How NFORS data can help departments decide where to house new response units

Written by Tyler Buffington, Tyler Garner, & Joe Chop

In this blog post, we will explore how the operational data collected in NFORS can help inform decisions involving the placement of new units in a fire department. As an example, we will analyze data from Delray Beach Fire Rescue to provide quantitative insight into the question:

“What would be the impact of adding an additional ALS unit to a station?”

First due vs. non-first due responses

Fire departments commonly divide up their jurisdiction into “first due areas.” These areas identify the optimal fire station response to any given location. When a unit is required at an emergency incident location within a station’s first due area, it is generally deployed from the station. If the required unit type is not available at the first due station, then another station outside the first due area must send a unit instead. This response from outside a station first due area generally results in an increased response time to the incident location. The graphic below shows the division of first due areas for Delray Beach Fire Rescue.

As EMS calls usually account for the majority of calls for service, the analysis will focus on this type of calls. In order to do this, we assess every incident when an ALS unit was dispatched in the available data. Based on the address of the incident, we can determine which station should be first due. If the unit belongs to the first due station, then we call this a dispatch from the first due station. Otherwise, it was a dispatch from a non-first due station. A cumulative distribution function (cdf) plot is useful for comparing the response time distributions of the two types of ALS dispatches, which is shown below. The faster the line “climbs” to the 100th percentile, indicates the higher frequency of responses from that type station (first due vs. non first due).

The above plot shows the unit response time plotted on the x-axis and the corresponding percentile (or quantile) on the y-axis. The percentile refers to the percentage of unit response times that fall below the response time on the x-axis. For example, we can see from the plot that roughly 30% of responses from first due stations are faster than 4 minutes, and roughly 30% of responses from non-first due stations are faster than 6 minutes. We can also see that 90% of responses from first due stations fall below 8 minutes, but only 60% of responses from non-first due stations fall below 8 minutes. The difference in medians (the 50th percentiles) is also about 2 minutes with first due responses being faster. This visualization is useful because it shows the comparison of the entire response time distributions as opposed to a comparison of a single quantity such as the mean, which emphasizes the statistical nature of response time. The two curves can be thought of as two different lotteries. It is possible to “draw” a short response time from the red distribution and it is possible to “draw” a long response time from the blue curve, but on average, the blue curve is a better lottery.

Breaking it down by first due area

It may also be useful to examine the consequences of non-first due dispatches for each of the separate first due areas. This is shown in the plots below:

As expected, the response time distribution is better for all units deployed from station to incidents in their first due areas. However, the above plots show that the consequences associated with non-first due dispatches are more severe in some regions than others. This essentially comes down to how well other stations are able to “fill in” for a given first due station. Most of the station locations in the more populated regions of the city are close to multiple stations. In other words, their first due areas are smaller geographically speaking. If an incident occurs in these regions and the first due station cannot respond, it is likely that another station can respond in a relatively timely manner. Conversely, Station 116 has a larger geographic first due area to cover, meaning that if Station 116 is unable to respond, the next closest unit must travel a much longer distance. At first glance, this may seem to indicate that Station 116 would be the best place to add a new unit. However, up until this point, our analysis has not considered two other important factors of an emergency response system — which are first due reliability and simultaneous call volume.

First due reliability and factors that influence it

As previously stated, a major consideration for deciding which station should house a new unit is the station’s reliability. Here we define the station’s reliability as the fraction of units dispatched to incidents in a station’s first due area that are sent from the first due station. Imagine that an ALS unit is required at an incident location in the first due area of Station X. What is the probability that Station X sends the ALS unit as opposed to some other station? That is the idea behind the first due reliability. This quantity is important because a station with a high first due reliability can offset the consequences associated with non-first due dispatches.

A major factor that influences the first due reliability of a station is the number of units it houses. Obviously a unit cannot respond to more than one call at a time. For Delray Beach Fire Rescue, we observe that 65% of non-first due dispatches for ALS units occur while all of the respective units from the first due station are already responding to other incidents. Additionally, the tendency for multiple incidents to occur simultaneously in the first due area also affects the first due reliability of a station. Using this information, we can model the impact of adding new units as an improvement to the first due reliability of the stations that house them.

Putting it all together and understanding tradeoffs

The last consideration that we explore is the overall call volume for each of the stations’ first due areas. Stations with large call volumes in their first due areas greatly influence the overall response time distribution of the department. The tree diagram below shows all six stations of Delray Beach Fire Rescue and the metrics we’ve discussed that influence the potential impact of adding a new ALS unit including call volume, first due reliability, and response time.

Moving from left to right in the tree diagram, the first column contains the percentage of call volume for each of the first due areas. For example, 27% of all ALS units dispatched are responding to incidents in the first due area of Station 111. Of those units, 66% of them belong to Station 111. The 90th percentile response time of ALS units belonging to Station 111 responding to incidents in the first due area of Station 111 is 7 minutes and 32 seconds. Note that the 90th percentile is displayed here for simplicity; in reality, the response time modeled as a random draw from a distribution.

The tree diagram is useful for showing the tradeoffs between stations that could affect the impact of adding additional units. For example, the first due area of Station 116 exhibits the largest average difference in response times between first due and non-first due dispatches, but ALS units are only sent there 4% of the time. On the other hand, Station 111’s first due area has a much smaller average response time difference, but it has 27% of the call volume and only 66% of the units sent to this region belong to Station 111.

Modeling tradeoffs

As previously mentioned, the historical data can be used to generate rough estimates of the impact of a new ALS unit at each station. At a high level, these estimates are calculated by identifying cases in which the first due station could not respond because all of its units were busy, but it is likely that the station could have responded if it had one more unit. For these cases, we assign hypothetical response times based on the “from first due” response time distribution for that station. The table below shows an example of the results produced from this model.

As shown above, the model predicts that the best place for a new ALS unit is Station 111, which is the busiest station. The model expects that adding a new unit to this station would save 1,653 minutes of response time per year. For this department, the expected improvement follows a similar trend for the stations’ call volume. This measure may be different for other departments depending on their station’ call volumes, first due reliability, and delays due to non-first due dispatches.

Conclusions

In this blog post, we explore how NFORS data can provide insight to a department facing a decision of whether to purchase a new unit and where a new unit should be placed. We examined three metrics that can be calculated from NFORS data that can influence the potential impact of adding a new unit to a station:

• How often units are required in a station’s first due area (call volume)
• How often the station is able to respond to calls in its first due area
• The difference in response times between cases when the first-due station is able to respond and when other stations must send units instead

Lastly, we briefly introduced a model that is able to identify cases in which the first due station could not respond because all of its units were responding to other calls when an additional unit was required. For some of these cases, the first due station would have been able to respond if it had an additional unit. For these cases, we can replace the actual response times with response times from cases in which the first due station could respond. This allows for the calculation of an expected improvement in response times associated with adding a new unit to each station in a department. It is important to note that this analysis may vary if your department uses proximity based dispatching (closest unit).

If your organization participates in NFORS and you would like to see a similar analysis for your department contact us today at hello@i-psdi.org