Modelling fire brigade responses

In my last post I explained some of the processing of the London Fire Brigade incident data. In this post I look at the actual data and begin to consider what the impact of the proposed closure of Bow Fire Station.

This analysis is my intellectual property and is produced for my intellectual curiosity and to encourage others to think how data can be used to understand the world around us. 

So as a quick recap from the last post, I have now calculated the distance from each of the 23,000 incidents in Tower Hamlets to eight fire stations (see below) using two methods.

With this distance data, I have flagged each incident as to whether or not the station nearest the incident was the first to respond. However, just because the nearest station didn’t respond doesn’t mean that a response will necessarily be slower; for example another station may have responded because of particular quirks of geography, or because of the designation of ‘grounds’ that each station serves.

Excluding the data that doesn't include  a record of which station responded, I can state that:

• In 64% of all incidents, the closest station responded first; which increases to 73% in the case of actual fires
• In incidents responded to by the nearest fire station, the response was on average 73 seconds quicker than for incidents not attended by the nearest fire station; this increases for instances of actual fire to 84 seconds.

We can see this visually in the chart below, where there is a significant difference in response time.

	False Alarm	Fire	Special Service	Grand Total
Number of incidents responded to by:
Nearest station	6,444	3,942	4,656	15,042
Other Station	2,793	1,103	1,161	5,057
Total	9,237	5,045	5,817	20,099
% of incidents responded to by:
Nearest station	66.36%	72.91%	56.23%	64.29%
Other station	33.64%	27.09%	43.77%	35.71%
Average time for first engine to arrive (seconds):
Nearest station	241	256	272	255
Other station	307	340	363	327
All	261	275	290	273

There are a small number of incidents which were responded to by fire stations outside of Tower Hamlets. To simplify and to avoid any potential skew in my analysis I’ll be applying some filters to the data.

The table below shows the number of incidents in Tower Hamlets that each fire station was the first to respond to. The six Tower Hamlets fire stations and ‘NULL’ (ie no station or response time was logged) make up the top 7. Millwall, which is ranked at number 7, responded to twice as many incidents as Shoreditch the next highest placed station, which in turn responded to 7 times as many incidents as Homerton, which gives an indication of the drop-off in responses from stations outside of Tower Hamlets.

Responding station	Number of incidents responded to by station	% of incidents responded to
Poplar	4,858	20.76%
Bethnal Green	4,445	19.00%
Whitechapel	3,315	14.17%
NULL	3,299	14.10%
Bow	2,668	11.40%
Shadwell	2,223	9.50%
Millwall	1,515	6.47%
Shoreditch	718	3.07%
Homerton	101	0.43%
Silvertown	66	0.28%
Kingsland	63	0.27%
Dowgate	49	0.21%
Dockhead	20	0.09%
Stratford	19	0.08%
Plaistow	18	0.08%
Greenwich	5	0.02%
Clerkenwell	3	0.01%
East Greenwich	3	0.01%
Islington	2	0.01%
Stoke Newington	1	0.00%
Woolwich	1	0.00%
Deptford	1	0.00%
Hainault	1	0.00%
Tottenham	1	0.00%
Old Kent Road	1	0.00%
Euston	1	0.00%
Paddington	1	0.00%

In tranche 1 of my analysis, I will filter on the 6 Tower Hamlets stations, plus Shoreditch and Homerton which are near the border. In mapping the nearest station I will also include Stratford which is the next nearest station to Bow.

Question 1: what would happen if all incidents were responded to by the nearest fire station?

We know from the first table that 65% of incidents are responded to by the nearest fire station. But what if every incident was? The answer lies below:

On average, the responding fire station is 862 metres from the incident, whereas, if all incidents were attended by the nearest station, this would reduce to 721 metres, or a 16% fall.

Direct distance
Average distance between responding fire station and incident	865	882	841	862
Average distance between incident and nearest station	706	741	728	721
Reduction in average distance per incident	159	141	113	141
% Reduction in average distance per incident	18%	16%	13%	16%

 A similar reduction is evident on my‘perpendicular’ measure of distance.

