transport research laboratory - department of the ...estimation of traffic flow using the...

Department of the Environment Department of Transport

TRRL SUPPLEMENTARY REPORT 802

ESTIMATION OF ANNUAL FLOW FROM SHORT PERIOD TRAFFIC COUNTS

by

Garwyn Phillips, Philip Blake and David Reeson (Local Government Operational Research Unit)

The work described in this Report was commissioned by the Transport and Road Research Laboratory

Any views expressed in this Report are not necessarily those of the Transport and Road Research Laboratory nor of the Department of the Environment or the Department of Transport

Traffic Systems Division Traffic Engineering and Control Department

Transport and Road Research Laboratory Crowthorne, Berks

1984 ISSN 0305--1293

CONTENTS

Abstract

1. Introduction

2. Choice of counting period

3. Theoretical basis

.

.

.

3.1

3.2

3.3

4.1

4.2

4.3

Estimation from a single short period count - multi-factor model

Estimation from two separate counts - multi-factor model

Estimation from two separate counts - general-factor model

Estimation of traffic flow using the general-factor model

Estimation of total annual flow from two daily flows

Estimation of total daily flow from a short period count

Estimation of annual flow for particular vehicle categories

4.4 Estimation of daily flow for particular vehicle categories

Estimation of traffic flow using the multi-factor model

5.1 Comparison of road classes and road types

5.2 Estimation of total traffic flow

5.3 Estimation of traffic flow for particular vehicle categories

Comparison of general-factor and multi-factor models

6.1 Estimation of annual flow

6.2 Estimation o f daily flow

7. Conclusions

8. Acknowledgements

9. References

10. Glossary

Page

1

1

2

3

3

6

8

10

11

12

14

15

16

16

19

20

21

21

21

22

24

24

24

Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on I st April 1996.

This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

11.

12.

13.

14.

15.

Appendix l :

Appendix 2:

Appendix 3:

Appendix 4:

Appendix 5:

Data sources

Assessing the accuracy of flow estimates

Multi-factor model applied to two counts

Statistical estimation of general E-factor

Statistical estimation of general M-factor

Page

38

45

47

50

51

© CROWN COPYRIGHT 1984 Extracts from the text may be reproduced, except for

commercial purposes, provided the source is acknowledged

ESTIMATION OF A N N U A L FLOW FROM SHORT PERIOD COUNTS

ABSTRACT

Short period manual counts of less than twenty-four hours duration are commonly used to measure traffic flow at particular sites. In a previous report, SR 514, the accuracy of the estimates of total annual flow from a single short period count was examined. Recommendations were given for the most appropriate length and timing of these counts. In this report, the previous work has been extended to cover the estimation of flow for individual vehicle categories. In addition, the value of mounting two counts, one in August and one in a neutral month, has been investigated. Recommendations are given for the appropriate timing of counts and methods of estimation.

1. I N T R O D U C T I O N

Short period manual counts of less than twenty-four hours duration are commonly used to measure traffic flow

at particular road sites. These counts can be used to estimate annual traffic flows for individual vehicle categories.

To do this, it must be decided how many counts to have, when they should occur, and how long they should be.

A previous report 1 described a method of estimating total annual flow from a single short period count.

The method is based on a two stage process using an E-factor and an M-factor. In the present report the earlier

work is extended to deal with the following questions:

What are the best times and the best methods for estimating annual flow for different vehicle

categories?

• What are the merits of mounting two short period counts instead of one?

Because traffic flow varies greatly between individual road sites, estimates of flow can be improved by

classifying road sites. Two classifications have been considered for grouping roads when estimating traffic flow:

Standard road classes, in which roads are designated as built up (b) or non-built up (n) and as trunk

(T), principal (P) or other (O). This is the classification of roads in Great Britain which is used for

administrative purposes and has been applied to the national traffic censuses.

Road types, in which roads with a similar mix of journey purposes are grouped together. Each road

can be allocated to a particular road type using objective criteria based on sample traffic counts.

The road types can be broadly described as either strategic, namely, main urban (M), inter-urban (I)

or recreational inter-urban (RI); or non-strategic, namely, recreational local (RL) or local (L).

A fuller description of this classification is given in a separate report 2.

The data used in the analysis consisted of continuous volumetric counts at eighty-two sites. For about half

of these sites there was some classified data available giving traffic flows for each vehicle category on selected days.

The vehicle categories considered in this report are cars, light goods vehicles (LGV) and heavy goods vehicles

(HGV). The sources of data and the site classifications are given in Appendix 1.

1

To carry out the analysis two models for estimating annual flow were examined and compared. The first,

called the multi-factor model requires separate factors for each type or class of road. The second, called the

general-factor model is less dependent on roads being classified.

2. CHOICE OF COUNTING PERIOD

The accuracy of an estimate of annual flow depends on the sample traffic count data available and the method

of estimation. Collecting traffic data is expensive, and often only one or two short period counts at a site can

be justified. The timing of these counts is crucial in determining the likely accuracy of the annual flow estimate.

In Supplementary Report 5141 recommendations were given for the most appropriate length and timing

of a single count to estimate the annual traffic flow for all traffic. The recommendation was that the single

short period count should be taken on a weekday in the late spring or early autumn. In general, May is the best

mon th to choose for the greatest accuracy.

The expected accuracy of different length counts for inter-urban sites is shown in Figure 1. The lower the

coefficient o f variation* the more accurate the estimate in annual flow is likely to be. If the count is of less than

ten hours duration, its mid-point should be either 4 pm or 5 pm. With this mid-point, a six hour count provides

almost as accurate an estimate of annual flow as an eight or ten hour count.

The choice of counting period becomes more difficult in estimating annual flow for each vehicle category.

The expected accuracy of the estimate of daily flow for cars, light and heavy goods vehicles is shown in Figures

2, 3 and 4. It may be observed that:

For counts of eight hours or less, the best time of counting differs between vehicle categories.

For example, the mid-point o f the count should be 4 or 5 pm for cars, but 2 or 3 pm for goods

vehicles.

For light and heavy goods vehicles, the expected accuracy of the daily flow estimate becomes

markedly worse as the length o f count decreases.

In order to have a single period of counting that provides reasonably good estimates for each vehicle category and

for total flow a count length of at least twelve hours is required. The best periods are either 7 am to 7 pm or

8 am to 8 pm.

A twelve hour count has the practical advantage of representing two 'full time' counting shifts of six

hours each. The 7 am to 7 pm period covers the t w o m a i n traffic peaks in the day, and also has a slightly

bet ter coverage of good daylight than the 8 am to 8 pm period.

Because of these advantages, short period traffic counts are increasingly undertaken as twelve hour counts

between 7 am and 7 pm. This standard has been adopted in the new rotating traffic census organised by the

Department of Transport and covering the whole of Great Britain.

* The definition and interpretation of the coefficient of variation is given in Section 3.

2

3. T H E O R E T I C A L BASIS

Historically, it has been common practice to count for sixteen hours (usually 6 am to 10 pm) and the daily

flow has often been taken as the 16:hour total. Following the recommendation in a previous report 1, shorter

periods of counting are becoming more usual. This suggests that it is now more appropriate to use the

statistical models to estimate first the 24-hour daily flow and then the annual flow.

Two statistical models are described here which are suitable for estimating the daily traffic flow and the

annual traffic flow for each vehicle category at a site. These models are called the general-factor model and the

multi-factor model. The multi-factor model requires roads to be formally categorised by type (or class), while

the general-factor does not. However, the multi-factor model can be applied using data from only a single

count, while the general-factor model can only be applied when two counts are mounted in two dissimilar months.

Both the multi-factor and general-factor models are developments of the two stage process described in

the previous report 1 . In this process, the annual traffic flow at a site may be estimated by expanding a short

period count, first to the daily total using the expansion factor (E); and then to the annual flow using the multiplication factor (M), so that:

Estimated annual flow = measured flow x E x M . . . . . . . . . . . . . . . . . . . . . . . . . . . O )

The~e may be more than one traffic count on which to base the estimate of daily flow. The factors E and M

are expresse.d in terms of ratios between traffic flows. A reasonable approximation to the actual factors to be

applied to a particular count or counts is the mean factor averaged over a number of sites and days of the appropriate type.

The accuracy of the prediction of annual flow can be expressed in terms of the coefficient of variation

(C) (which is the ratio of the standard deviation of the estimating factors to their means). This is because the proportional error in the estimating factors is equal to the proportional error in the predicted annual flow.

As a result the expected proportional root mean square (PRMS) error in the predicted annual flow is equal to

(he coefficient o f variation in the estimator of that flow (see Appendix 2). This is true of both the multi-factor

and general-factor models, irrespective of whether daily flow or annual flow is being estimated. The coefficient

• of variation in the estimating factors can be interpreted as follows: in two out of three cases the true annual

flow is expected to lie within C per cent of the mean.

3.1 Estimation from a single short period count -- multi-factor model

The first stage is to estimate the daily flow from the measured short period flow, using an expansion

factor (or E-factor). The second stage is to estimate the annual flow from the daily total, using the multi-

plicative factor (or M-factor)*. The two stages of estimation are considered in turn.

The part o f the model used to convert the short period flow to a daily total, using an expansion factor, can be expressed as:

E i j = E + ~ij

* The daily flow may be taken as the 24-hour total or 16-hour total. In this report E-factors are assumed to expand to the 24-hour total and M-factors from the 24-hour total to the annual total, unless otherwise stated.

