MATHEMATICAL MODELLING

OF

SRI LANKA'S OPERATIONAL VEHICLE FLEET

AND ITS USAGE

Dr. Amal S. Kumarage,

Dept. of Civil Engineering,

University of Moratuwa,

Moratuwa, Sri Lanka.

Paper Submitted to the 49th Annual Sessions of the

Sri Lanka Association for the Advancement of Science,

December 6-10, 1993

University of Peradeniya, Peradeniya.

i

Abstract

The statistics on the vehicle fleet in Sri Lanka are compiled by the Department of Registration of Motor

Vehicles. Annual records of all new registrations have been maintained since 1928. However, of the

vehicles that have been scrapped, only those which have been officially reported have been removed from

the register. Accordingly, the present operational fleet is reported to be over one million vehicles.

Computation of the operational fleet from vehicle revenue licenses issued and by fuel consumption

estimates, places the active fleet at a much lower value.

Multiple Linear Regression has been used in modelling the relationship between the survival rate of vehicles

in a given registration series and the mean age of the series. Revenue license data has been used in this

calibration. Most vehicle types have shown a s-curve where scrappage is low in the initial period, increasing

in subsequent years to end up with a very low survival percentage, presumably those which are maintained

as collectors items. The regression modelling has successfully enabled the calibration of eleven different

vehicle types as two-part models, where the s-curve has been approximated into a linear-exponential

relationship to facilitate analysis.

The relative use of different types of vehicles and the variation of usage with age of vehicles has also been

modelled using regression. Using field data collected for this purpose, usage is modelled as a function of the

negative exponential value of age of vehicle.

These models can be used to estimate the operational fleet by type and corresponding annual kms. operated.

This is a basic but vital piece of information necessary for transport planning in Sri Lanka.

1

1.INTRODUCTION

Statistics maintained by the Department of Registration of Motor Vehicles (RMV) do not indicate the active

vehicle population in Sri Lanka. Accurate records are not available from annual licensing authorities either.

An alternate means of obtaining the statistics of the operational vehicle fleet is to investigate the number of

annual revenue licenses renewed for each vehicle type. This information is not available in complete for the

entire island for the present times. The last such complete figure is for the year 1980. Since then the civil

disturbances in the north and east and subsequent decentralising of the revenue licensing to the provincial

governments have made the compilation of the island wide fleet impossible. Only the figures of the

Colombo District are available for the period since 1980. The total vehicles registered till end of 1980 was

337,382. In comparison the licenses renewed in 1980 were only 216,158 (64%).

From the above discussion we see that there is no provision at the moment to get an accurate estimate of the

operational fleet. The only conclusion we can arrive at with confidence is the irrefutable evidence that the

number of the licenses renewed is much less (around 60-65%) than the number of total registered vehicles.

This leaves us with three possible answers to bridging the gap, viz; (a) all registered vehicles since 1928 are

operational and that there is a very large percentage (35-40%) of vehicles operating without revenue

licenses, (b) that a large number of vehicles (over 290,000) have been taken out of operational service but

that all operating vehicles have obtained valid revenue licenses and (c) a combination of the scrappage of

less than 290,000 plus a rate of non renewal of licenses which is less that 35%. The most logical hypothesis

to begin testing would be the latter wherein both scrappage and evasion rates can be tested.

2.APPROACH

The basic approach in determining the operational vehicle fleet and its operational characteristics comprises

of several stages. These can be described as follows:

Stage 1.Observation of the revenue licenses renewed, by series for some representatively selected areas.

Stage 2.Developing of a mathematical model to estimate the renewal rate by vehicle type and mean age of

series.

Stage 3.Grouping of vehicles in each series into categories suitable for analysis.

Stage 4.Estimation of the island-wide fleet of vehicles operating with valid revenue licenses.

Stage 5.Estimation of the percentage of vehicles in each category operating without valid revenue licenses.

Stage 6.Adjustment of the mathematical model to account for the percentage of renewal evasions in each

category.

Stage 7.Estimation of the total operational fleet by vehicle category and age.

Stage 8.Observations of the relative activity levels of each vehicle category identified by age of vehicle.

Stage 9.Developing a mathematical model to estimate the relative activity rate of each vehicle type as a

function of age of vehicle.

Stage 10.Mathematical modelling process, to estimate the operational characteristics of the fleet and the

2

relative operational level by each vehicle category.