Perpendicular distance
	False Alarm	Fire	Special Service	Grand Total
Average distance between responding fire station and incident	1,099	1,120	1,065	1,094
Average distance between incident and nearest station	892	942	919	912
Reduction in average distance per incident	207	178	146	182
% Reduction in average distance per incident	19%	16%	14%	17%

However, this is looking at all incidents. If we focus attention on those where the nearest station didn’t respond, we logically see a greater difference. Indeed, the data shows that if the nearest station responded, the distance reduces by 40% on both measures, reducing the average distance by 600m. What’s most interesting is that I have already excluded the incidents responded to by stations beyond the immediate boundaries of the borough.

Direct distance: incidents where the nearest station didn’t respond
	False Alarm	Fire	Special Service	Grand Total
Average distance between responding fire station and incident	1,289	1,536	1,448	1,379
Average distance between incident and nearest station	743	863	855	795
Reduction in average distance per incident	546	673	593	584
% Reduction in average distance per incident	42%	44%	41%	42%

  

Perpendicular distance: incidents where nearest station didn’t respond
	False Alarm	Fire	Special Service	Grand Total
Average distance between responding fire station and incident	1,648	1,917	1,817	1,745
Average distance between incident and nearest station	945	1,084	1,073	1,004
Reduction in average distance per incident	703	832	745	741
% Reduction in average distance per incident	43%	43%	41%	42%

Question 2: What would be the impact of Bow Station closing?

So for this question, I looked at the incidents that Bow Fire Station attended. Had Bow station closed pre-2009, fire appliances would have been required  to travel 67% further on the direct basis and 56% on the perpendicular basis. It is sensible to assume an increase in response time would be inevitable.

  

Direct distance: impact of closure of Bow station
	False Alarm	Fire	Special Service	Grand Total
Average distance between Bow fire station and incident	982	883	873	915
Average distance between incident and nearest station other than Bow	1,460	1,564	1,578	1,531
Increase in average distance per incident	478	681	705	616
% Increase in average distance per incident	49%	77%	81%	67%

Perpendicular distance: impact of closure of Bow station
	False Alarm	Fire	Special Service	Grand Total
Average distance between Bow fire station and incident	1,283	1,138	1,125	1,186
Average distance between incident and nearest station other than Bow	1,748	1,913	1,912	1,853
Increase in average distance per incident	465	776	787	667
% Increase in average distance per incident	36%	68%	70%	56%

However, in 80% of the incidents dealt with by Bow, Bow was actually the closest station. Had Bow been closed the average distance to the next nearest station would on average be a further 1km further away. For these incidents we are broadly talking about more than doubling of distance.

Direct distance: impact of closure of Bow station on incidents where Bow was the closest station
	False Alarm	Fire	Special Service	Grand Total
Average distance between Bow fire station and incident	705	715	740	721
Average distance between incident and nearest station other than Bow	1,723	1,708	1,708	1,713
Increase in average distance per incident	1,018	993	968	991
% Increase in average distance per incident	144%	139%	131%	137%

Perpendicular distance: impact of closure of Bow station on incidents where Bow was the closest station
	False Alarm	Fire	Special Service	Grand Total
Average distance between Bow fire station and incident	901	923	951	927
Average distance between incident and nearest station other than Bow	2,045	2,081	2,062	2,062
Increase in average distance per incident	1,144	1,159	1,110	1,135
% Increase in average distance per incident	127%	126%	117%	122%

Question 3: How would that affect the response time?

To understand the impact on response time, we need to know the relationship between distance and speed. For each incident I calculated an average speed to see if longer distances allowed faster average speeds to be achieved. I plotted distance and speed on a scatter graph to see if visually there was a relationship. There were some very odd results.

The speed of sound is about 340m per second. The vertical axis below shows speed in metres per second.

On further probing, there were 88 lines of data where average speed was greater than 30 metres per second (67.5mph) and the maximum speed I calculated was over 479m per second, or just over 1,000mph.

I initially thought that this might be the result of the rounded location affecting very short distances- in fact, this particular data point was for a journey of over a kilometre. I don’t know if this is indicative of a systematic flaw in how response times are recorded, or just a few erroneous outliers. I reran the above analysis excluding these data points and the difference was immaterial (these are, after all, 88 points averaged over 23,000).

Eye-balling the data plotted in the scatter graph below indicates a positive correlation, though the nature of the correlation needs investigation.

So, there does appear to be some link between speed and distance (greater distance allows faster speed) but the relationship is not clear and would require a regression to establish what factors, such as time of day affects the speed. If I find time I might investigate further.