3

t The error term/~ij has two independent components , a site deviation b i and a residual error/J ij so that:

= E + bi + ~'ij . . . . . . . . . . . . . . . . . . . . . . . . . . . %

where:

Eij Eij E

Fij b i

= X jFij

= actual E-factor applicable at site i on day j

= mean E-factor for all sites and all days

= twenty- four hour daily flow at site i on day j

= short period f low at site i on day j

= mean deviation in E-factor for site i

= normally distr ibuted random variable with zero mean and constant variance.

The variance o f the total error is equal to the sum o f the variances o f the two component errors as follows:

( 2 )

Var (~ij) = Var (bi) + Var ~ ' i j )

The part o f the model used to convert the daily flow to an annual flow, using a multiplication factor,

can be expressed as:

Mij = M + aij

The er ror term ~ j has two independent components , a site deviation a i and a residual error ¢gij so that:

e Mij = M + a i + ~ i j . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

where:

i j

M =

Yi =

a i =

O¢'ij =

Yi/Xij

actual M-factor applicable at site i on day j

mean M-factor for all sites and all days

total annual flow at site i

twenty- four hour daily flow at site i on day j

mean deviation in M-factor for site i

normally distr ibuted random variable with zero mean and constant variance.

The variance o f the total error is equal to the sum o f the variances o f the two component errors as follows:

Var (aij) = Var (ai) + Var~(a'ij)

4

Separate E-factors and M-factors in equations 2 and 3 may be quoted for different road types, days of the

week and months. A major cause of error is the site to site differences. This can be reduced by classifying sites

into similar groups. These groups may either be road classes or road types. Grouping road sites into the

administrative classes is not altogether satisfactory, since sites with very dissimilar traffic patterns are often

classed together. On the other hand, the problem with using the road type classification is that it requires some

data from two dissimilar months (eg. May and August) for any road site to be classified objectively and with

confidence.

The overall model for estimating annual flow is obtained by combining equations (2) and (3). The actual

annual flow Yi is given as:

Yi = Fij " E i j Mij

A The estimated annual flow Yi is then given by:

A Yi = Fij • E . M

This, in symbols, is the same as equation (1). The variance in "the estimated annual flow is given as:

Var (Yi) = F~ EE 2 . Var(ai j)+ M 2. Var~i j ) ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

No covariance term in this expression because no significant correlation between the error in the E-factor

(/~ij) and the error in the M-factor (aij) was found when examining data from weekdays (Monday to Thursday).

The proportional root mean square error in the estimated annual flow is the same as the coefficient of

variation in the overall estimator (EM). As illustrated in Appendix 2 an appropriate measure of accuracy is the

coefficient of variation, which for a single count in month K can be obtained from the following expression:

C~(K) = C~(K) + C~(K) . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

where:

CE(K)

CM(K)

CT(K)

is the coefficient of variation of the E-factor

is the coefficient of variation of the M-factor

is the coefficient of variation of the overall estimator.

The method of estimation described in this section may be applied to total traffic flow or to the flow of

an individual vehicle category. Clearly, the values of the E-factors and M-factors are likely to differ among

different vehicle categories. It may be noted that the total traffic flow for all vehicles combined may be

estimated in two ways: either an all-vehicle E-factor and M-factor may be applied to the all vehicle count, or

the total flow may be taken as the sum of the estimated flow for each of the individual vehicle categories. In

current circumstances the former is preferable, because the extent and quality of the data available for

volumetric counts is greater than for classified counts. This means that the estimated values of the all-vehicle

E-factors and M-factors can be used with more confidence.

5

To improve the accuracy of the estimated annual flow from a single count several options are possible:

• the month and time of day may be chosen so as to provide a lower value of the coefficient of

variation;

• the length of counting may be increased, for instance, a twelve hour count may be preferred to

a ten hour count;

• the count may be repeated on another day in the year.

The theory needed for the third option of using two counts is considered in the next sections.

3 . 2 E s t i m a t i o n f r o m t w o s e p a r a t e c o u n t s -- m u l t i - f a c t o r m o d e l

This section describes how annual flow may be estimated from two counts, using the multi-factor model.

The formulae used are derived in Appendix 3.

The case considered is where two short period counts are taken at the same time of day on two different

days of the year. To distinguish the months under consideration an extra subscript k is used. For example, if a

count is mounted in month k the measured flow is denoted as Fij k.

I f two counts are mounted on similar days, one in month 1 and the other in month 2, the annual flow

could be estimated for the two counts separately. These might then be combined to produce a pooled estimate

o f annual flow. This may be done by attaching weigl~ts to each estimate such that greater weight is given to the A

more accurate estimate. The estimated annual flow ~i is then given as:

A Yi = wt Fijl. E1 M1 + w2 Fij2. E2 M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

where:

wl ,w2 are the weights attached to counts in month 1 and 2

MI ,M2 are the mean M-factors in the two months

E1 ,F_.2 are the mean E-factors in the two months.

The weights used in equation (6) should sum to one. In addition, to ensure that greater weight is given to

the more accurate individual estimate, they may be made to be inversely proportional to the variance in the

individual estimate of annual flow, that is:

Wl+W2 = 1

w, c r(2)

C rO )

where:

CT(1), CT(2 ) are the overall coefficients of variation in the estimator for each month as given in equation (5).

6

The improvement expected by estimating the annual flow from two counts will now be considered.

Repeating a count will result in the variance due to the residual errors of equations (2) and (3) being reduced.

The reduction is one-half if the weights w~ and w2 are equal. This is because the residual errors are generally

about the same magnitude in different months and are uncorrelated between months. However, the effect on

the site terms aik and bik in these equations is more difficult to predict, because the site terms are correlated.

If two counts are mounted in two different months, it will be necessary to take account of this correlation in

order to obtain a reasonable estimate of the accuracy of the predicted annual flow. The best choice of months

will be where the residual errors are relatively small and where the site terms tend to balance each other.

The accuracy in the predicted annual flow when two counts are mounted in d i f f e ren t months can be

assessed as follows. Repeating a count in another month will reduce the expected error by an amount which

depends on: the weights attached to each count; the correlation between the site terms of the M-factors; and

the size of the residual errors. The accuracy of the pooled estimate can be assessed using the total coefficient

of variation CT(1,2) of the estimator. This is derived in Appendix 3 and given as:

C~('1,2)= w 2 C,]-(1) + w 2 C,]-(2) + 2wl w2 [pa CMa (1). CMa (2) + PbCEb (1). CEb (2)] . . . . . . (7)

where:

Pa is the correlation coefficient between the site terms of the two M-factors

Pb is the correlation coefficient between the site terms of the two E-factors

CMa is the coefficient of variation of the site term of the M-factor

CEb is the coefficient of variation of the site term of the E-factor.

Although the equation is complicated, it can be readily solved provided we know the variances in the

M-factors and E-factors, and the coefficients Pa and Pb" The coefficients need to be estimated for each paired combination of months separately.*

The accuracy in the predicted annual flows when two counts are mounted in the same month can be

assessed as follows. The general expression for the total coefficient of variation of the estimator given by

equation (7) simplifies when the two counts occur on similar days in the same month. In this case weights to

be attached to each count are the same and equal to one-half. The coefficient of variation CT(1,1 ) o f the

estimator when two counts are mounted at the same time of day, on similar days in the same month 1, is then given by:

C~(1,1) = ½C~(1) + ½C~a(1 ) + ½C~_q9(1 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

The improvement by repeating a count in the same month depends on the size of the residual errors • r

otij I and/3ij I . Repeating a count in the same month results in the variance of these errors being halved.

* It may be noted that the general expression for the total coefficient of variation of the estimator given by equation (7) simplifies greatly when we consider a single count. In this case wl equals one and w2 equals zero and the coefficient of variation of the estimator becomes equal to CT(1 ) given by equation (5), as would be expected.

7

The improvement in the accuracy of the annual flow estimate obtained by repeating a count may be

measured using equations (7) and (8). The improvements will be due to the following causes:

• First, the variance in the residual errors of the E-factors and M-factors will be reduced.

Second, if the two counts are in different months, such that the site terms are not perfectly and

positively correlated (Pa ¢ + 1 ; Pb :/= + 1) the variance in the site terms of the E-factor and M-factor

will be reduced.

3 .3 Es t imat ion f r o m t w o separate counts - - General - factor model

The multi-factor model described in section 3.2 requires separate E-factors and M-factors for each road

class or road type. In this section a model is described in which a single E-factor and M-factor is applicable.

As a result, the model largely eliminates the problem of classifying sites. This model can be used if a count in

a neutral month (e.g. May or October) is combined with a count in August.

The first stage is to estimate daily flow from the measured short period flow using an E-factor. In the

previous report 1 the best short periods for mounting a traffic count to estimate total flow were derived. For

these periods, the E-factor for all-vehicle flow is lower for sites which have a large seasonal variation. This effect

can be catered for by using a monthly E-factor that differs from site to site, depending on the seasonal variation

at the site. This is done in the general-factor model and avoids the need to classify sites. The basic model is:

Eij = Eij+/3ij

or Eij = Ei j+ b i +/3ij

whe re:

Eij Eij

sij

. . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

is the actual E-factor at site i on day j for a particular month, that is: Eij = Xij/Fij

is the estimate of the E-factor at site i on day j for a particular month. Its value is based on a

formula given in Appendix 4 Eij = A ( 1 - B X ~ i j )

:is the seasonal index, which is the ratio of the measured short period flow in August to that in a

neutral month

A, B are parameters the values of which depend on the length and timing of the traffic count.

In this model there are two error terms, the sizes of which depends principally on the sample fraction (1/Eij).