In following the above procedure, it will be necessary to make a number of plausible assumptions regarding

missing or incomplete information. However, no modelling result would be accepted without conclusive

statistical acceptance, in order to achieve reliability of the assumptions made.

Vehicle Classification

The following vehicle categories have been used in this analysis:

1.Motor Cycles:All motor cycles excluding challys.

2.Challys:Motor Cycles identified with CF engine classification.

3.Three Wheelers:All three wheel vehicles.

4.Cars (Petrol):All four wheel covered petrol vehicles up to station wagons, but not including Pick ups,

Jeeps & Vans.

5.Cars (Diesel):All four wheel covered diesel vehicles up to station wagons, but not including Pick ups,

Jeeps & Vans.

6.Vans (Petrol):Petrol driven Pick Ups, Jeeps and Vans up to and including the size of the Toyota Hi Ace

(new model).

7.Vans (Diesel):Diesel driven Pick Ups, Jeeps, Pajeros and Vans up to and including the size of the Toyota

Hi Ace (new model).

8.Lorries/Trucks:All lorries larger in size than a van typified by the four wheel Isuzu 150 as the smallest

category. This includes all six wheel trucks and multi-axle trucks.

9.Buses:All vehicles designed for the carriage of passengers larger in size than the biggest Van (Toyota Hi

Ace), except for the cases where smaller vehicles are used for regular

public transportation route operations.

10.Land Vehicles:All four wheel and two wheel tractors.

3.DATA COLLECTION

The data necessary for the analysis was obtained from a number of sources. The registration figures, ages of

vehicles at registration, dates of registration, weight categories etc were obtained from the RMV. This data

is given in Appendices IV & V of Reference 1. All other data were obtained from specially designed

surveys conducted by the University of Moratuwa, for the Transport Studies and Planning Centre, Ministry

of Transport & Highways. The method by which the field data was obtained is described below:

Vehicle License Renewal Surveys

These surveys were done in order to obtain the number of vehicles for which licenses have been renewed by

series for the year 1991. This information was obtained for Colombo District from the Provincial

Commissioner of Motor Traffic, for North Central Province, from the Provincial Secretariat at

Anuradhapura, for the Kandy, Matara and Thihagoda AGA divisions from the respective AGA offices. This

information was obtained from the books of prime entry. The number of vehicles renewals recorded from

3

each source and the date(s) on which it was recorded are given as follows:

Colombo District - 168,548 Renewals

Matara AGA Div. - 3,118 Renewals

Thihagoda AGA Div. - 672 Renewals

Kandy AGA Div.- 13,342 Renewals

North Central Prov. - 11,459 Renewals

------------------

197,139 Renewals

A complete breakdown of this data can be found in Appendix II of Reference 1. The above areas were

selected as a sample that would represent the entire country. As shown in Table 1, in order to get this

representation, the number of samples obtained from each location has been compared with the number of

license renewals made in 1980 in all the areas represented by each locality. The rate between them has been

defined as the proportional rate. By multiplying the actual observations per series per locality the total

license renewal island-wide was obtained.

Table 1: Computation of Proportional Rates for Revenue License

Survey Analysis

Area Sampled No of

Samples

Obtained

Other Areas

Represented

1980 Est

Renewals

in Rep

Areas

Proportional

Rate

Colombo Dist. 168,548 133,251 0.79

Kandy AGA. 11,459 Uva + S'gamuwa + 50% of

NWP

33,715 2.94

North Central Prov. 13,342 50% of NWP + EP + NP 31,812 2.38

Matara AGA +

Thihagoda AGA

3,790 SP + Gampaha + Kalutara Dist. 17,380 4.59

Total 197,159 216,158

License Plate Surveys

These surveys were carried in order to obtain the relative activity level of different categories of vehicles

and to investigate the effect of age within these categories. The surveys were done in four provinces, namely

the WP, SP, CP and NCP. The surveys were done on A, B and C class roads in each of these provinces and

in addition within the Greater Colombo Area which was considered separately. This data is given as

Appendix III of Reference 1.

4

4.ESTIMATION OF THE OPERATIONAL FLEET

The estimation of the operational fleet will be preceded by the model estimation of the vehicle licenses

renewed for the year 1991 by vehicle type. An adjustment for the non-renewals will lead us to the estimated

operational fleet sizes.

