Transportation 4 (1975) 5 5 - 6 6 © Elsevier Scientific Publishing Company, Amsterdam - Printed in the Netherlands

DESIGN C HAR TS F O R E S T I M A T I N G T R A N S P O R T A T I O N P L A N N I N G STATISTICS F R O M A R E A P O P U L A T I O N

K E N N E T H ROSE

Associate Professor of Civil Engineering, Queen's University, Kingston, Ontario, Canada

A B S T R A C T

Utilizing data collected for urban transportation studies in Ontario, regression analysis has been used to establish relationships between the daily number of person trips in an urban area and the area population. In particular the number of trips by auto drivers, auto passengers and mass transit riders have been investigated. Further, auto driver trips have been stratified into the following destination trip purposes: return home, work and related business, shopping, social-recreational and miscel- laneous. The results of this analysis have been used to prepare a set of design charts. These charts are presented graphically and in the form of a nomogram. The accuracy of these charts has been investigated and found satisfactory for most planning purposes.

Introduction

This paper discusses the deve lopmen t of a set o f design charts cons t ruc t ed to help planners es t imate some t r anspor t a t ion planning statis- tics fo r an urban area, f rom a knowledge o f the area popula t ion .

The t radi t ional t r anspo r t a t i on planning process has b eco m e the sub- jec t o f considerable discussion and criticism. The cur ren t process requires the co l lec t ion o f vast a m o u n t s o f data which are used to cal ibrate the various c o m p u t e r models inc luded in the planning process. These data are very detai led and expensive to collect, y e t the end result is a p ro ced u re that canno t be used to give quick responses to quest ions posed by planners. This def ic iency has led to a search for simplified planning p rocedures (De Leuw, Cather 1970).

One approach that can be used to aid planning is to use j u d g e m e n t and infer planning statistics fo r a par t icu lar munic ipa l i ty f rom o the r similar municipal i t ies for which data exist. A n o t h e r approach available to

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the planner is to estimate the value of some parameter using a more easily available statistic as a proxy.

The basic philosophy of this study is that it should be possible to establish norms that would be helpful in estimating travel characteristics in urban areas. These norms should be estimated from readily available statistics, such as area population, and should be available to the planner in the form of simple charts.

Earlier studies (Wilbur Smith 1961, 1966) have utilized data from a

wide geographic base (continental U.S.A.). It seemed reasonable to assume that an analysis of data from a limited geographic area, (the Province of Ontario), might produce more consistent results, because differences in soc ioeconomic characteristics and patterns of living would not be as pronounced.

Study Procedure

The government of Ontario has had some 50 urban transportation studies completed since 1960. It was not possible to include all of these studies in this present investigation because the data collected as part of some of these studies were no longer available.

Secondly, because area population was to be used as the estimating parameter, studies were selected to cover as wide a range of populat ion size as possible. Because of these limitations the studies undertaken in the urban areas listed in Table 1 were selected for use in the study. The table

TABLE I

Studies Used in the Regression Analysis

Data Point City Date of Population of Code # Survey Study Area

1 Metropolitan Toronto 1964 2,820,000 2 Ottawa- Hull 1963 496,800 3 Hamilton 1961 372,233 4 London 1963 172,885 5 Kitchener - Waterloo 1965 118,636 6 Thunder Bay 1968 105,922 7 Burlington - Oakville 1963 97, 559 8 Guelph 1965 50,236 9 Orillia 1969 22,075

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shows the coding used when plotting the data points on graphs, along with the names of the cities and their population at the time the data were collected.

Once the study areas had been selected, copies of the transportation study reports were obtained and the relevant data were extracted. If the data were incomplete letters were sent to the respective consultant, who produced the report, requesting the missing information. Much of the information requested from the consultants was no longer on file, in particular data concerning trips to and from the C.B.D. of the study areas was not widely available. Because of this deficiency in the data, the study was restricted to investigating the possibility of estimating planning para- meters such as the total number of person or vehicle trips in an urban area.

The data were checked for consistency between the reports. Any inconsistencies that did occur in reporting the basic data were removed as far as possible by regrouping the data.

Two important factors affecting the planning of urban transportation systems are the modes by which urban residents travel and the purposes for which they make their t'rips. This analysis represents an at tempt to obtain a better understanding of these factors. To do this the numerical data were summarized into person trip characteristics by mode of travel and also automobile driver trip characteristics by trip purpose.

Three main modes of person trips were considered: automobile driver, automobile passenger and mass transit.

Automobi le driver trips comprised the major mode of travel in all the study areas. Therefore automobile driver trips were analyzed further by stratifying these trips according to trip purpose at the destination.

