Appendix A - An Independent analysis of Vehicle Activated Sign (VAS) data for Lindsay Road
Background
A Vehicle Activated Sign, installed on the pavement outside the Victoria Education Centre in Lindsay Road,
has been measuring westbound traffic speeds for a number of years. In response to a Freedom for
Information request, Transportation Services have provided the latest available data from the VAS, as
processed by VMS Ltd, which covers a 24 hour period starting at 4:48 am on 29 August 2011. (The VAS is
reportedly still functioning, but there are data communication issues with VMS Ltd). Data was also provided
for another, this time randomly selected, 24 hour period starting at a similar time on 15 April 2011.
VMS Safewatch data display
The VMS Safewatch data sheet 1 describes the system’s data logging capabilities as:
Also optional is the Safewatch capability of recording, monitoring and reporting traffic flows. Vehicle
detection units capture data and a simple web-based graphical interface provides an overview of vehicle
speeds and traffic density from any internet-connected PC. Raw data is easily extracted to enable detailed
analysis and reporting.
Raw data apparently is not available, only the overviews.
The screen shots reproduced in Figures 1 and 2, show the VMS data displays for the two 24 hour periods.
The displays include the following information:

date and time that logging began,

date and time of logfile, (the times shown are 3 minutes less than 24 hours after the start of logging)

the total number of vehicle detections made during the data logging period,

a spreadsheet-style 2 dimensional table with 4km/h speed bands (columns) and twenty four one
hour time bands (rows),

the total number of vehicle detections for each speed band and a column chart of these totals,

the hourly number of vehicle detections and a bar chart of these quantities,

the hourly 85% speeds (in mph) and a bar chart of these speeds (the 85% speed is assumed to be
shorthand for the 85th percentile speed),