The basic approach herein would be to compute the estimated number of vehicle licenses renewed in 1991

based on our field observations described in Section 3. Based on the premise that vehicles at time of

registration will have 100% renewals, a pro-rata factor has been obtained for the renewal rate by taking the

division between renewals estimated for the series and the total number of licenses issued under the

particular series. This rate adjusted to read 1.0 for vehicles being registered for the first time in 1991, will

yield us the survival rate for each series in the year 1991. We have for each vehicle type then examined the

relationship between the survival rate and the age and attempted to model a relationship whereby mean

survival rate can be explained as a function of age of the vehicles.

CARS

The mean age, mean age at registration, survival rate in 1991 have been given in Table 2, for the series

under which cars have been registered.

5

Table 2: Input Parameters for Cars

SERIES AGE AT

REGISTRATION (Years)

AVERAGE AGE

(Year)

SURVIVAL

RATE

17 2.59 2 1.00

16 4.13 2 0.96

32 4.32 1 0.96

15 5.24 2 1.01

14 6.65 2 0.99

13 9.07 2 0.91

12 11.79 3 0.86

11 13.50 3 0.81

31 15.56 1 0.69

10 15.64 4 0.38

9 17.33 5 0.50

8 17.71 5 0.46

7 18.23 4 0.41

6 19.61 2 0.44

5 23.39 1 0.33

4 28.08 0 0.29

3 31.55 0 0.32

2 32.62 0 0.28

1 34.06 0 0.24

The Figure 3, shows the plot of the relationship between survival rate and age (since manufacture) of cars. It

can be seen that the survival rate is somewhat constant over the first six years. Thereafter, the rate drops, but

at a rate which decreases with time. This type of relationship is close to a `inverted- S' type of function.

However, these functions are extremely difficult to fit and hence we shall consider this relationship to be

explained in two part, that is a linear constant part for the first six years and an exponential function

thereafter.

6

Figure 1: CARS: Survival Rate by Age (Years)

┌┴────┴────┴────┴────┴────┴────┴────┴──┐ ┤ ├ S 1.0 - *** * │ u │ * │ r │ ** │ v │ │ i .7┤ * ├ v │ │ a │ │ l │ ** │ │ ** │ R .35┤ * * * ├ a │ * * │ t │ * │ e │ │ │ │ 0┤ ├ └┬────┬────┬────┬────┬────┬────┬────┬──┘ 6 18 30 42

0 12 24 36

Age (in years)

The regression of the exponential function is given below, where an extremely well fitting relationship has

been obtained to explain survival rate as a function of age. As shown, the adjusted 0 of 95% indicates

the percentage of variation about the mean explained by the model. The model

also has a F significance less than the 0.0000 level, or a 99.99 percent level

of confidence. The coefficient for the variable AGE 0 is acceptable at a t-

statistic significance of the same order. The value for the constant is

statistically not different from 1.0 (survival rate when age = 6 yrs.

* * * * M U L T I P L E R E G R E S S I O N * * *

R Square .95306

Adjusted R Square .94945

Standard Error .10618

Analysis of Variance

DF Sum of Squares Mean Square

Regression 1 2.97577 2.97577

Residual 13 .14657 .01127

7

F = 263.94159 Signif F = .0000

------------------ Variables in the Equation ------------------

Variable B SE B Beta T Sig T

AGE -.04367 2.68827E-03 -.97625 -16.246 .0000

(Constant) .01817 .05442 .334 .7438

The model can then be written as Equation 1 where it is shown that the survival rate (Y) decreases at an

exponential function of 0.044 times the age (X) after six years. Thus the estimated mean survival rate of a

car ten years old will then be 0.84. At twenty years this reduces to 0.54. At thirty years it will be 0.35, with

a survival rate of only 0.13 at fifty years.

MOTOR CYCLES

An 0 coefficient of -0.099 for AGE (X) was obtained for the survival rate (Y) of motor cycles. This

coefficient, as anticipated is more than twice as much as that obtained for cars in the previous regression,

indicating that the life span of motor cycles is approximately half that of motor cars.

VANS

(1)

8

The modelling for vans, which included both petrol and diesel vehicles, was done after assigning an intrinsic

variable to identify the fuel difference. The results of the regression, show that petrol vans have a much

higher scrappage rate than the diesel vans. This is intuitively plausible since, there is a tendency towards the

conversion of petrol vans to diesel because of the high price difference between the two fuel types.

