Appendix A - An Independent analysis of Vehicle...

Appendix A - An Independent analysis of Vehicle Activated Sign (VAS) data for Lindsay Road

BackgroundA 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 dataEach 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

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http://www.vmslimited.co.uk/pdf/Safewatch.pdf

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 speedThe emphasis in the VMS data display is on the 85 th 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 2The 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 4These 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

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http://www.metrocount.com/downloads/files/flyers/Speed_analysis_1.pdf

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

(mph)

Average speed

(mph)

85th percentile speed (mph)

From plots VMS value

15/16 April 2011 28.2 27.8 32.2 31

29/30 August 2011 29.7 29.4 33.9 33

Figure 6This 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 7The 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 8The 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 9The 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 10The 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 11This 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 2011and a normal distribution 'bell' curve

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88Speed (km/h)

Vehicle detections(% of total)

Normal distributionVehicle detections

Normal distribution parameters:Mean = 45.9 km/h (28.5 mph)Standard deviation = 6 km/h (3.7mph)

Figure 3

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Histogram of vehicle speeds for 29/30 August 2011and a normal distribution 'bell' curve

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104Speed (km/h)

Vehicle detections(% of total)

Normal distributionVehicle detections

Normal distribution parameters:Mean = 48 km/h (29.8 mph)Standard deviation = 6.1 km/h (3.73mph)

Figure 4

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Cumulative speed distributions over 24 hours

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15 20 25 30 35 40 45 50Speed (mph)

Cumulativepercentage

85th percentile speedsMedian speeds

15/16 April 2011 data

29/30 August 2011 data

Normal distributions shown as red dashed curves

Figure 5

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Hourly number of vehicle detections versus time of day

0

100

200

300

400

500

600

700

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)

Vehicle detectionsper hour

15/16 April 2011

29/30 Aug 2011

Figure 6

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Hourly 85th percentile speed versus time of day

25

30

35

40

45

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)

Speed (mph)

15/16 April 2011

29/30 August 2011

Figure 7

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Hourly 85th percentile speed versus hourly quantity

25

30

35

40

45

0 100 200 300 400 500 600 700Hourly quantity (vph)

Hourly 85th percentilespeed (mph)

15/16 April 2011 29/30 August 2011 Linear trendline

Figure 8

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Hourly median speed versus hourly quantity

20

25

30

35

40

0 100 200 300 400 500 600 700Hourly quantity (vph)

Hourly median speed (mph)

15/16 April 2011

29/30 August 2011

Linear trendline

Figure 9

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Cumulative speed distributions during 15/16 April 2011

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

10 15 20 25 30 35 40 45 50Speed (mph)

Cumulativepercentage

00:00 - 06:00 (77 vph)

06:00 - 12:00 (433 vph)

12:00 - 17:00 (538 vph)

17:00 - 18:00 (595 vph)

18:00 - 24:00 (329 vph)

Time of day (average flow)

85th percentile range28.5mph to 39.5mph

Figure 10

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Number of vehicles per day exceeding 30mphin Lindsay Road plotted against excess speed

1

10

100

1000

10000

0 5 10 15 20 25 30 35Excess speed (mph)

Number in 24 hours(log scale)

15/16 April 2011

29/30 August 2011

Trendline 15/16 April 2011

Example: on 29/30 August 2011, 50 vehicles exceeded the speed limit by 20mph and over.

Example: on 29/30 August 2011, 200 vehicles exceeded the speed limit by 10mph and over.

Figure 11

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