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Construction of a dynamic arrival time coverage map for emergency medical services

Adam Piórkowski
  • Corresponding author
  • AGH University of Science and Technology, Department of Geoinfomatics and Applied Computer Science, A. Mickiewicza 30 Av., 30–059 Krakow, Poland
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Published Online: 2018-06-11 | DOI: https://doi.org/10.1515/geo-2018-0013


This article presents a design of coverage maps for emergency journeys made by emergency medical services. The system was designed for the Malopolskie Voivodeship Office in Cracow, Poland. The proposed solution displays maps of the ambulance coverage of areas and ambulance’s potential journey times. There are two versions of the map: static and dynamic. The static version is used to appropriately allocate ambulances to cover an area with the ability to reach locations in less than 15 or 20 minutes; the dynamic version allows monitoring of ambulance fleets under normal conditions or in the event of a crisis.

The article also presents the results of archival data related to the movement of ambulances on the roads of Malopolskie Voivodship. Particular attention was paid to the relation between the speed of vehicles and the traffic on the road, the day of the week or month, and long-term trends. The collected observations made it possible to assume a general model of ambulance movement in the voivodeship to calculate arrival time coverage maps.

Keywords: routing; GIS; network analysis; ambulances; emergency medical services; coverage maps; arrival time coverage map; vehicle characteristics

1 Background

Coverage maps are commonly associated with analyses of the availability of mobile telephony. These maps display areas according to the power of the available telecommunications signal, but this is not the only application. Various map solutions are implemented in the field of health and safety: for example, coverage maps can be created for the analysis of immunization areas [1] or the degree of patient choice and competition between Adult Congenital Heart Disease Centers, based on a feasible travel time of 120 minutes [2]. A similar case of hour service areas for hospital are presented in [3]. Another example is presented in [4], which describes a solution that provides the geographic information needed to support real-time routing of alerts for accidents to the nearest air medical transport service. This paper describes the authors’ development of the Atlas Database and the Air Medical Services Database. The map shows circular areas that can be reached by aircraft in 10, 20 or 30 minutes. Coverage maps can be also treated as a component of the Smart City solutions [5].

In the context of ambulance travel, some examples of coverage maps can be also given. In [6], polygon map overlays showing 8- and 15-minute arrival times for the city of Haifa are presented. Time-based Ambulance Zoning was presented in [7], and [8] presents simulation-based probability-of-coverage maps that demonstrate the probability that the nearest available ambulance can respond to a call. Probability-of-coverage maps are also mentioned in [9]. Another strategy to reduce the average response time from the initial call to the arrival of ambulances in Singapore using geospatial-time analysis is presented in [10] and are presented as coverage maps. Analysis of ambulance coverage within 10 minutes in Samsun, Turkey is the scope of [11]. [12] shows a solution which makes it possible to plan ambulance distribution to maximize the coverage efficiency for a given number of ambulances in any particular area in Johor Bahru (Malaysia). In [13], a predicted future call coverage map is discussed. [14] presents another solution in which maps display analyses of the fastest routes to incidents and the average response time with associated serviceability in North Dakota, USA. A computational model of demand, bases and distribution of hospitals in Melbourne is presented in [15]. An analysis of rural area coverage by EMS in Western Cape, South Africa is presented in [16]. The ambulance deployment and demand coverage for Odunpazari District (Turkey) is shown in [17] with a 5 minute response time as the goal. In [18], the probability of the nearest ambulance arriving within 4 minutes is presented for Toronto using the city road grid as the reference map. The general issue of ambulance redeployment has also been covered by numerous additional articles [12, 15, 19, 20, 21, 22, 23, 24, 25].

This papers outlines the construction and determination of ambulance coverage mapping that can be updated in real time. For a given area (represented by a properly prepared grid), it graphically represents the shortest driving time of a ambulance. The aforementioned solution was designed in 2015 for the Malopolskie Voivodship Office [26]; and includes not only static analysis of sample stationary ambulance patterns, but also real-time dynamic analysis of emergency situations.

2 Methods

2.1 Maps

The basic element of the project is the map. The WGS84 reference system is used for all visualizations and calculations. The project was limited to the map of the Malopolskie Voivodship. The most important issue here is the representation of the area in context of the visualization of the potential travel times of ambulances. In [27, 28], the analyzed area is represented as a grid of intersections; in [2], a coverage map defines travel times from general medical practitioners (a list of 11,631 postal codes) to ten ACHD (Adult Congenital Heart Disease) centers. The project described in this article assumes representation of an area as an orthogonal grid whose points are 250 m apart in urban areas, while 1000 m intervals are considered sufficient in rural areas. The grid G is constructed as a list of points Pi, for which each is assigned coordinates and a unique identifier.