BUSES

Buses were also very difficult to subject to a mathematical regression, primarily because the peoplised

services had not obtained revenue licenses for the year 1991 due to a clarification being sought on the basis

of licensing of their buses. Therefore the modelling considered all the peoplised buses as being among those

which had not obtained renewals for vehicles operating on the roads (evaders). This is evident from the

coefficient obtained for buses which shows it to be even higher than that obtained for motor cycles.

LORRIES

A total of eight series were used as input for the modelling of the survival rate for lorries. The plot of the

survival rate with age is given in Figure 2. The results of the regression reveals that the coefficient of the

variable AGE for lorries is -0.062 which is a higher rate of scrappage than diesel vans and cars, but a lower

rate than motor cycles.

Figure 2: LORRIES: Survival Rate by Age

┌┴────┴────┴────┴────┴────┴────┴────┴──┐ ┤ ├ S 1.00│ │ u │ * │ r │ │ v │ │ i .75┤ * ├ v │ * │ a │ * * │ l │ * │ │ │ R .375┤ * ├ a │ │ t │ │ e │ * │ │ │ 0┤ ├ └┬────┬────┬────┬────┬────┬────┬────┬──┘

9

6 18 30 42

0 12 24 36

Age (in years)

LAND VEHICLES

Because of the smaller number of series for these types of vehicles, it was not possible to separate between

the two wheeler and four wheeler categories. The results of the regression indicates a coefficient of -0.069

for land vehicles.

The summary of the results of the multiple linear regression of survival rate as the dependant variable and

mean age as the independent variable have been given in Table 3, where the general form of the model is as

given in Equation 2. The coefficients obtained have all been tested at the 5% level of significance and the R

squared value in each model has been over 80% (except in the case of land vehicles where it was 70%).

Table 3: Summary of Regression Analysis

Vehicle Type n

yrs

0 Evasion Rate at

Mean Age

0

Car 6 -0.043 9% -0.035

Motor Cycles 3 -0.099 12% -0.080

(2)

10

Vans (Petrol) 4 -0.096 6% -0.065

Lorry 2 -0.062 3% -0.053

Bus 3 -0.100 33% -0.044

Trailers 0 -0.046 20% -0.031

Land Vehicles 2 -0.069 20% -0.047

ADJUSTMENT FOR NON-RENEWALS

The result obtained in the previous section is that of the coefficient for the survival rate assuming that there

are no evaders of the renewal system. A separate survey documented in Reference 2 revealed that the

evasion figure to be quite high in almost all types of vehicles. In some categories such as jeeps and tractors it

is reported to be exceeding 20%.

The adjustment that is required is therefore quite significant. It was observed that older vehicles appeared to

have a greater percentage of non-renewals when compared to newer vehicles. Thus the procedure adopted to

adjust for the non-renewals was based on an assumption that the evasion rate which increase with age, is

such that the rate observed is the rate at the modelled mean life of the vehicle type. Table 3 shows the

observed mean rate of evasion at mean age of each vehicle type and correspondingly adjusted coefficient 0.

Therefore the equations derived in the previous sections have to be adjusted to the new coefficient value

given in Table 3. These values we will use in the following section to determine the operational

characteristics of the vehicle fleet.

5.ESTIMATION OF THE OPERATIONAL CHARACTERISTICS OF THE VEHICLE FLEET.

The procedure adopted in this section is to first investigate the relative usage between different types of

vehicles and the variation of usage with age within the same category. In order to do this, the observations

from the License Plate Surveys have been used.

PETROL CARS

Cars have been further separated into petrol and diesel vehicles, as they have different usage characteristics.

Table 4 gives the estimated number of cars surviving from each series, the mean age of the series and the

relative rate of observed usage by series based on the rate between the aggregated license plate observations

and the estimated survival rate of the particular series. This relative rate of usage is graphically represented

as a function of age in Figure 3. We can see that an obvious relationship exist between the use of vehicles

11

and age.