This needs to be taken into account because a significant proportion of the day's traffic flow occurs during the

counting period. The two errors may be represented as follows (substituting E i for Eij):

• the residual error where:

Expectat ion (flij) = 0

• the fixed site deviation where:

Var (flij) = (1-1 /Ei ) a~,

Expectat ion (bi) = 0 Expectation (b~) = (1 -1 /E i) o~

8

The overall error is related to these two components as:

The accuracy of the estimate of daily flow at a site can be assessed using the coeff icient o f variation in the E-factor:

CE i = ~ i - o~ x 100% E i

For practical purposes the expected value of this coefficient o f variation can be taken as cons tant (equal to

CE) over all sites for a particular counting period.

The justification for using a square root relationship between the E-factor and the seasonal index is

given in Appendix 4. This general relationship observed for total traffic is also valid for est imating the daily

flow of cars, although the parameters A and B m a y have different values for cars. However , the relationship is

not valid for goods vehicle traffic. For these vehicle categories a cons tant E-factor for all sites is adequate.

The second stage of the model, used to convert daily flow to an annual flow, makes use of an M-factor

A single M-factor is applied to the average o f the two flows in different months , so that:

Yi = Mij Xij

where Xij = ½(Xij , + Xij2)

j represents a particular count combination, for example, a Tuesday in May with a Tuesday

in August.

For a given pair of months the M-factor for site i and count combina t ion j varies abou t the mean

M-factor for all sites and all count combinations as:

Mij = M + a i j

The error term aij has two components , a fixed site deviation a i and a residual error aij so that:

Mij = M + a i + a i j . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

Both the site deviation and the residual error tend to be large for sites with a high seasonal index. This is

taken into account by modelling each error term as follows:

the residual error where:

Expectat ion (aij) = 0

the fixed site deviation where:

Expectat ion (ai) = 0

. . . . . . . . . . . . . . . . . . . . . . . . . . ( l o )

t Var (rvij) = ¼(1 + Si)2 o~,

2 2 Expec ta t ion (a~) = ¼(t + Si) o a

9

The expected variance in the total error is therefore given as:

2 = ¼ ( 1 +Si)2 2 2 a s (o a + as , )

It may be noted that the form of the general model for the M-factor is similar to that of the multi-factor

2 is different. For model (compare equations 3 and 11). However, the expected variance in the total error o a

the multi-factor model this variance is kept constant by grouping sites. In contrast, the general factor model

uses a general relationship between the expected variance at a site and its seasonal index.

The accuracy in the estimate of annual flow at a site can be assessed using the coefficient of variation of

the M-factor which is estimated as:

CM= " = ½( l+S i i ) . °o r x 100% 1

M

. . . . . . . . . . . . . . . . . . . . . . . . . . (12)

The M-factor and the variance of the total error can be estimated from the data for sites with continuous

traffic counts. These estimates can be used to assess the accuracy of the predicted annual flow at a particular

site using the measured seasonal index.

The two stages of estimation can be combined so that the annual flow is estimated as:

A Yi = E'M'½(Fij~ + Fij2)

The error in the annual flow prediction may be assessed using the overall coefficient of variation at site i which

is estimated as:

cA2T1 + C 2 . = C~ Mi

For counts of an appreciable length, such as twelve hours, the coefficient of variation of the E-factor is much

less than that of M-factor. As a result, the error in the annual flow prediction can be estimated as:

A = CMi CTi H +

where H is the average extra error in annual flow prediction from two twelve hour counts, compared with two

24-hour (or two 16-hour) counts.

4. ESTIMATION OF TRAFFIC FLOW USING THE GENERAL-FACTOR MODEL

The general-factor model, discussed in Section 3.3, uses a single M-factor (and E-factor) which is generally

applicable to all sites. The method requires data from two traffic counts, one in August and one in a neutral

month.

1 0

4.1 Estimation of total annual flow from two daily flows

In the general-factor model a general M-factor is applied to the average daily flow for the two days of

counting. For example, if the two counts are mounted in May and August the model can be expressed as

Total EMay Aug stl annual = M-factor x ½ daily + daily

flow flow flow

. . . . . . . . . . . . . . . . . . . . . . . . . . . (13)

To estimate the general M-factor graphs can be plotted of the mean site M-factor in the neutral month

against the seasonal index for that site. The statistical details of the procedure are given in Appendix 5. In

Figure 5, the mean May M-factor for Monday to Thursday for each site is plotted against the mean August to

May seasonal index. The following observations may be made:

• There is an increasing linear trend in the May M-factor as the seasonal index increases.

For sites in holiday areas the linear trend is at a lower level than for sites in other areas. Apart

from this, there is no distinction between other types of sites, eg. motorways or non-strategic

roads.

The reason for the linear trend, which is also observed for the October M factor, is as follows. May and

October are not exactly neutral times of the year. For example, Figure 1 of SR514 indicates that the times

when weekday M factors are approximately equal for all sites, are at the end of May, and in mid September.

At seasonal sites, weekday M factors are relatively high before the end of May and in October. As a result,

weekday M factors for May as a whole (and October as a whole), will tend to be higher the more seasonal the

site.*

The reason for the lower level in the linear trend for sites in holiday areas may be explained as follows.

For such sites, there is a significant amount of holiday traffic on weekdays in May. This effect depresses the

weekday May M factor at these sites. The effect is more widespread on Fridays when virtually all seasonal

sites have a relatively depressed Friday M factor in May. This is shown in Figure 6 where it may be noted that

a linear trend is fitted for all sites in or leading to holiday areas.

If the general M factor model were to be applied on Monday to Thursday in holiday areas, it would be

necessary to distinguish holiday sites from other sites. This would pose a classification problem which may be

reduced by choosing to count on Fridays at such sites. A general rule that may be applied is that the counts

should normally be mounted on Monday to Thursdays at most sites. However, i f the site is considered to be

in a holiday area then the counts should be mounted on Fridays. The rule is robust in application, since any

weekday is appropriate for counting for the intermediate case of sites near or leading to holiday areas.

* May is a neutral month in the sense that the average weekday flow in May is close to the average weekday flow throughout the year, as shown in Table 5 of SR 437. When weekends are taken into account, Ma~, is

not quite neutral because the more seasonal the site, the greater is the relative amount of traffic that occurs

at weekends.

11

For example, a Tuesday count may be mounted in May and August, at any local, main urban, or inter-

urban road, or any recreational inter-urban road leading to holiday areas. In this case, the appropriate M-factor

to apply in equation (13) is 342 (Table 1). On the other hand, a Friday count may be mounted in May and

August, at any recreational local or recreational inter-urban road, or any inter-urban road leading to a holiday

area. In this case, the appropriate M-factor to apply in equation (13) is 282 (Table 1). The quoted M-factors

were derived from strategic sites, but are also applicable to non-strategic sites, because the statistical

differences in the M-factors are not significant.

The expected accuracy in the annual flow estimate may be assessed using the formula for the coefficient

o f variation, based on equation (12) and shown in Table 1. The formula takes account of the fact that

accuracy is likely to be lower for sites with a large seasonal variation. For example, for a Tuesday count the

expected error* is 5.6 per cent and 7.0 per cent, for two sites which have a seasonal index of 1.0 and 1.5

respectively.

TABLE 1

M-factors for total traffic - May/August, 24 hour day

Type of day

Monday to Thursdays

Fridays

General Coefficient M-factor of variation

M C M per cent

342 2.8 (S + 1)

282 2.9 (S + 1)

Number of sites in

sample

51

28

Notes:

Sources;

M is used in equation 13

S is the measured seasonal index

Data set IIs, 1978 for Monday to Thursday values

Data set Ills, 1978 for Friday values

(see Appendix 1)

4.2 Estimation of total daily flow from a short period count

In section 4.1, the general-factor model was used to estimate total annual flow from two daily flows.

Usually, traffic flows are measured for a shorter period than a day (eg. for 12 hours) and it is necessary to

estimate the daily flow. This may be done using a monthly E-factor as described in section 3.3.

The daily flow can be estimated as:

Total measured monthly

daily = x short period E-factor

flow flow

. . . . . . . . . . . . . . . . . . . . . . . . . . (14)

* The expected proportional root mean square (PRMS) error in the predicted annual flow is equal to the coefficient of variation in the estimator of that flow, (see Appendix 2).

12

The 12-hour E-factors fall into two distinct month types. Within each mon th type the E-factors are not

significantly different. The first month type, May, June, July and August, contains days with long light evenings.

The second group of months, April, September and October, produce rather lower E-factors, probably because

the darker evenings may be expected to give rise to a proportionately lower traffic flow between 7 pm and, say,

10 pm.

The averaged E-factors for May and August (Mondays to Thursdays, and Fridays respectively) are shown

in Figs 7 and 8. It will be noted that there is a tendency for the mean E-factor to be lower for sites with a large

seasonal index. This may be due to a tendency for recreational traffic to occur in the main part of the day,

which is when the short period counts are mounted.

To estimate the E-factor, a relationship of the form E-factor = A ( 1 - B x /S- ) is used (see Appendix 4

for the justification of this model). The values of the coefficients A and B are determined by fitting the above

model to the appropriate data. Table 2 summarises the results for the case where 12-hour counts are mounted

between 7 am and 7 pm.

TABLE 2

12-hour E-factors for total traffic - May or August, 24 hour day

Type of day

Monday to Thursday

Fridays

Parameters

A B

1.42 0.12

1.42 0.09

Measures of expected error

(per cent)

C E H

2.4 0.5

2.4 - 0 . 6

Number of sites in sample

51

28

E-factor = A (1 -Bx / - f f )

where S is the measured seasonal index.