  • Pi - point of grid,

  • G - grid of points (set of points).

This solution allows for flexible representation of an area, with high-density classification in urban areas (Fig. 1, e.g. Cracow and neighborhoods) and low-density classification in areas where points are meaningless (e.g. lakes). Selected points can be moved to other representative locations, and special points such as hospitals or known fixed ambulance stations can be added.

Grid example for Cracow and neighborhood
Figure 1

Grid example for Cracow and neighborhood

The locations of stationary ambulances A on standby are essential and are rounded to the closest grid point of G. In order to increase the accuracy of the point grid, the appropriate ambulance stationing points designated by the Voivodship Office were added. In Malopolskie Voivodeship, the number of ambulances is variable and was 119 at the time the project was created.



  • A - set of ambulances,

  • Ai - current location point of ambulance i, Ai is equal to Pj (closest point of grid G).

2.2 Determining the pre-calculated times of ambulance journeys

In order to determine the ambulance journey times for the entire coverage map in real-time, a map of pre-calculated travel times (PT) was created that shows travel times between any two points of the grid in both directions [29, 30, 31, 32].


where PT[x, y] - travel time from Px to Py.

Determining travel times for a map of pre-calculated values is time-consuming because of the Cartesian product of all possible routes, therefore limits are imposed that allow irrelevant calculations to be rejected [33]. A custom plug-in for MapPoint was used for this project; calculations were then made on a cluster of 30 computers with Intel Core i7 processors, which took a several days to complete a map of the city of Krakow (distance 250 m) and Malopolskie Voivodship (distance 1000 m).

2.3 The model of ambulance velocities

One very important issue is to choose the general model of velocities that are characteristic for ambulances [34]. The typical driving model used by Google Maps and MapPoint determines the characteristic speed values for five types of roads:

  • Interstates (motorways),

  • Limited access roads,

  • Other (major) roads,

  • Arterial (minor) roads,

  • Streets.

The standard values for vehicles complying with standard traffic rules are determined by the vector (104, 96, 80, 56, 32) [km/h]. However, in the case of ambulances, these speeds are considerably higher, and so based on data collected from real-world systems, the value of these speeds were determined. For this, a system for calculating the inverse problem was created [35]. A Monte Carlo algorithm was used to match the velocity values of the simulated ambulance journeys that were closest to historical data. In this way, a velocity vector (145, 121, 82, 71, 38) was compiled with a compensation error of 13%. Further consideration is needed however to determine whether this model is sufficient to describe traffic regardless of time of day, or day of the week or month.

2.4 Verification of the model based on instantaneous speeds

Creating an ambulance traffic model is not an easy issue. There are few works that theoretically or empirically estimate this form of vehicle movement model [8, 9, 18, 27]. The primary problem is determining whether periodic increases in road traffic actually affect travel times [36] with or without traffic signal control [37, 38]. The author used data obtained from the Malopolska Office which contain approx. 450,000,000 records describing the time, current position of the ambulance, its status and instantaneous speed. These data were collected in the period 2013-2017 (2017: I-VI) from GPS devices mounted in ambulances. Records were generated every 2 minutes when stationary and every 30 seconds when moving (technical or call-related). These data were analyzed for daily fluctuations of traffic congestion with an accuracy of one hour, and graphs of mean instantaneous velocities were constructed. Also shown were the days of the week, months, and variations in subsequent years. The research outlines are shown in the graphs (Fig. 2, 3).

Average ambulance instantaneous speed for the entire voivodship by hour and day of the week; E - emergency trip, T - technical trip
Figure 2

Average ambulance instantaneous speed for the entire voivodship by hour and day of the week; E - emergency trip, T - technical trip

Average ambulance instantaneous speed for the entire voivodship by month; E - emergency trip, T - technical trip
Figure 3

Average ambulance instantaneous speed for the entire voivodship by month; E - emergency trip, T - technical trip

Analysis of the results allowed many intriguing conclusions to be drawn. The most important conclusion is that despite peak traffic, ambulance speeds on emergency callouts do not significantly change (max 2-4 km/h, in opposite to Shenzhen, [39]). This can be explained by the use of special bus lanes in cities and the culture of the drivers on the roads. This explanation also confirms the result that during technical trips (i.e. non-emergency), there is a significant reduction in ambulance speeds at peak road usage hours. Moreover, ambulances are not slowed down by traffic jams at weekends (Saturday and Sunday). Annually, there is a slight reduction in ambulance speeds (4km/h) in the winter. However, by comparing the speed of emergency trips to technical trips it can be concluded that one general ambulance model can be used if small deviations in speed are accepted.