Table 4: Input Parameters for Cars (Petrol)

--------------------------------------------------------

SERIES SURVCARP SURVCARD FUEL AGE CARPC CARRATE

--------------------------------------------------------

1 2477.35 .00 1 34.81 1.00 1.36

2 2588.12 .00 1 33.37 1.00 2.44

3 2879.15 .00 1 32.29 1.00 4.45

4 2909.18 .00 1 28.82 1.00 2.50

5 3261.35 .00 1 24.13 1.00 2.41

6 3770.32 .00 1 20.36 1.00 2.43

7 3715.11 .00 1 18.97 .97 3.81

8 3147.15 .00 1 18.45 .68 4.22

9 2920.49 .00 1 18.08 .86 5.63

10 1301.83 .00 1 16.39 .43 5.84

11 5800.54 .00 1 14.24 .95 6.42

12 7326.33 .00 1 12.53 .98 6.28

13 7940.03 .00 1 9.81 .98 12.87

14 8748.46 .00 1 7.39 .93 11.21

15 8542.00 .00 1 5.99 .87 14.07

16 6823.00 .00 1 4.88 .73 16.04

17 5755.00 .00 1 3.33 .62 17.93

--------------------------------------------------------

12

FIGURE 3: CARS: (Petrol) Km Rate by Age

┌─┴────┴────┴────┴────┴────┴────┴────┴─┐ 18┤* ├ │ │ │ * │ │ * │ K │ * │ m 12┤ ├ │ * │ R │ │ a │ │ t │ │ e 6┤ * * * * ├ │ * * │ │ * │ │ * * * * │ │ *│ 0┤ ├ └─┬────┬────┬────┬────┬────┬────┬────┬─┘ 4.25 12.75 21.25 29.75

8.5 17 25.5 34

Age (in years)

From a multiple regression of the variable AGE with the rate of usage, we find the existence of a very

significant negative exponential relationship, the coefficient of which is -0.069. The adjusted R squared

statistic, the F statistic and the t statistics for the model as well as for the coefficient are all acceptable. The

magnitude of the constant term is an indication of the differential rate of usage between vehicle types when

AGE = 0 years.

13

For cars, the model obtained is given as Equation 3, and the corresponding regression statistics are given

below.

* * * * M U L T I P L E R E G R E S S I O N * * * *

R Square .82548

Adjusted R Square .81384

Standard Error .33311

Analysis of Variance

DF Sum of Squares Mean Square

Regression 1 7.87238 7.87238

Residual 15 1.66440 .11096

F = 70.94788 Signif F = .0000

------------------ Variables in the Equation ------------------

Variable B SE B Beta T Sig T

AGE -.06924 8.21987E-03 -.90856 -8.423 .0000

(Constant) 2.92062 .16766 17.419 .0000

MOTOR CYCLES (Excluding Challys)

The plot of age with the rate of use of motor cycles indicates a much larger scatter than petrol cars, but

(3)

14

nevertheless the negative coefficient and the exponential function are significantly determined.

Figure 4: MOBIKES: Km Rate by Age

┌─┴────┴────┴────┴────┴────┴────┴────┴─┐ 6┤ ├ │ 32 │ │332 1 1 │ │ 2 1 11 │ K │ 11 1 2 1 │ m 4┤ 11 121 1 2 ├ │ 2 1 1 │ R │ 11 │ a │ 1 │ t │ 1 │ e 2┤ ├ │ 1 │ │ │ │ │ │ 1 │ 0┤ 1 1 1 11 1├ └─┬────┬────┬────┬────┬────┬────┬────┬─┘ 4.25 12.75 21.25 29.75

8.5 17 25.5 34

Age (in years)

In the modelling we observe that the rate of depreciation in the usage of motor cycles is comparable to cars;

but the constant term indicates a much lower absolute level of usage when compared to cars. The model in

this case is given as Equation 4.

15

CHALLYS

Unlike cars and motor cycles, challys do not indicate a depreciation in usage with age. However, the

absolute rate is 40% less than that of the motor cycles.

THREE WHEELERS

The corresponding modelling for three wheelers indicates a rate of decrease in usage much higher than that

observed for cars and motor cycles. This is a rather surprising observation given that most of these vehicles

are used as taxis and should not have a very high differential, unless of course they are subject to a higher

rate of breakdown and subsequent lower availability.

VANS

Petrol and diesel vans have been subject to the same modelling shows that the rate of decrease in usage

observed for diesel vans is about 50% higher than that of the diesel cars. However, this usage of petrol vans

is found to be less than that of diesel vans as well as diesel cars. The rate of decrease in usage with age is

comparable to diesel vans.

LORRIES

The rate of decrease of lorries is the lowest observed in our modelling. The constant for lorries is high but

not higher than diesel vans as one would expect.