the overall 85% speed for the 24 hour period,

the cells in the table are coloured red to indicate speeds over the 85% hourly speed, and blue for
speeds under the 85% hourly speed. The intensity of the colour increases with the number in a cell.
Tabulated data
Each cell (or bin) of the 2 dimensional table contains vehicle detection data for a one hour period and a
4km/h speed band. However, instead of tabulating the actual number of vehicle detections in each cell, the
detections have been scaled as a percentage of the highest number of detections in any one hour period
and 4km/h speed range during the 24 hour period. The text above the table states: Graph showing the
quantity of vehicle detections per Hour per Speed Bin plotted as a percentage of the highest quantity. On this
basis (although the table is not a graph) one would expect there to be at least one cell containing the number
100. However, in the screen-shots and in the example shown in the VMS Safewatch data sheet, the highest
number in all cases is only 99. This is presumably to restrict the cell contents to two digits, but it is not clear
as to whether 99 means 99% or 100%.
The table rows are labelled 00:00 – 01:00, 01:00 – 02:00 etc. indicating one hour time periods, but the
columns are labelled <44, <48, <52 etc. This is somewhat misleading since the data in a cell with a column
heading of, say, <52 is not the data for all speeds up to 52km/h (ie cumulative data) but is the data for the
4km/h speed range 48km/h to 52km/h.
The row at the bottom of the table, gives speeds in miles per hour, but the conversions from km/h to mph
have all been rounded down to an integer rather than to the nearest integer. For example 48km/h should
convert to 29.83mph (to 2 decimal places) which is 30mph to the nearest integer, but only 29mph is shown.
This rounding down produces unnecessary biased errors of minus 0.5mph on average. There is likely to be
1
http://www.vmslimited.co.uk/pdf/Safewatch.pdf
Page 1 of 14
the same rounding down error in the 85th percentile speeds. It is also likely that rounding down has been
used for the cell contents making re-construction of the original data an impossible task.
85th percentile speed
The emphasis in the VMS data display is on the 85th percentile speed. The 85th percentile speed, in relation
to traffic flows, is discussed in MetroCount’s Speed_Analysis_1.pdf 2 and is defined as:
The speed at or below which 85% of all vehicles are observed to travel under free flowing conditions past a
nominated point.
Free flowing conditions are defined as:
A vehicle is considered to be operating under free flowing conditions when the preceding vehicle has at least
4s headway.
According to MetroCount the 85% speed under free flowing conditions is the normal operating speed for a
road, regardless of any speed limit. In order to obtain the speed for free-flowing conditions, the data for
vehicles with less than 4s headway is filtered out and therefore not included in the 85% speed calculation.
The rationale for using such a filter is that vehicles passing a point within 4s of each other is indicative of
traffic congestion and not free flow.
The VMS data display and Safewatch data sheet make no mention of a headway filter so that it must be
assumed that all of the recorded data has been used to calculate the 85% speeds. This means that the true
free flow 85th percentile speeds will generally be higher than those shown.
It is worth noting that if the vehicle speeds are normally distributed, then the 85 th percentile speed is equal to
the mean (or average) speed plus 1.04 standard deviations for the normal distribution. Under free flowing
conditions, the 85th percentile speed is likely to be around 10% to 15% higher than the average speed. The
data as presented does not give average speeds.
Figure 1
The Lindsay Road VMS screen-shots for the 15/16 April 2011 are reproduced in figure 1.
The cell with the highest value (99) is for the speed band < 44km/h and the time period 16:00 – 17:00.
Summing the cell contents for this speed band gives a total of 898 whilst the number of detections is shown
underneath the column as 1669. Assuming no rounding errors in the cell contents, then 99 equates to
99*1669/898 = 184 detections. Cross-checking this result by summing the row contents for 16:00 – 17:00
and using the hourly quantity shown at the end of the row gives 187 detections, but there is no data shown
for speeds below 12km/h which will influence the result.
Summing the hourly quantities gives 8322 vehicles, the same figure as given for the total quantity, but the
sum of the speed band detections only gives 8287 vehicles, indicating that 35 detected vehicles were
probably travelling at less than 12km/h or over 88km/h.
Figure 2
The Lindsay Road VMS screen-shots for the 29/30 August 2011 are reproduced in figure 2.
The cell with the highest value (99) is for the speed band < 48km/h and the time period 11:00 – 12:00. This
equates to around 144 detections.
Summing the hourly quantities gives 5954 vehicles, which is 141 vehicles less than the total quantity shown
as being 6095. The sum of the speed band detections is 5933 vehicles, which in this case includes speeds in
the 8km/h to 12km/h range, but not below.
Figures 3 and 4
These show histograms of the detections per speed band for the 15/16 April 2011 and 29/30 August 2011
respectively. The data is taken from the detection quantities per speed band shown in the screen-shots
expressed as a percentage of their sum. Also plotted are normal distribution curves that fit the central part of
the histograms. It can be seen that the data at high and low speeds (the tails of the distribution) do not fit the
normal distributions very well, especially at low speeds. Congestion will contribute to the low speed tail
unless it is filtered out, which does not appear to be the case.
Figure 5
2
http://www.metrocount.com/downloads/files/flyers/Speed_analysis_1.pdf
Page 2 of 14
It is easier to interpret the data when it is plotted as a cumulative speed distribution. (A cumulative
distribution is obtained by adding bin quantities together progressively, normally from right to left. This is a
numerical integration process).
The cumulative distributions shown in Figure 5 use the same data as in Figures 3 and 4, but the speeds
have been converted (exactly) from km/h to mph. Cumulative normal distributions that fit the data around the
median speed (the 50th percentile speed) are also plotted. Both the median and 85 th percentile speeds are
