EMS. Addressing these questions is intricate, and we will explore how the SEMSIM tool can aid in decision making by providing objective results.

We have modified the SEMSIM code to simulate the 4001 incidents occurred in TE during 2018-2019 with only three ALS ambulances, considering all possible configurations. In this case, having three ambulances distributed across four bases gives us a total of 20 different configurations, i.e., combination with repetition m = 4 bases, n = 3 ALS. We simulated all CR_3,4 = 20 different configurations and we show the $$ and $$ in Table 12.

We can notice that the four most favorable configurations (in the top of the table) involve distributing the three ambulances among the four bases, with a difference of more than 1 min to the rest of configurations that have two or more ambulances at the same base. The best configuration in Table 12 is 1011, with an RT of 11.39 min. This configuration involves removing the ambulance assigned at the base L’Ametlla de Mar. The remaining three ambulance bases would be located on the map as shown in Figure 14. The RT with configuration 1011 (11.39 min) would be 3 min higher than the current configuration 1111 (8.28 min), see Table 10, and more than 4 min higher compared to configuration 11111 (7.10 min), see Table 9.

7.7. Discussion of the Previous Simulation Results

To close Section 7, we add Appendix 1 at the end of the manuscript where we summarize the main results of the RT achieved by each alternative ambulance configuration. Additionally, we also add Appendix 2 to include a basic cost analysis associated with each configuration to further aid decision making with the available budget. Also, we discuss the trade-off between RT reduction and cost incurred for each option.

To evaluate the SEMSIM performance with more recent data, we requested the latest dataset from SEM, which includes 2322 incidents from 2023 (after cleaning and filtering, as outlined in Section 4.2). We then calculated the same statistics presented in Section 4.4 for the 2018/2019 dataset to compare them with the new 2023 dataset. We have observed that they align closely, as it is shown in Appendix 3. We have plotted the 2023 incident locations on the map (see Figure A4 in Appendix 3), to compare them with the 2018/2019 incident locations shown in Figure 5. We can see that the incidents occur in similar areas.

Furthermore, by splitting the dataset into Winter/Summer, Weekday/Weekend, and Morning/Afternoon/Night, we observed comparable temporal distributions of incidents throughout the year, yielding results similar to those presented in Section 7.2.

Finally, we have fed the SEMSIM simulator with the new 2023 incident dataset for most of the alternative configurations analyzed in this study, and the results and conclusions closely align with those presented in the paper. Specifically, for the 1111 configuration (one ambulance per base) used to validate SEMSIM (see Section 6), we compared the simulation results to actual outcomes from the SEM dataset.

The percentage of mismatch in selecting the same ambulance is now 12.83%, which corresponds to 298 different selections out of 2322 incidents in the 2023 dataset. This mismatch rate is quite comparable to that of the 2018/2019 dataset, which stands at 13.49%. The reasons behind the discrepancy in the ambulance chosen in real life and in the simulator SEMSIM for the 2018/2019 dataset (13.49%) were analyzed in Section 6. Similar discussion applies for the 2023 dataset, since the mismatch rate is very similar (12.83%).

Based on this analysis, we can conclude that the SEMSIM simulator provides accurate results for evaluating the RTs of any ambulance and base location configurations, offering valuable insights for EMS decision makers.

7.8. Discussion of the Utility of SEMSIM for the EMS Decision Makers

Concluding, with SEMSIM the EMS can evaluate the potential outcomes of alternative base and ambulance configurations. Achieving this level of analysis in real life would be nearly impossible due to the logistical and operational challenges involved.