Constructing the arrival coverage map

To calculate the coverage map CM, each grid point Pi should have calculated the minimum travel time from all standby ambulances:



  • Ai - current location point of ambulance i,

  • Pi - grid point i.

As a result, the calculated values for each grid point can be applied to the base map by giving the grid coverage of ambulances with the lowest call times. The coverage can be represented with color, e.g. the example scale uses shades of blue for times of 0-10 minutes; green for 11-15 minutes; yellow for 16-20 minutes; and red or black for more than 20 minutes. This is related to statutory travel times of 15 minutes within the city and 20 outside the city.

3 Results

The illustration shows an example of an arrival time coverage map for Cracow (Fig. 4, where two ambulances are on standby: one in the northwest and one in the south. Attention should be paid to the nonlinear nature of such coverage maps, as the journey time for points near motorway exits is significantly shorter than that for points in other areas. The coverage map also illustrates that the northeastern part of the city remains uncovered by emergency medical services within the 20 minute statutory time limits.

An example of arrival coverage map for Cracow (two ambulances) and time scale used (minutes); times in minutes refer to the following colors: 0-10 blue, 11-15 green, 16-20 yellow, 21-25 red.
Figure 4

An example of arrival coverage map for Cracow (two ambulances) and time scale used (minutes); times in minutes refer to the following colors: 0-10 blue, 11-15 green, 16-20 yellow, 21-25 red.

The coverage designated in the manner described above varies according to the type of urban area: densely built up with a regular and extensive road network (Figure 5(a)); adjacent to main roads with many junctions (Fig. 5(b)); and mountainous (valley) (Fig. 5(c)). Therefore, coverage maps could be of great use to local authorities when creating ambulance station mapping or in crisis situations. The system also implements additional layers related to population density and frequency of accidents based on historical data [29].

Heterogeneity of area characteristics
Figure 5

Heterogeneity of area characteristics

3.1 Real-time application

The calculation time of the coverage map in the tested model, with 21448 points covering the city of Krakow with an accuracy of 250 m and the remaining areas of the province with an accuracy of 1000 m, takes about 40 ms on a typical computer with Intel i5 Core CPU. A longer processing time may be caused by preparing a graphic view of map, but such tasks can be performed on the GPU. Therefore, the low requirement for computing power allow realtime depiction of the coverage of ambulance services. Fig. 6 presents a fragment of the map depicting a vehicle drive for two time moments (point A and point B). It is noticeable that the 10-minute access area (blue) is moving with the vehicle position. Such an application has been prepared for implementation by ambulance units of the Malopolskie Voivodeship Office.

An example of real-time coverage map. The ambulace is marked as a violet circle with a white dot.
Figure 6

An example of real-time coverage map. The ambulace is marked as a violet circle with a white dot.

4 Conclusions

This article describes a novel approach which supports ambulance fleet planning, management, and redeployment. The proposed solution makes it possible to present service coverage of urban and rural areas by EMS and produces real-time coverage maps that can be used by dispatch or crisis management centers.

The construction details of the proposed system are described in the article. An interesting issue related to the ambulance model based on instantaneous speed was discussed. The results of matching the characteristic velocities used by the network calculation systems are presented. Based on the collected speed data, it was determined that in the administrative area of Malopolskie Voivodeship the speed of ambulances traveling on call is not significantly affected by traffic jams. This proves that one general coverage map is a sufficient approach.

The first implementation of the system took place in 2015 and it was submitted for the Malopolskie Voivodeship Office as a tool supporting the Medical Rescue and Sanitary Unit of the Social Policy Department.

A sample application demo is available on the site:



The author would thank to Governor J. Miller; M. Lechowicz, S. Janusz and S. Choroba from Malopolskie Voivodeship Office; F. Banas from KPR and supporting team of M. Lupa, K. Szostek, I. Plokita, P. Lukasik, T. Pazdalski and R. Rumanek.

This work was financed by the AGH - University of Science and Technology, Faculty of Geology, Geophysics and Environmental Protection as a part of statutory project.


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About the article

Received: 2017-11-24

Accepted: 2018-02-22

Published Online: 2018-06-11

Citation Information: Open Geosciences, Volume 10, Issue 1, Pages 167–173, ISSN (Online) 2391-5447, DOI: https://doi.org/10.1515/geo-2018-0013.

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© 2018 Adam Piórkowski, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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