(4)

16

BUSES

Figure 5: BUSES: Km Rate by Age

┌─┴────┴────┴────┴────┴────┴────┴────┴─┐ 40┤* ├ │ * │ │ * │ │ │ K │ │ m 30┤ ├ │ * │ R │ │ a │ │ t │ * │ e 20┤ ├ │ │ │ │ │ │ │ *│ 10┤ ├ └─┬────┬────┬────┬────┬────┬────┬────┬─┘ 4.25 12.75 21.25 29.75

8.5 17 25.5 34

Age (in years)

While the rate of decrease is lower than for other diesel vehicles, the absolute rate of buses is found to be the

highest.

LAND VEHICLES

From the scatterplot and the modelling exercise, we observe that unlike in other vehicle types, we cannot

establish an apparent rate of decrease.

SUMMARY OF MODEL COEFFICIENTS

The coefficients obtained from the modelling exercises are given in Table 5. The survival rate (y) as a

function of age (x) is given by the Equation 5 and the mean operational kms. per year (z) can also be

computed as a function of age (x) is given by Equation 6, where C0 is the estimated annual kms operated at

0 years (new).

17

(5)

(6)

18

Table 5: Summary of Calibration Coefficients

Vehicle Type 0 0 n yrs Percent non-

renewal

0 Kms per

Year

0

Car (p) -0.043 -0.039 6 yrs 9% 34,267 -

0.069

Car (d) -0.043 -0.039 6 yrs 9% 37,660 -

0.044

Motor Cycles -0.099 -0.080 4 yrs 10% 11,230 -

0.054

Chally -0.198 -0.120 4 yr 25% 3,000 0

3 Wheeler -0.099 -0.080 2.5 yrs 6% 34,400 -

0.101

Van (d) -0.053 -0.040 4 yrs 6% 63,620 -

0.096

Van (p) -0.096 -0.065 4 yrs 6% 37,470 -

0.089

Lorry -0.062 -0.053 2 yrs 3% 53,870 -

0.029

Bus -0.100 -0.044 3 yrs 33%1

90,617 -

0.040

Land Vehs -0.069 -0.031 2 yrs 20% 3,180 0

Trailers -0.046 -0.036 0 yrs 20% 0

6. ESTIMATION OF OPERATIONAL FLEET AND ANNUAL VEHICLE KMS.

The operational fleet at any given time can be calculated from the models given above, provided that the

number of registrations per series and the mean age of vehicles by series (or otherwise) are known. Other

operational statistics such as the total operational fleet, the total fleet annual kms, estimated mean vehicle

life, estimated total vehicle lifetime kms can be computed from these equations.

1Includes the Peoplised buses

19

6.1 ESTIMATION OF OPERATIONAL FLEET

Using the calibration coefficients given in Table 5 and the vehicle registration data as at 31/3/92 (Appendix

VIII: Ref 1), we can calculate the estimated licensed vehicles operating in the country, and the operating

fleet. The vehicles registered under each category are given in column 2 of Table 6, the estimated licensed

fleet is given in column 3 while column 4 gives the estimated operating fleet. The mean age of the operating

fleet computed by the weighted average of survival number multiplied by mean age is given in column 6.

Table 6: Estimate of Vehicle Fleet (As at 31/3/92)

Vehicle Type Vehicles

Registered up to 31/3/92

Estimated

Licenses Renewed 1992

Estimated

Operational Fleet

Mean Age of

Operational Fleet

Car (p) 146,457 84,602 88,817 15.7

Car (d) 5,600 4,798 4,872 7.9

Motor Cycles 407,664 276,838 295,099 7.1

Chally 61,134 50,716 54,395 4.8

3 Wheeler 12,603 9,939 10,679 4.3

Van (d) 64,699 49,364 52,893 8.7

Van (p) 33,760 12,931 17,083 13.3

Lorry 59,196 24,922 28,576 13.9

Bus 33,302 12,355 19,680 13.0

Land Vehs 64,144 27,702 35,376 13.6

Total2 897,549 554,168 607,460 9.3

Trailers 20,970 10,604 13,065 -

Total3 918,519 564,772 620,525

2Without Trailers

3With Trailers

20

6.2 ESTIMATION OF ANNUAL VEHICLE KMS

Using the calibration coefficients and the vehicle registration details as at 31/3/92, we can calculate the

annual vehicle kms operated by each category of vehicle. This can be done using the following equation,

which is the integral of the product of Equations 5 & 6.