Sources: Data set IIs, 1978 for Monday to Thursday values

Data set IIIs, 1978 for Friday values

(see Appendix 1)

Table 2 shows also, two measure of expected error. One of these, CE, is the coefficient of variation for

the E-factor. This is equal to the PRMS error in the prediction of the 24-hour daily flow. The other measure, H,

is the average extra error in annual flow prediction from two 12-hour counts compared with two 16-hour counts.

The extra term needs to be added to the coefficient of variation in the M-factor (C M of Table 1), when

estimating annual flow from a 12-hour count compared to a 24-hour count. The value of this term for Monday

to Thursdays (0.5) is as expected, on the assumption that the E-factor is not correlated with the M-factor.

However, for the set of sites for which Friday is an appropriate counting day the extra term ( - 0 . 6 ) is negative.

This means that two 12-hour counts in May and August may be expected to provide a more accurate estimate

of annual flow than two 16-hour counts for certain sites. For these sites the M-factor and E-factor are negatively

correlated (and so~ a covariance term is needed in equation 4 for Fridays at recreational sites). This effect is most

marked for those sites belongingto the recreational inter-urban set, principally the following:

13

278 M5 at Bridgwater

631 A30 at Okehampton

630 A303 in Somerset

47 A9 at Piflochry

407 & 430 A27 in West Sussex

312 & 313 M4 in Wiltshire

A possible explanation for the negative correlation at sites such as these is as follows. The general

M-factor for two Friday counts is lower than average because these days carry a greater than average proportion

o f weekday flow. On the other hand, the general E-factor for 12-hour counts on Fridays is higher than average

because a greater than average proport ion of the Friday flow occurs in the evening after the 12-hour count has

ended.

4.3 Estimation of annual flow for particular vehicle categories

So far, this chapter has dealt wi th the use of the general-factor model to estimate total traffic flows at a

site. This section and the next describe how this model can be used to estimate flows for particular vehicle

categories. A difficulty arises in that the available classified traffic flow data is much more limited than the data

for continuous volumetric flows (Appendix 1). As most of the available data is for 16-hour counts, the daily flow

has been taken as the 16-hour total, in this section. To estimate the category M-factor graphs can be plotted of

the mean category M-factor for a site against the seasonal index for that vehicle category.

The estimation of car traffic will be considered first. Generally, the M-factor for cars in May is not

appreciably different from that for October. In Figure 9 the average Friday M-factor for cars in these two

months is plotted against the seasonal index. There is an increasing trend in the M-factor as the seasonal index

increases. As cars represent approximately three-quarters of total traffic at a site, it is not surprisingthat the

general trend is similar to that for total traffic (Figure 6). The best fitting line for sites in or leading to holiday

areas shows that at such sites an M-factor of 304 may be applied in equation (13) for cars on Fridays.

For goods vehicles the traffic flows are less seasonal than for cars. It was found that April data may be

combined with that for May and October, and no distinction is needed for holiday areas. The linear trends for

these vehicle categories are shown in Figures 10 and 11. The best fitting line gives an M-factor of 306 for light

goods vehicles and 292 for heavy goods vehicles on any weekday for any strategic site.

The 16-hour M-factors derived here are appropriate when a count in May is combined with a count in

August. The values are consistent with the overall 16-hour M-factors derived for total traffic as shown in

Table 3.

14

T A B L E 3

M-factors for vehicle categories May/August - 16 hour day

Vehicle category

Cars

LGV

HGV

Total

traffic

Type of day

Mon-Thu b

Fri c

Mon-Fri

Mon-Fri

Mon-Thu b

Fri c

Coefficient M-factor of variation a

M C M per cent

381 2.6 (S + 1)

305 2.7 (S + 1)

307 3.5 (S + 1)

293 3.6 (S + 1)

366 2.8 (S + 1)

302 2.9 (S + 1)


Data Source

- - d

18 IIIc May, Oct, Aug

26 Isc Apr, May, Aug, Oct

27 Isc Apr, May, Aug, Oct

51 Ilsc May, Aug

28 Ills May, Aug

Note s: a. S is the measured seasonal index for the particular vehicle category. For example, for cars S is

the ratio of the measured car flow in August to the measured car flow in May.

b. For sites distant from holiday areas (all local, main urban and inter-urban roads, plus the less

seasonal recreational inter-urban sites).

c. For sites in or near holiday areas (all recreational local and recreational inter-urban roads, plus

the more seasonal inter-urban sites). /

d. See Appendix 1. There was no Monday to Thursday data available for cars in the relevant months.

As a result the M-factor for cars has been estimated assuming a traffic composition of 80 per cent

cars, 10 per cent LGV, 10 per cent HGV. C m has been estimated as

C m (cars, Mon-Thu) = C m (total traffic, M o n - T h u )

C m (cars, Friday) C m (total traffic, Friday)

4.4 Estimation of daily flow for particular vehicle categories

This section presents the appropriate E-factors for different vehicle categories that are appropriate in

estimating the 16-hour daily flow. The short period count is taken as the twelve hours from 7 am to 7 pm.

To make the most of available data several assumptions have been made in deriving the category E-factors

given in Table 4. First, it is taken that the 12-hour E-factors for goods vehicles are the same for all weekdays

including Fridays. Secondly, it is assumed that the relationship between E-factors for Fridays and for Monday

to Thursdays for cars is the same as for total traffic. Because of the limitations of the data, factors have not

been derived for the low flow vehicle categories of pedal cycles, motor cycles and public service vehicles.

It may be observed that the extra error resulting from a shorter count than sixteen hours, H, is negative

for cars and total traffic on Fridays. The effect is the same as was observed for the two stage estimation of

annual flow via the'24-hour daily total, as discussed in section 4.2. The explanation given in that section could

equally apply here.

1 5

T A B L E 4

12-hour E-factors for vehicle categories - 16 hour day

Vehicle category

Cars

LGV

HGV

Total

traffic

Type of day

M o n - T h u b

Fri c

Mon-Fr i

Mon-Fr i

f M o n - T h u b Fri c

Parameters a

A B

1.42 0.16

1.42 0.12

1.11 0

1.08 0

1.33 0.12

1.33 0.09

Measures of expected error

(per cent)

C E H

2.5 0.3

2.5 -0 .4

3.0 0.6

4.5 1.3

2.5 0.3

2.5 -0 .4


- d

18 IIIc

26 Isc

27 Isc

51 IIs

28 Ills

Data SOUrCe

May

Jun

and

Aug

Notes: a. E-factor = A(1 -- B x/-S--) (see Appendix 4).

b. For sites distant from holiday areas (all local, main urban, and inter-urban sites, plus the less

seasonal recreational inter-urban sites).

c. For sites in or near holiday areas (recreational local and recreational inter-urban sites, plus the

more seasonal inter-urban sites).

d. See Appendix 1. There was no Monday to Thursday data available for cars in the relevant

months. As a result the parameters (A, B, C E and H) for cars have been estimated using the

relationship:

parameter value (cars, Mon--Thu) parameter value (total traffic, Mon-Thu)

parameter value (cars, Friday) parameter value (total traffic, Friday)

5. ESTIMATION OF TRAFFIC FLOW USING THE MULTI-FACTOR MODEL

The multi-factor model, discussed in section 3.1 and 3.2, can be used to estimate annual traffic flows from

either a single count or from two separate counts. The method requires calculating monthly M-factors (and

E-factors) for separate road types or road classes.

5.1 Comparison of road classes and road types

M-factors may be based on either road classes or road types. The results of using each of these are given

in Tables 5 and 6. These tables can be used to compare three counting procedures for estimating annual flow

using the multi-factor model:

method 1, mounting a single 16-hour count in May

method 2, mounting two 16-hour counts in May

1 6

• method 3, mounting two 16-hour counts; one in May, and one in August.

The accuracy of the annual flow estimate is measured using the coefficient of variation in the overall

estimator. The values quoted in Table 5 and 6 are based on 1978 data for Monday to Thursday. This was the same

set of data that was used to estimate the parameters of the model. The following observations may be made:

Overall, the level of accuracy in the annual flow estimates is only slightly better using road types

than using road classes. In either case the estimates are likely to be rather inaccurate for sites with

a large recreational component in the traffic.

For both road classes and road types there is an improvement from repeating a count. However,

the improvement is relatively small for the more recreational type of site.

TABLE 5

Accuracy in 1978 annual flow estimates - road classes

Percentage coefficients of variation for 16-hour M-factors

Road class* Tb/Pb Tn Pn On Ob M'way Overall

Number of sites 11 12 17 17 4 21 82

in sample

Single May count

Two May counts

May and August counts

7.9 10.1 9.8 15~ 6 ~ 8.2

6.7 8.8 8.3 13.7 5.2 7.3

6.3 8.8 7.9 103 5.3 5.0

10.1

8.9

7.5

* T(runk), P(rincipal), O(ther), b(uilt up), n(on-built up)

Note : The overall coefficient of variation is the average of all the individual coefficients of variation.

Source: Data set I, 1978 (see Appendix 1).

17

TABLE 6

Accuracy in 1978 annual flow estimates - road types


Road type*


Single May count

Two May counts

May and August counts

M I RI RL L Overall**

23 17 20 9 13 82

7.5 8.2 10.0 15.0 10.9 9.6

6 ~ 7 ~ 8.5 13.2 9.6

4.8 6.7 9.3 9.6 7.8

8.4

7.3

* M(ain urban), I(nter-urban), R(ecreational) I(nter-urban), R(ecreational) L(ocal), L(ocal).

Note: The overall coefficient of variation is the average of all the individual coefficients of variation.