indicated. It can be noted that there are significant differences between the measured distributions and the
normal distributions outside of the range from 25mph to 35mph, particularly at low speeds. This has the
effect of making the average speeds generally somewhat less than the median speeds. The average speed
can be estimated by assuming that the vehicles in each speed band are travelling at the mid-band speed.
The table below shows the median and 85th percentile speeds obtained from the cumulative plots, the
estimated average speed from the total detections in each speed band, and the overall 85% speed shown in
the VMS data displays.
Date
Median speed
Average speed
(mph)
(mph)
85th percentile speed (mph)
Figure 6
This figure shows how the traffic flow varies during the two 24 hour periods. The hourly quantities shown in
the VMS data displays have been plotted against the midpoint of each one hour period. The graphs replicate
the hourly quantity bar charts in the VMS displays.
Figure 7
The hourly 85th percentile speeds shown in the VMS data displays are plotted against the midpoints of each
one hour period in figure 7. The graphs replicate the hourly 85% mph bar charts in the VMS displays.
Figure 8
The hourly 85th percentile speeds (as calculated by VMS Ltd and plotted in figure 7) are plotted against the
hourly quantities (shown in figure 6). The linear trendline for the speed/flow relationship is also shown. This
approximates the 85th percentile speed to (38.8 – 0.0176*Q)mph where Q is the traffic flow in vehicles per
hour (vph). It can be seen that there is a fairly strong correlation between 85 th percentile speeds and the
traffic flow.
Figure 9
The median speeds for each one hour period were estimated from the VMS data (by accumulating the
values in the relevant speed bins, normalising and interpolating to find the 50 th percentile speeds). These
estimates are plotted against the hourly quantities. The linear trendline is also shown. This approximates the
median speed to (33.75 – 0.0116*Q) mph where Q is the traffic flow in vehicles per hour (vph).
Figure 10
The cumulative vehicle speed distributions for different periods of the day (15/16 April 2011) are plotted in
figure 10. These distributions were obtained using the data shown in the cells of the VMS data display table.
The data was summed to give totals for the periods midnight to 6am, 6am to noon, noon to 5pm and 6pm to
midnight. The data for 5pm to 6pm was not included in the 6 hour period from noon since it had the highest
traffic flow and lowest speeds and is shown separately. The traffic flows for each period were calculated and
are shown alongside the time periods.
Figure 11
This figure shows the number of vehicles exceeding the speed limit plotted against their excess speed for
each of the two 24 hour periods. Due to the large numbers exceeding the 30mph limit, a logarithmic scale is
used. A trendline for the 15/16 April 2011 indicates an exponential relationship N = 2655 e -0.3V between the
number of speeding vehicles (N) and their excess speeds (V). It can be noted that around 600 vehicles a day
exceed the recommended Fixed penalty speed of 35 mph.
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Figure 1
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Figure 2
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Histogram of vehicle speeds for 15/16 April 2011
and a normal distribution 'bell' curve
Vehicle detections
(% of total)
30.00%
25.00%
Normal distribution
Vehicle detections
20.00%
Normal distribution parameters:
Mean = 45.9 km/h (28.5 mph)
Standard deviation = 6 km/h (3.7mph)
15.00%
10.00%
5.00%
0.00%
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
Speed (km/h)
Figure 3
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Histogram of vehicle speeds for 29/30 August 2011
and a normal distribution 'bell' curve
Vehicle detections
(% of total)
30.00%
25.00%
Normal distribution
Vehicle detections
20.00%
Normal distribution parameters:
Mean = 48 km/h (29.8 mph)
Standard deviation = 6.1 km/h (3.73mph)
15.00%
10.00%
5.00%
0.00%
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96 100 104
Speed (km/h)
Figure 4
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Cumulative speed distributions over 24 hours
Cumulative
percentage
100%
90%
80%
29/30 August 2011 data
70%
Normal distributions shown as
red dashed curves
60%
50%
40%
15/16 April 2011 data
30%
20%
10%
0%
0
5
10
15
20
25
30
Median speeds
35
th
40
85 percentile speeds
45
50
Speed (mph)
Figure 5
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Hourly number of vehicle detections versus time of day
Vehicle detections
per hour
700
600
500
400
300
200
15/16 April 2011
29/30 Aug 2011
100
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time of day (24 hour clock)
Figure 6
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th
Hourly 85 percentile speed versus time of day
Speed (mph)
45
40
15/16 April 2011
29/30 August 2011
35
30
25
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time of day (24 hour clock)
Figure 7
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th
Hourly 85 percentile speed versus hourly quantity
Hourly 85th percentile
speed (mph)
45
15/16 April 2011
29/30 August 2011
Linear trendline
40
35
30
25
0
100
200
300
400
500
600
700
Hourly quantity (vph)
Figure 8
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Hourly median speed versus hourly quantity
Hourly median speed
(mph)
40
15/16 April 2011
29/30 August 2011
Linear trendline
35
30
25
20
0
100
200
300
400
500
600
700
Hourly quantity (vph)
Figure 9
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Cumulative
percentage
Cumulative speed distributions during 15/16 April 2011
100%
90%
80%
Time of day (average flow)
00:00 - 06:00 (77 vph)
70%
06:00 - 12:00 (433 vph)
60%
12:00 - 17:00 (538 vph)
17:00 - 18:00 (595 vph)
50%
18:00 - 24:00 (329 vph)
40%
30%
20%
th
10%
85 percentile range
28.5mph to 39.5mph
0%
10
15
20
25
30
35
40
45
50
Speed (mph)
Figure 10
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Number of vehicles per day exceeding 30mph
in Lindsay Road plotted against excess speed
Number in 24 hours
(log scale)
10000
15/16 April 2011
Example: on 29/30 August 2011, 200 vehicles
exceeded the speed limit by 10mph and over.
29/30 August 2011
1000
Trendline 15/16 April 2011
Example: on 29/30 August 2011, 50 vehicles
exceeded the speed limit by 20mph and over.
100
10
1
0
5
10
15
20
25
30
35
Excess speed (mph)
Figure 11
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