The following classifications of trip purpose were used:

1 ) Return home 2) Work and related business 3) Shopping and personal business 4) Social and recreational 5) Miscellaneous

The miscellaneous category included purposes such as "change travel mode" and "serve passenger."

These data, with the exception of those for Metropolitan Toronto were used in the statistical analysis required to establish relationships between the number of trips per day in each trip category and the area population.

The data for Metropolitan Toronto were not used in this analysis because the population of Toronto is larger than the second largest city by

57

a factor of seven. It was felt that the inclusion of the Toronto data would bias the analysis in favour of this large city. Instead the data for Toronto were used to help select the best equations.

Statistical Analysis

The basic data for each city were used to establish statistical relation- ships between the dependent and independent variables. The best fit parameters for several models were calculated on an unweighted least squares basis and a statistical t-test taken of their significance. The 95% level of significance was adopted but in most cases the levels of signifi- cance were better than this, hence the standard errors of the estimate tend to be small.

The models considered were:

a) a simple linear law

y = a + b x

b) a non-linear quadratic law

y = a + b x + c x 2

c) a non-linear exponential law

y = a + b log x

d) a power function

y = ax b

This latter model can be rewritten as

logy = loga + b logx

In each of these models y is the number of trips per day for a particular trip classification, x is the area population and a, b and c are constants.

Each of these types of model has been used previously in transpor- tation planning and each of the models gave a reasonable fit to the data.

The statistical analysis included calculations of the coefficient of determination (R 2) and of the standard error of the estimate ( S x y ) for each of the equations tested. A value o f R 2 close to 1.0 indicates that the estimated equation is a good fit to the data points and a low value for S x y

indicates that the value of the dependent variable can be accurately predicted from the independent variable. These two statistics formed the basis for selecting the preferred equations and are tabulated in Table II.

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TABLE II

Statistics Associated with the Regressions Models

Quadratic Function Exponential Power Function Function

D e p e n d e n t R 2 S /~2 S R 2 S xy % xy % xy %

Variable ), y ),

Total Person Trips 0.99 5 0.96 15 0.96 1.7 Auto Driver Trips 0.97 10.5 0.97 9 0.94 1.8 Auto Passenger Trips 0.99 2.9 0.96 14 0.93 2.4 Mass Transit Trips 0.98 19 0.81 5.6 0.97 2.6 Auto Driver Return

Home Trips 0.97 ! 1.9 0.94 14 0.95 1.7 Auto Driver Work Trips 0.99 5.4 0.98 8.6 0.94 1.9 Auto Driver Shopping &

Personal Business Trips 0.93 19 0.93 17 0.92 2.8 Auto Driver Social -

Recreational Trips 0.77 33 0.80 28 0.82 4.3 Auto Driver Miscellaneous

Trips 0.92 18 0.94 13 0.90 2.3

The values o f R 2 are acceptable for all the models. The best values were ob ta ined with the quadra t ic equat ion. The values o f R z also decrease as the data were stratif ied, thus the values for S o c i a l - R e c r e a t i o n trips are cons is tent ly smaller than the values for Tota l Person trips.

Using these cri teria there was very lit t le d i f ference be tween the quadra t ic func t ion and the power funct ion. However , the rapid increase in the size of the s tudy area popula t ions resul ted in considerable grouping of the data points at the lower end o f the scale, when the func t ions were p lot ted . I f the quadra t ic funct ions were to be used as design charts, the equa t ions had to be ex t r apo la t ed well b e y o n d the range o f the data points. Because this ex t r apo la t ion was non-l inear it was decided that this would reduce the ut i l i ty of the design charts, consequen t ly these func- t ions were exc luded f rom fu r the r considerat ion.

The power func t ions and exponen t ia l relat ionships were comparable , but tests on the abil i ty o f these relat ionships to predic t ex t r apo la t ed data indica ted tha t the exponen t i a l relat ionships consis tent ly underes t ima ted the true value.

As a result, all the design charts developed in this work are based on the power func t ion model . The parameters developed for these models are shown in Table III. The table also shows the Coeff ic ien t of De te rmina t ion of each equa t ion and the Standard Er ro r of the Es t imate expressed as a percen tage of the mean value.