The two models were also compared in years other than 1978, the year in which the parameters of the

model were estimated. The results are shown in Tables 7 and 8. Again, the estimates based on road types are

only slightly better overall than for road classes. It should be noted that these tests have been used for estimating

the actual flow in the particular year and not the typical flow for that type of site over a period of years.

T A B L E 7

Accuracy in 1977, 1979 annual flow estimates - road classes


Road class Tb/Pb Tn Pn On Ob Overall

Number of sites 11 4 10 17 4 46

May and r 1977 5.5 8.2 8.4 10.1 7.7 8.3

August l 1979 6.4 9.7 9.7 11.7 6.2 9.3 counts

Source: Data set I, fifty-point census sites, 1977, 1979 (see Appendix 1).

1 8

TABLE 8

Accuracy in 1977, 1979 annual flow estimates -- road types


Road type M I RI RL L Overall

Number of sites 10 10 4 9 13 46

May and [ 1977 4.4 6.1 9.8 11.0 8.3 7.6

August l 1979 5.5 6.7 11.9 10.8 8.2 8.1 counts

Source: Data set I, fifty-point census sites, 1977, 1979 (see Appendix 1).

5.2 Estimation of total traffic flow

In estimating annual flow from a short period count, it would be best to use factors derived for that year.

However, these would not be available until the following year, so that the factors for previous years must be

used.

A reasonable set of average Monday to Thursday M-factors are those given in.Table 9 derived for eighty-two

sites in 1978. The coefficients of variation given in Tables 7 and 8 can be used as a measure of the accuracy of the

annual flow estimate. If the period of counting is less than sixteen hours, E-factors are needed. Appropriate

Monday to Thursday E-factors to estimate the 16-hour daily flow are given in Table 10.

TABLE 9

M-factors for multi-factor model - 16-hour day

Road class


May

August

Road type


May

August

Tb/Pb Tn Pn On Ob M'way

11 12 17 17 4 21

367 409 399 374 362 387

(0.75) (0.67) (0.8) (0.7) (0.9) (0.5)

357 296 289 341 343 364

(0.25) (033) (0.2) ( 0 3 ) (0.1) (0.5)

M I RI RL L

23 17 20 9 13

362 393 411 403 368

(0.5) (0.5) (0.75) (0.67) (0.55)

374 347 282 240 380

(0.5) (0.5) (0.25) (0.33) (0.45)

The figures in brackets give the appropriate weights to apply to the annual flow estimates from each of

the two months.

Source: Data set I, 1978 (see Appendix 1). 19

TABLE 10

12-hour E-factors for multi-factor model - 16-hour day

Road class


May or

August

Road type


May or

August

Tb/Pb Tn Pn On Ob M'way

11 12 17 17 4 21

1.185 1.149 1.146 1.182 1.193 1.151

(2.5) (2.2) (3.0) (3.7) (2.3) (2.0)

M I RI RL L

23 17 20 9 13

1.170 1.155 1.144 1.154 1.219

(2.5) (2.2) (2.4) (2.1) (1.7)

The figures in brackets give the percentage coefficients of variation in the E-factors.


5.3 Estimation of traffic f low for particular vehicle categories

This section presents the vehicle category M-factors and E-factors for each road type for Fridays. Vehicle

category data for other weekdays were not available for May and August. The figures are based on the assumption

that a 12-hour Friday count is first expanded to the 16-hour total and then to the annual total. The values of the

factors are given in Table 11.

TABLE 11

Road type factors for particular vehicle categories - 16-hour day

Cars

Main urban

Inter-urban

Recreational Inter-urban

Recreational Local

Local

LGV All road types

HGV All road types

May/August

E CE%

1.24 4

1.22 3

1.21 3

1,20 3

1_33 4

1.12 3

1.09 3

M

May

CM%

354 8

401 12

461 22

503 35

411 18

319

284

15

22

M

August

CM%

351 14

285 15

250 14

234

381

Source: Data set Ic, 1978 (see Appendix 1).

310

313

17

10

14

16

2 0

6. COMPARISON OF GENERAL-FACTOR AND MULTI -FACTOR MODELS

In this section the respective merits of the two models for estimating annual traffic flow are compared. The

comparisons are based on the case where a May count is combined with an August count and the daily flow is

taken as the 16-hour total. Section 6.1 compares the M-factor stage of estimation and section 6.2 the E-factor

stage.

6.1 Estimation of annual flow from 16-hour counts

The general-factor model has several theoretical advantages over the multi-factor model. These are:

• There is no need to formally classify sites with the general-factor model,

• The general-factor model applies equal weights to the May and August counts, thus reducing the

residual variance. The multi-factor model for some sites applies only a small weight to the August

count, thus reducing its value.

The general-factor model is also superior to the multi-factor model in practice, especially for the more seasonal

sites. Table 12 compares the accuracy of total flow estimates, based on two 16-hour counts on Monday/Thursday in May and August.

TABLE 12

Comparison of models - 16-hour counts

Percentage coefficients of variation in annual flow estimates

Road class


Multi-factor

General-factor

Road type


Multi-factor

General-factor

Tb/Pb Tn Pn On Ob

11 4 10 17 4

5.8 8.4 8 3 8.6 6.3

5.2 6.7 8.3 7.2 4A

M I RI RL L

10 10 4 9 13

4.8 6.5 10.8 9.8 6.9

4.7 6.3 8.1 9.5 6.1

Overall

46

7.6

6.7

Overall

46

7.3

6.7

Note:

Source:

The overall coefficient of variation is the average of all the individual coefficients o f

variation.

Data set I, fifty-point census site, 1977, 1978, 1979 (see Appendix 1).

6.2 Estimation of annual flow from 12-hour counts

The aim of counting for shorter periods than sixteen hours is to obtain nearly as accurate estimates of

annual flow at considerably lower cost. The annual flow is estimated by multiplying the measured flow by an

E-factor as well as an M-factor. The expected accuracy in the annual flow estimate is shown in Table 13, based

on two 12-hour counts on Monday/Thursday in May and August. It may be observed that, as in section 6.1, the

general-factor model is superior to the multi-factor model.

21

TABLE 13

Comparison of models - 12-hour counts

Percentage coefficients of variation in annual flow estimates

Road class


Multi-factor

General-factor

Road type


Multi-factor

General-factor

Tb/Pb Tn Pn On

11 4 10 17

Ob Overall

4 46

7.2 8.3

4.7 6.9

6.3 9,3 8.7 9.5

5.8 6.6 8.3 7.6

M I RI RL L

10 10 4 9 13

5.8 7.1 11.2 10.5 8.4

5.8 7.2 7.4 8.8 6.2

Overall

46

8.1

6.9

Note:

Source:

The overall coefficients of variation are the averages of all the individual coefficients

of variation.

Data set I, fifty-point census sites, 1977, 1978, 1979 (see Appendix 1).

7. CONCLUSIONS

This report has examined two models for estimating annual traffic flow from short period counts. The previous

research in this field has been extended to cover the possibility of repeating a count and of estimating traffic

flows for particular vehicle categories.

The general conclusion is that the most satisfactory model is the general-factor model. This model

requires two counts, one in a neutral month and one in August.

I f only a single count is available then the multi-factor model must be used. In this case M-factors and

E-factors based on either road types or road classes may be used, as described in Section 5.

Procedure for estimating annual traffic f low from two counts

The total traffic flow at a site and its annual composition should normally be estimated from two short

period counts using the general-factor model.

For a count in May and a count in August, the annual traffic flow is estimated as follows:

E measured Estimated total annual flow = E x M x ½ May flow

measured 1 + August flow

where E and M are the appropriate E-factor and M-factor for either total traffic or for a particular vehicle

category, as given in Table 14.

2 2

The best times for mounting the counts are on Monday to Thursdays for sites distant from holiday areas,

and Fridays for sites in holiday areas.

TABLE 14

Appropriate factors in the general-factor model, May/AtJgust - 16-hour day

Vehicle Type of day

category

Cars Mon-Thu b

Fri c

LGV Mon-Fr i

HGV Mon-Fr i

Total Mon-Thu b

traffic Fri c

Parameters a for 12-hour count M-factor

7 am to 7 pm M

A B

381 1.42 0.16

305 1.42 0.12

307 1.11 0

293 1.08 0

366 1.33 0.12

302 1.33 0.09

Notes: a. E-factor = A(1 -B x/S-) where S is the measured seasonal index; that is, the ratio of

the measured August flow to the measured May flow, for the particular vehicle

category considered.

b. For sites distant from holiday areas (all local, main urban and inter-urban sites, plus the

less seasonal recreational inter-urban sites).

c. For sites in or near holiday areas (all recreational local and recreational inter-urban sites,

plus the more seasonal inter-urban sites).

TABLE 15

Accuracy of traffic flow estimates based on general-factor model

Vehicle category Type of day

Mon-Thu Cars

Fri

LGV Mon-Fr i

HGV Mon-Fr i

Total Mon-Thu

traffic Fri

Measures of expected error (per cent)

C M H

2 . 6 ( S + 1 ) 0.3

2 . 7 ( S + 1 ) - O A

3 . 5 ( S + 1 ) 0.6

3 . 6 ( S + 1 ) 1.3

2 . 8 ( S + 1 ) 0.3

2 . 9 ( S + 1 ) - 0 . 4

A measure of the expected accuracy of the annual flow prediction is provided by the values O f C M and H

given in Table 15. These measures may be interpreted as follows:

23

The PRMS error in the prediction of total annual flow based on two 16-hour counts in May and

August is equal to the coefficient of variation C M in the M-factor. For example, the PRMS error

for two Thursday counts is assessed as 5.6 per cent for a site with a seasonal index of 1.0 and 7.0

per cent for a site with a seasonal index of 1.5 (using the formula in Table 15: C M = 2.8 (S + 1)).