Using the coefficients given in Table 5, we can then compute the annual kms for each vehicle type. These

are given in column 3 of Table 7. The mean annual vehicle kms of the vehicle categories are computed by

dividing the fleet vehicle kms by the operational fleet numbers given in column 2.

Table 7: Estimate Vehicle Kms(As at 31/3/92)

Vehicle Type Est. Oper'al

Fleet as at 31/3/92

Est. Annual

Vehicle Kms mil. (1992)

Mean Ann.

Kms of Oper'al Fleet

Car (p) 88,817 1,303 14,700

Car (d) 4,872 146 15,650

Motor Cycles 295,099 2,460 5,530

Chally 54,395 187 2,720

3 Wheeler 10,679 258 13,170

Van (d) 52,893 1,543 15,650

Van (p) 17,083 216 12,200

Lorry 28,576 1,062 33,160

(7)

21

Bus 19,680 1,067 41,650

Land Vehs 35,376 112 3,180

Total4 607,460 8,290 13,170

Trailers 13,065 - 13,065

Total5 620,525 8,290

6.3EXPECTED MEAN LIFE

The expected mean life of a vehicle can be computed from its estimated scrappage rate. Since the scrappage

rate has been derived in Section 4, as a function of age, then the integral of the survival rate (Y) over age

will give the mean age. This can be shown as Equation 8 which is the integral of Equation 9.

As an example, the expected mean life of petrol cars 0 can be calculated from Equation 9 using the survival

coefficient 0 = -0.039 and the period of assumed non-scrappage where n= 6 years. This amounts to 26.2

years for cars. Using the coefficient statistics obtained in sections 4 and 5, the other estimates have been

calculated and shown in column 2 of Table 8.

Table 8: Summary of Operational Statistics

Vehicle Type Est. Mean Estimated Estimated Estimated Mean

4Without Trailers

5With Trailers

(8)

(9)

22

Lifetime Kms per Vehicle

Annual Kms

when Age is 3

yrs

Lifetime kms per Vehicle

Ann. kms per Vehicle

Cars (p) 26.2 27,880 278,000 14,700

Cars (d) 26.2 36,040 410,000 29,800

Motor Cycles 13.1 9,910 72,500 8,130

Challys 9.2 3,600 25,000 3,450

3 Wheelers 14.5 26,190 191,000 24,180

Vans (d) 25.3 47,700 396,000 29,180

Vans (p) 15.9 28,690 194,000 12,650

Lorry 19.0 49,380 630,000 37,180

Bus 23.0 80,370 633,000 54,180

Land Vehs 21.4 3,180 68,000 3,180

6.3ESTIMATED TOTAL VEHICLE LIFETIME KMS.

The estimated lifetime kms per vehicle type can be calculated as

By substituting the values given in the previous section, the lifetime kms expected from each vehicle type

can be calculated. These are given in column 4 of Table 8.

(10)

(11)

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6.4ESTIMATED MEAN ANNUAL KMS

This can be obtained by the division of the lifetime km estimate by the estimated mean life. For example,

petrol cars which have a mean life of 26.2 years and a lifetime km estimate of 278,000 kms, will have an

estimated mean annual km rate of 10,610. the corresponding values for the other vehicle types can be found

in column 5 of Table 8.

7.SUMMARY

Using sample data of annual vehicle registrations and by observations of the composition of the traffic

flows, two basic models have been developed to determine the survival rate of vehicles as a function of age

of vehicle and the annual kms operated also as a function of age. Different coefficients have been obtained

for different vehicle types using regression analysis.

Using these models, estimates have been made of the operational vehicle fleet, its mean age and mean

annual kms operated by each vehicle type. Other important statistics such as lifetime kms and mean lifetime

of each vehicle type has been computed.

This information is used in the calculation of road user charges, annual revenue fees and other fees used in

the recovery of the cost of providing road space, for vehicle operations.

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8.ACKNOWLEDGEMENTS

The funding for this research was provided by the Transport Studies & Planning Centre, Ministry of

Transport & Highways.

9.REFERENCES

1.Kumarage, A.S. ``Estimation of Operational Vehicle Fleet and Annual Vehicle Kms'', Research Report No

AK/92-2, Dept. of Civil Engineering, University of Moratuwa, July 92.

2.Kumarage A.S. & S. Bandara ``Analysis of Free Speeds on Sri Lanka Highways'', Research Report No.

TD/92-1, Dept. of Civil Engineering, University of Moratuwa, July, 1992.