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T A B L E llI

Equations Developed by the Regression Analysis

All the equations are of the form Log,0 (Dependent Variable) = C + K Logl0 (Area Population)

Dependent C K Coefficient of standard error Standard error Variable Determination of the estimate as % of mean

R 2 S Sx y x~_ % Y

Total Person Trips 1 .1546 0 . 8 4 3 6 0 .96 0 . 0 8 9 9 1.7 A u t o Driver Trips 1 .3240 0 . 7 6 8 8 0 .94 0 , 0 9 2 9 1.8 Auto Passenger Trips 0 . 5 1 9 2 0 . 8 6 2 3 0.93" 0 . 1 1 8 0 2.4 Mass Transit Trips - 1 . 7 9 6 0 1 .2173 0 .97 0 . 1 1 1 5 2.6 Auto Driver Return

Home Trips 0 . 5 7 0 2 0 . 8 4 3 5 0 .95 0 . 0 8 2 9 1.7 A u t o Driver Work Traps 0 . 3 2 0 2 0 . 8 5 2 5 0 .94 0 . 8 8 7 6 1.9 A u t o Driver Shopping &

Personal Business Trips - 0 . 2 8 9 6 0 . 9 2 7 5 0 .92 0 . 0 5 7 9 2.8 A u t o Driver Social -

Recrea t iona l Trips - 0 . 3 9 8 2 0 . 9 0 9 6 0 .83 0 . 1 7 6 7 4.3 Auto Driver Miscellaneous

Trips 0 . 9 2 3 7 0 , 6 5 5 4 0 ,90 0 . 1 0 6 2 2.3

All of the equations, with the exception of the daily number of Mass Transit trips have slopes less than unity. This implies a declining growth curve, while each additional increase in area population increases the number of trips made, it does so at a decreasing rate. Mass Transit on the other hand is an increasing growth curve.

Results

Figure 1 is typical of the relationships developed in the statistical analysis. As can be seen the equations plot as straight lines on full logarithmic graph paper. The shaded band on the chart indicates the range of values +- one standard error away from the regression line. This shaded area gives an indication of the expected range of the value of the dependent variable.

These regression equations are only valid within the range of the available data points and caution must be used when extrapolation is required.

Because it is reasonable to expect the population of urban areas to grow with time, it was decided to investigate the effect of extrapolating

60

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Fig. 1, A u t o m o b i l e driver Return H o m e trips per day as a funct ion of study area populat ion

the regression equations beyond the range of the data points. To do this the corresponding data point for Metropolitan Toronto

was plotted on each of the graphs developed to see whether this data was within the expected range obtained by linear extrapolation. This point is shown in Figure 1.

With the exception of shopping and personal business trips the corresponding data point for Toronto fell with the expected band. Conse- quently it seems reasonable to develop these equations into design charts.

Design Charts

Two forms of design charts have been developed. The first examples are shown in Figures 2 and 3. Each of these figures shows plots of the regression equations developed.

61

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Fig. 2. Design chart for estimating the daily trips by various modes of transportation

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Fig. 3. Design chart for est imating the daily trips for various trip purposes

In Figure 2 the abscissa is the area population and the ordinate is the expected number of trips per day by each mode of transportation. In Figure 3 the abscissa is again the area population and the ordinate is the expected number of automobile driver trips per day for various destina- tion trip purposes.

Each of these diagrams also shows the width of the confidence band associated with each of the predicted values.

An alternative method of presenting these charts is shown in Figure 4. This is a simple homograph that allows estimates of various trip types and purposes. The population scale is available on each side of the nomograph. A horizontal line joining the population scales allows the estimated value for the various classification of trip types to be made from the other scales in the chart.

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An example will best illustrate the use of these design charts. Con- sider an urban area with a population of 400,000 people. Using the nomograph it will be reasonable to expect this area to have 765,000 person trips per day.

These person trips will be distributed among the three modes of transportation as follows:

automobile driver automobile passenger mass transit rider

440,000 220,000 100,000

Considering only the automobile driver trips it can be expected that these trips will be made for the following destination trip purposes:

Return Home 199,000 Work 125,000 Shopping 80,000 Socia l -Recreat ion 40,000 Mis cellan eous 39,000

Because each of the equations used in the charts was developed independently, the total number of daily automobile driver trips obtained by summing the number of trips for each trip purpose does not necessarily agree with the value calculated for the number of daily automobile driver trips from the raw data. As can be seen the difference is less than 10% which is satisfactory for most planning purposes.

The agreement between the total daily person trips and the value obtained by summation of the number of trips by each mode is much better. This is to be expected because the raw data was less stratified in this case.

Conclusions

This paper has presented the development of some design charts which allow various transportation planning statistics to be estimated from a knowledge of the area population. The ability of these charts to predict values that have to be extrapolated to suit larger population areas has been demonstrated.

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References

De Leuw, Cather & Co. of Canada Ltd. (1970).. A New Procedure for Urban Transportation Planning, Toronto.

Wilbur Smith & Associates (1961). Future Highways and Urban Growth, New Haven, Conn.

Wilbur Smith & Associates (1966). Transportation and Parking for Tomorrow's Cities, New Haven, Conn.

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