The PRMS error in the prediction of the annual flow of cars based on two 12-hour counts in May

and August is equal to the sum of C M and H. For example, the PRMS error for two Friday counts

is assessed as 5.0 per cent for a site with a seasonal index of 1.0 and 6.35 per cent for a site with a

seasonal index of 1.5 (using the formula in Table 15: C M + H = 2.7 (S + 1) - 0.4).

8. ACKNOWLEDGEMENTS

The research presented in this report was commissioned by Traffic Systems Division of the Traffic Engineering

and Control Department of TRRL. The authors are particularly grateful for the guidance and advice given by

Mr D H Mathews and Mr D E Allnutt.

1 .

.

9. REFERENCES

PHILLIPS, GARWYN. Accuracy of annual flow estimates from short period counts. Department o f the Environment, Department o f Transport, TRRL Report SR 514, Crowthorne, 1979 (Transport and Road

Research Laboratory).

PHILLIPS, GARWYN and REESON, DAVID. A road classification for use in traffic modelling.

Department of the Envirionmen t, Department o f Transport, TRRL Report SR (in preparation)

(Transport and Road Research Laboratory).

Standard road classes:

M'way

Tb

Tn

Pb

Pn

On

Ob

Standard road types:

M

I

RI

RL

L

10. GLOSSARY

motorway

trunk road, built up

trunk road, non-built up

principal road, built up

principal road, non-built up

other road, built up

other road, non-built up

main urban

inter-urban

ree~.eational inter-urban

recreational local

local

2 4

Terms used in the estimation models:

a i

b i

C E

CE b

Cz i

C M

CM a

CM i

CT(K)

CT i

E

Eij

Eij Fij H

i

J k ,K

M

Mij

s, sij

T

Var

W

Yi

A Yi

mean deviation in the M-factor for site i

mean deviation in the E-factor for site i

the coefficient of variation of the E-factor for all sites

the coefficient of variation of the site term of the E-factor

the coefficient of variation of the E-factor for site i

the coefficient of variation of the M-factor for all sites

the coefficient of variation of the site term of the M-factor

the coefficient of variation of the M-factor for site i

the coefficient of variation of the overall estimator (EM) from a count in month K

the coefficient of variation of the overall estimator (EM) for site i

the mean E-factor over all sites and all days

the actual E-factor at site i on day j

the E-factor to be applied at site i on day j

the measured traffic flow counted at site i on day j

the extra error in annual flow prediction from two 12-hour counts compared with two

24-hour (or two 16-hour) counts

denotes the site

denotes the day or days of counting

denotes the month

the mean M-factor for all sites and all days

the actual M-factor at site i for the day(s) of counting j

the seasonal index at site i for the days of counting j; it is the ratio of the measured

flow in August to the measured flow in May

denotes the overall estimator of annual flow

denotes the variance of the term that follows

the weight attached to an estimate of annual flow

the actual daily flow at site i on day j

the actual annual flow at site i

the estimated annual flow at site i

25

PaPb

~qj ~ij ]

o a o a

the correlation coefficient between the site terms of two M-factors and two E-factors respectively

error terms

variances of error terms

Data sets I, II, III as in Appendix 1 with suffix s denoting strategic sites and suffix c denoting classified data available.

26

16

A +.a ¢-

¢J

O .

0

¢--

¢0

. B

O~

c-

t -

O

t+..

0 ¢_)

14

12

10

E

6 --

4 - -

2 --

0 8

Fig. 1

14h 16h

I I I I 10 12 14 16

Mid point of count (h)

18

Expected accuracy of annual f low estimate--all vehicles (Source: 1978 50 point census: Inter-urban sites, Monday to Thursday, neutral months)

4h

6h

A

C-

¢ J

Q . v

" 0

(13 Q .

X

c "

0 o - -

. B

"6

(J

14 - -

12 --

10 - -

8 - -

6 --

4 --

2 --

0

16

,2h /

10 12 14 16


1 8

Fig. 2 E x p e c t e d accu racy o f d a i l y f l o w es t imate- -cars

(Source: 1978 200 p o i n t census: In te r -u rban sites,

M o n d a y to T h u r s d a y , neu t ra l months)

A

E

CL

E O

X

¢ -

O

o~

¢.)

Fig. 3

16

14

12

10

- 6h

8h

n

12h

I I I 10 12 14 16 18


Expected accuracy of daily f low e s t i m a t e - - l i g h t goods veh ic les (Source: 1978 200 point census: Inter-urban sites, Monday to Thursday, neutral months)

16

A

t -

CL

t - _o t -

Q . X o~

"6 t - O

¢o >

¢.)

0

14 --

12 --

10 - -

8 - -

6 - -

4 - -

2 - -

0 10

4h

6h

8h

12hi I I I

12 14 16


18

Fig. 4 E x p e c t e d accuracy o f d a i l y f l o w e s t i m a t e - - h e a v y goods vehicles

(Source: 1 9 7 8 . 2 0 0 p o i n t census: In te r -u rban sites,

M o n d a y t o T h u r s d a y , neut ra l m o n t h s )

q

0 0

\. . ~ , : o

011

i'0 0

0

0 0 "::1"

0 0

I. N JO:l.Oell-lA I Ag N

C'D

~ . ~

~ II

~ LK~

O0 ~

0 0

0

r

q "iT I I

0

0

1 o

l I

o

"o c o

o tl.

I o l

0

0 CJ ~O

U I

l

U l

q

0 0

4

0 ~0

Q ~

I o o

I I o o o o

+

II

0 "O • -- "0

Q;

0 "--

"~, " ~ , _

$

0 0

o .--

o

-- 6

o

o

GO r-.

4-' Q;

t~

r~

P

o

, m

0 e-

l

,Ma

0

0 t~

°~ U.

o/ o°

0 ° • • • D • ° °

• • e

O 0

, •

r O 0

- -

• ~ oO ~o • O 0 ) • e e c o O / • , • 0

o I

v CN

Jl

ILl ..

O O0

~D

" O

LL

I I

I, 3 ' jo~,oe~t-- 3 ~ s n O n v / A e ~ aOeJaA v

q

" 0

-5

0

" 0 r "

0

0 r "

I (l~ A

f - 4..o

b . ,

l i t O

Lt3

O 0 C-

q l .

° ~ t J

O

o°/ . / •

• O 0 •

O0 -/ • O O O • • O o

O 0 • -/- • I~ o •

Oo oJ°O ° O O • ~

O O

0

I I

I. 3 'Jo~oe~-=l J, sn6nv /Ae~ a6eJa^V

0

d I

cl)

Q~0

on

_ q

A

v

nn

0

nnn

""5

0 e " -

qe ~

nn

0

0 0

I c ) o

0

~1 ~1

0

0

0

0

• o O 0 0 •

• O 0 0 0 O 0

! I o o o o

LN (sJeo) Jo~oet-lal

T~ r~ A "~ ~ +

:B ~" E -

.~_ .~_ , -

o o~ 00 LE

• 0 ~1

I Q 0

o o o

q

A

8 ~ m

E

8

o ~

U . "(3

0

0

0 0

A

II

°o

° _

0

° _

na

0 0

o o

• -

~o •

I I O ( ~ O O c ~

I'W (AO-I) Jo~0~J.-IAI

O O

o.

o.

O

O

o

r ~

,._1

x

r-

B

o

r ~

A r.)

" O

--S

O

CO

G) G, )

O (--

I

O O

r~

o ~ - - I

A

C~

O

O

O

C

c~

A

II

. .

~D . m

0

~J

" 0

U -

I o c3 o o

• w

• oOa

DO

I l o Q o o

I,~ '(ADH) Jo~.oej.-

o , o

q

>

o

9

0

0

0

0

v '

0 e,,,,

I

0 0

,-r

A

v

0

0

0

c

o m

<

0 ~ nn

11. A P P E N D I X 1

DATA SOURCES

This appendix sets out the data used in the study. There were data available for a total of eighty-seven sites as

summarised in the first table. The other five tables give the location and designations of each site. At the end

of the appendix is a list of the sites in each of three data sets. These data sets were used in calculating the

parameters quoted in tables of the main text. The standard road classes are denoted as:

M motorway 0 other

T trunk b built up

P principal n non built up

Summary of available data

Number of sites

Site numbers

50 point census

4 4*, 6, 7*, 30

33

13

1 - 3 , 5 , 8 , 9 , 1 0 " , 1 1 , 1 4 , 1 5 " , 1 6 - 1 8 , 2 0 - 2 4 2 6 " , 2 7 , 3 1 - 3 3 , 3 5 - 3 9 41--45

1 2 , 1 3 , 1 9 " , 2 5 2 8 , 2 9 , 3 4 , 4 0 , 4 6 4 7 , 4 8 * , 4 9 , 5 0

Traffic flow monitof ingcensus

4 9 3 , 1 0 0 , 1 4 6 , 1 4 8

1 0 9 , 2 0 4 , 2 0 7 , 2 2 9 12+ 3 2 6 , 4 0 7 " , 4 2 4 , 4 2 9 " ,

5 1 2 , 6 2 7 , 6 3 0 , 6 3 1

I(M) 252*

3(M) 2 5 6 " , 2 6 4 " , 2 7 8 "

Motorway census

4(M) 250", 251", 258", 263*

13(M) 3 0 0 - 3 0 7 * 3 0 9 - 3 1 3 "

Period of data

Continuous volumetric

flow

1974-1979

1974-1979

1974-1979

1978

1978

1977,1978

1978,1979

1977-1979

1977-1979

Occasional classified

flow

1978-1980

1978

1978

1978

1978

1978-1980

M denotes motorway sites

* denotes two directional continuous traffic flow data available.

The site numbers are those used in the 200 point census except those marked + which are those used in

the Traffic Flow Monitoring Census.

38

Location of twenty-three main urban sites

50 point

census

TFM sites

Motorways

Site No.

1

3

9

14

15

19

22

25

26

48

252

264

250

251

263

300

301

303

305

306

307

308

310

Road No.

A602

A312

B4012

C12a

A1

A58

B5251

A43

A614

A727

M1

M62

M1

M45

M6

M1

M3

M4

M4

M40

M40

M6

M6

Location

Hitchin, Herts

Ealing, London

Bullingdon, Oxon

Durham

Newcastle

Bolton, Lancs

Chorley, Lancs

Kettering, Northants

Nottingham

Renfrew, Strathclyde

Stapleford, Derbyshire

Morley, West Yorkshire

Friars Wash, Herts

Dunchurch Spur, Northants

Ansty, Warwick

Newport Pagnell, Bucks

Staines Lane, Surrey

Harlington

Chiswick

Abbey Barn Farm, Bucks

Handy Cross, Bucks

Cosford, Warwick

ExhaU, Warwick

Standard class

eb

Pb

On

On

Pb

Pn

Ob

Tb

Tb

eb

M

M

M

M

M

M

M

M

M

M

M

M

M

39

Location o f eighteen inter-urban sites

50 point

census

TFM sites

Motorways

Site No.

4

6

7

10

21

23

27

28

Road No.

A3

A272

A35

A45

A595

A621

A49

A454

Location

Guildford, Surrey

Petersfield, Hants

New Forest, Hants

Newmarket, Cambs

Wigton, Cumbria

Bakewell, Derbyshire

Church Stretton, Salop

Wolverhampton

30

42

45

256

258

302

304

311

312

313

A44

A96

A92

M4

M5

M3

M4

A1

M4

M4

Martley, Worcs

Inverurie, Grampian

St. Andrews, Fife

Severn Bridge, Avon

Rashwood, Hereford and Worcs

Up Nately, Hants

Winnersh, Berkshire

Sawtry, Cambs

Leigh Delarnere, Wiltshire

Membury, Wiltshire

Standard class

Tn

Pn

Pn

Tn

Pn

Pn

Tb

Pb

Pn

Tb

Pn

M

M

M

M

M

M

M

4 0

Location o f twenty-one recreational inter-urban sites

50 point

census

TFMsites

Standard Site No. Road No. Location class

18

41

43

47

278

109

123

201

204

207

229

326

407

424

430

512

627

629

630

63 I

641

A59

A40

A1

A9

M5

A166

A170

A595

A66

A55

A591

A148

A27

A29

A27

A458

A36

A30

A303

A30

A390

Skipton, North Yorkshire

Haverfordwest, Dyfed

Berwick, Borders

Pitlochry, Tayside

Bridgwater, Somerset

Nafferton, Humberside

Pickering, North Yorkshire

Halbeck, Cumbria

Keswick, Cumbria

Rhuallt, Clwyd

Ambleside, Cumbria

Coxford, Norfolk

Paines Wood, West Sussex

Ockley, Surrey

Fishbourne, West Sussex

Middleton, Powys

Stoford, Wiltshire

Camborne, Cornwall

Leigh Common, Somerset

Okehampton, Devon

Lostwithiel, Cornwall

Tn

Tn

Tn

Tb

M

Pn

Pn

Pn

Tn

Tn

Pn

Pn

Tn

Pn

Tn

Tn

Tn

Tn

Tn

Tn

Pn

Location o f eleven recreational local sites

50 point

census

Site No. Road No. Location Standard

12

13

16

31

33

35

37

38

40

46

49

C9

B1387

B1229

A389

B3157

B3188

B5106

A4120

C223

A831

B709

Tiptree, Essex

Blyth, Suffolk

Bridlington, Humberside

Wadebridge, Cornwall

Weymouth, Dorset

WilLit or, Somerset

Conwy, Gwynedd

Aberystwyth, Dyfed

Corwen, Clwyd

Cannich, Highland

Selkirk, Borders

class

On

On

On

Pn

Ob

On

On

Pn

On

Pn

On

41

Location o f fourteen local sites

50 point

census

Site No.

2

5

8

11

17

20

24

29

32

34

36

39

44

50

Road No.

C5

C9

B2056

C156

C539

C309

C320

C174

C133

C273

A525

C125

Location

Southwark, London

Winslow, Bucks

Deal, Kent

Chatteris, Cambs

Todmorden, West Yorkshire

Congleton, Cheshire

Welton, Lines

Dunchurch, Warwick

Axminster, Devon

Wellington, Somerset

Chippenham, Wiltshire

Wrexham, Clwyd

Thornhill, Dumfries

Stifling, Central

Standard class

Ob

On

Ob

On

On

On

On

On

On

On

On

Pb

On

On

Note: For four sites in the traffic flow monitoring census there are two alternative sets of site numbers as

follows:

TFM 200 point

site site number number

Location

123 93

201 146

629 148

641 100

Pickering, North Yorkshire

Ha!beck, Cumbria

Camborne, Cornwall

Lostwithiel, Cornwall

The following data sets deffme the sites used in calculating the parameters quoted in the tables of the main

text. A suffix s is used to denote strategic sites in a particular data set. Similarly, a suffix c is used to denote

sites with classified data. Not all sites are necessarily included in a calculation because of data limitations.

For example, some sites with classified flows do not have classified flows in August available.

Data Set I

This set consists of all sites with continuous data available, excluding some very low flow sites. In total

there are eighty-two sites. Sixty of these sites are strategic, of which thirty-one have classified data available.

Of the remaining twenty-two non-strategic sites, sixteen have classified data available.

4 2

Census s o u r c e

Fifty

point

(46 sites)

Traffic flow

monitoring

(19 sites)

Motorway

(I 7 sites)

Site designation

s & c

(19 sites)

s (5 sites)

c (16 sites)

neither s nor c

(6 sites)

s & c (8 sites)

s (11 sites)

s & c ( 4 s i t e s )

s (13 sites)

Site numbers

1 3 4 6 7 9 14 15 18 21 22

23 26 27 30 41 42 43 45

19 25 28 47 48

2 5 8 11 16 20 24 31 32

33 35 36 37 38 39 44

12 13 17 29 34 46

93 100 146 148 252 256 264 278

109 204 207 229 326 407 424 429

627 630 631

250 251 258 263

3 0 0 - 307, 3 0 9 - 313

Data S e t h

This set consists of those sites in data set I that are distant from holiday areas. They include all main

urban, inter-urban and local sites and some recreational roads leading to holiday areas. In total there are sixty-

five sites. Fifty-one of these sites are strategic of which twenty-six have classified data available.

Census site designation Site numbers s o u r c e

Fifty

point

Traffic

flow

monitoring

Motorway

s & c

(18 sites)

s (4 sites)

c (10 sites)

neither s nor c (4 sites)

s & c

(4 sites)

s (8 sites)

s & c (4 sites)

s (13 sites)

1 3 4 6 7 9 14 15 18 21

22 23 26 27 30 42 43 45

19 25 28 48

2 5 8 11 20 24 32 36 39 44

12 17 29 34

252 256 264 278

109 207 326 424 430 627 630 631

250 251 258 263

300 - 307, 309 - 313

Data Set III

This set consists of those sites in data set I that are in or near holiday areas. They include all recreational

inter-urban and recreational local sites and some inter-urban roads leading to holiday areas. In total there are

forty-two sites. Thirty-two of these sites are strategic, of which eleven have classified data available.

4 3

Census Site designation Site numbers source

Fifty

point

Traffic

flow

monitoring

s & c (6 sites)

s (1 site)

c (7 sites)

neither s nor c (3 sites)

s & c (5 sites)

s (15 sites)

6 18 27 30 41 43

47

16 31 32 33 35 37 38

12 13 46

93 100 146 148 278

109 123 201 204 207 229 326 407

424 430 627 629 630 631 641

Motorway s(5 sites) 258 302 304 312 313

44

12. APPENDIX 2

ASSESSING THE ACCURACY OF FLOW ESTIMATES

The accuracy of traffic flow estimates is assessed using the coefficient of variation o f the estimator, (the E-

factor or the M-factor as appropriate). The reason for this is illustrated in this appendix, for the case where a

single day's traffic flow is multiplied by an M-factor to estimate the annual flow.

If at a site i, a count is taken on day j, the annual flow Yi is estimated from the daily flow Xij using a monthly M-factor as follows:

A Yi(j) = M Xij

A where Yi(j) is the estimate of annual flow at site i, based on the measured flow on day j; and M is the appropriate

M-factor for a given road type, day type and month. The true annual flow is given as:

Yi = Mij Xij

The proportional error in the predicted annual flow is equal to the proportional error in the estimating M factor, as follows:

A Yi - Yi (j) = Mij Xij - M Xij

Yi Mij Xij

A Yi - Yi (j) _ Mij - M

Yi Mij . . . . . . . . . . . . . . . . . . . . . . . . . . . ( i )

1 Pi = Yi

so that:

The proportional root mean square error in the predicted annual flow at site i, (Pi) is given as:

Pi 2 l Yi - Yi(j)

nj Yi

A replacing Yi by its estimator Yi(j) in the denominator leads to an expected value of the proportional root mean square as follows:

Ai 1 Yi (J)

nj J \ Yi (j) /

4 5

expressing annual flows in terms of M-factors (compare equation 1), leads to:

The estimate of the proportional root mean square error for any site, of a given road type, is given at:

J 1 ~ i A. J 1 i~~j IMij--M I' ~-- . Pi = n i n j 1~

where n i is the number of sites considered of the given road type.

. . . . . . . . . . . . . . . . . . . . . . . ( 2 )

The right hand side of equation (2) is identical to the coefficient of variation in the M-factor (CM).

So the expected proportional root mean square error in the predicted annual flow is equal to the coefficient of

variation in the M-factor. Similar arguments apply when estimating daily flow using an E-factor, or estimating

annual flow by combining an E-factor with an M-factor.

46

13. APPENDIX 3

MULTI-FACTOR MODEL APPLIED TO TWO COUNTS

In this appendix, formulae are derived for the method of estimating annual flow from two counts and for predicting

the expected error in this estimate.

The estimation of the annual flow at site i is first considered. This is given by a linear combination for the two

counts in months 1 and 2, as follows:

Yi(1,2) = ~ w kFij kEij kMij k k = l

where

w k

Fijk

Eijk

Mijk

is the weight attached to the count in month k

is the measured flow at site i, on day j in month k

is the actual E-factor for site i, day j, month k

is the actual M-factor for site i, day j, month k.

Normally, mean values of the E-factor and M-factor are used, and the annual flow from two counts is

obtained by pooling the separate estimates from each count, so that:

2

Ai(1,2) = ~ WkFi jkEkMk k = l

. . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where E k and M k are the mean E-factor and M-factor in month k.

Next, suitable equations for obtaining the weights will be considered. The weights used should sum to

one and may be inversely proportional to the variances of the individual estimates. The variance of annual

flow from a single count in month k is given by:

A 2

V(Yi(k)) = Fij k . V (Eij k . Mijk)

To estimate this variance, the following equation is used for the short period count Fijk:

A Fij k = Yi(k)/Ek M k . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

Substituting in this value for Fij k leads to:

A A2 2 V(Yi(k)) = Yi (k). CT(k )

where CT(k ) is the coefficient of variation of the overall estimator EM in month k.

47

A Finally, it may be noted that the expected value of the estimated annual flow is Yi(k) and is the same for

all months. Therefore, the weights applied in equation (1) are given by:

wl + w2 = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 3 )

2

wt CT(2) " 2

w2 CT(1 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

The use of equations (1), (3) and (4) can provide a reasonable estimate of annual flow from two counts in

different months. Now a formula will be derived for assessing the expected accuracy of this pooled estimate.

The variance in this pooled estimate is given as:

2 A 2

V(Yi(1, 2)) = E w~ Fij k . V(EijkMijk) + k = l

2wlw2 Fij I Fij 2 . Cov(Eij I Mijl; Eij 2 Mij2)

To estimate this variance the value of the short period flow Fij k given by equation (2) could be substituted.

However, a more convenient measure of accuracy is the coefficient of variation CT(1, 2). Since the expected A

value of the estimated annual flow Yi(k) is the same for all months, the coefficient of variation can be

estimated as:

2 C ~ ( 1 ) + 2 2 C~(I, 2) = w 1. W2CT(2 ) + 2wl w2 Cov(Eij 1 Mij t;Eij2 Mij2)

E1 Mr. E2 M2

In this expression all the covariance terms are negligible, except those between the site terms. This means that if the size of the site terms a and b in a particular month is known, the size of these terms in another month may be inferred with some confidence. The correlation will be expressed using the correlation

coefficient, defined as follows:

• site correlation in M-factor:

Cov(ail, ai2 ) Pa =

x/V(aii ) . V(ai2 )

• site correlation in E-factor:

C°v(bil, bi2 ) p b =

x/V(bil ) . V(bi2 )

4 8

Using these expressions the overall coefficient of variation is given as:

2 2 2 2 2 CT(1, 2) = wleT(1) + W2CT(2) +

2wl w2 E PaCMa(1 )CMa(2 ) + Pb CE b (1)CEb (2)

where

CMa(k)

CEb(k)

is the coefficient of variation of the site component of the M-factor in month k; that is

x/V(aik)/Mk

is the coefficient of variation of the site component of the E-factor in month k; that is

Ve-~ik)/Ek •

(5)

49

14. A P P E N D I X 4

STATISTICAL ESTIMATION OF GENERAL E-FACTOR

The E-factor is used to expand a short period count to the daily total. For a number of short period counts

the E-factor tends to decrease as the seasonal component increases. The relationship is shown in the following

diagram for the case where a 12-hour count is mounted between 7 am and 7 pm on a weekday in May or

August.

E-factor

1 2 3

Seasonal index

The value of 2 (equals 24/12) is the expansion factor that would be used if the flow levels in each hour

were equal. The E-factor cannot be less than 1. The general decrease in the E-factor as the seasonal index

increases may be expressed using an exponential model, where n is the length of count and b is a parameter:

E = 1 + ( 2 4 x n -- 1) e - b S

In practice, provided the seasonal index is not too large (S < 2.5), the following simpler model can be

used which is a close approximation to the exponential model:

E = A(1 - Bx/-S-)

where A and B are parameters chosen to fit the data.

5 0

15. APPENDIX 5

STATISTICAL ESTIMATION OF GE NERAL M-FACTOR

The general M-factor is applied to the average of a daily flow in May and a daffy flow in August.

flow at a site i is then given as:

Yi = ½Mij(Xijx + Xij2)

Dividing throughout by the May flow Xij 1 results in:

Mij 1 = ½Mij(Sij + 1)

where the seasonal index Xij2 Sij - Xija

The annual

. . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 )

or Mij I = Mij Zij . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 3 )

where Zij equals ½(Sij + 1)

The general M-factor (Mij) is not correlated with the seasonal index (Sij) because of the way in which each

depends on the measured traffic flows in May (Xij I ) and August (Xij 2 ). These two flows are independent

random variables which are added in calculating the M-factor (equation 1) and divided in calculating the seasonal

index (equation 2). Nothing can be inferred about the distribution o f a quot ient o f two variables merely from

a knowledge o f the distribution o f the sum of two variables. To illustrate the point, the correlat ion between the

general M-factor and the seasonal index was calculated for each o f nine inter-urban sites using 1979 data. The

results confirmed the lack o f correlation where the average correlation coefficient was found to be -0 .05 . On

the sample data, the calculated values were found to be equally likely to be positive as to be negative. As a

result the variables in equation (3) may be averaged over all the possible combinat ions (j) of counts in May and

August to give:

Mil = M i Z i

Mil = ½M i (S i + 1 )

where

Mil

M i

S i

Z i

= mean May M-factor for site i

= mean general M-factor for site i

= mean seasonal index for site i

= ~ ( 1 + s i)

51

Since M i = M + ai:

Mil = M(Zi) + ai(Z i) (4)

To est imate M the May M-factor at a site (Mi l ) m a y be linearly regressed against Z i. The regression is an

example where a straight line is fi t ted through the origin, and the error term is linearly increasing with Z. The

best es t imate o f M is simply:

A ~ '~Mil M -

2;Z i

To es t imate the expected accuracy o f the annum flow when using this value of the mean M-factor we

proceed as follows. From equat ion (3) it m a y be no ted that:

Mij I = MZij + a i jZ i j

estimate error

Consequent ly , the coefficient o f variation in the M-factor at a site CMi depends on Zij and therefore the

seasonal index; such that:

CMi = C M • Zij

where

C M = x/~ar--(°tij) x 100%

M

. . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

The pa rame te r C M is es t imated in a similar way to the mean general M-factor:

A x CMi C M =

2~Z i

It m a y be noted tha t the propor t ional root mean square error in the annual flow estimate is the same as

the coeff ic ient o f variation in the general M-factor. Consequently the value of CMi given in equation (5) can be

used to assess how accurate the es t imated annual flow at a site is likely to be.

52

(1364) Dd8041376 1,400 6/84 H P L t d S o ' t o n G3371 PRINTED IN ENGLAND

ABSTRACT

Estimation of annual flow from short period counts: GARWYN PHILLIPS, PHILIP BLAKE and DAVID REESON: Department of the Environment Department of Transport, TRRL Supplementary Report SR 802: Crowthorne, 1984 (Transport and Road Research Laboratory). Short period manual counts of less than twenty-four hours duration are commonly used to measure traffic flow at particular sites. In a previous report, SR 514, the accuracy of the estimates of total annual flow from a single short period count was examined. Recommendations were given for the most appropriate length and timing of these counts. In this report, the previous work has been extended to cover the estimation of flow for individual vehicle categories. In addition, the value of mounting two counts, one in August and one in a neutral month, has been investigated. Recommendat ions are given for the appropriate timing of counts and methods of estimation.

ISSN 0305-1293

ABSTRACT

Estimation of annual flow from short period counts: GARWYN PHILLIPS, PHILIP BLAKE and DAVID REESON: Department of the Environment Department of Transport, TRRL Supplementary Report SR 802: Crowthorne, 1984 (Transport and Road Research Laboratory). Short period manual counts of less than twenty-four hours duration are commonly used to measure traffic flow at particular sites. In a previous report, SR 514, the accuracy of the estimates of total annual flow from a single short period count was examined. Recommendations were given for the most appropriate length and timing of these counts. In this report, the previous work has been extended to cover the estimation of flow for individual vehicle categories. In addition, the value of mounting two counts, one in August and one in a neutral month, has been investigated. Recommendat ions are given for the appropriate timing of counts and methods of estimation.

ISSN 0305-1293

transport research laboratory - department of the ...estimation of traffic flow using the...

Documents