The travel characteristic that determines the choice of using toll roads is based on data from the latest national household survey carried out in 2008 as part of the project to create the national OD matrix. In various geographical regions of Hungary, more than 50,000 individuals were interviewed in approximately 24,000 households, in 70 subregions. Respondents were asked about the origins and destinations of their non-local trips, the time of departure and arrival, trip purpose, and travel mode. Respondents who made trips as car drivers were also asked whether they used a toll road and how long the ‘motorway vignette’ was valid.
First, we selected car trips that were made using toll roads. Then, trips using yearly or monthly motorway ‘vignettes’ were filtered out, as the choice of a toll road was not the result of a decision made for that particular trip but the consequence of some other decisions. These types of trips could/should be described with different travel characteristics than trips using short-term vignettes. According to our assumption, the decision about buying a monthly or yearly vignette is influenced by the total number of journeys to be undertaken within the given validity period. The choice of longer- term vignettes (monthly, yearly) may as well be justified by the relatively small savings of time and/ or distance of planned trips for the validity period or greater safety and comfort of motorways, too. For those, however, who choose to buy a short-term vignette, we presume that the decision about buying or not buying a vignette is primarily based on the extent of time and/or distance savings to be achieved by using toll roads. It is evident that for trips for which paying the road toll would not bring any savings, travellers would only choose the more expensive and longer trip on a toll road for a special reason.
After filtering out car trips and deducting data referring to people travelling in cars as passengers, 19,410 weekday car trips were available for the analysis. There were 626 trips that used a vignette and for which toll roads were also used. Obviously, not all trips can be made using toll roads. Only about one-eights of all trips (2,533 trips) could potentially use toll roads. These trips were made on routes on which the use of toll roads would have meant a time and/or distance saving. Drivers eventually used toll roads for about 25% of the trips that could have potentially used toll roads. Table 1 presents data on car movements by toll road use.
table 1: passenger vehicles’ movements according to toll payment
In the second part of the paper, we concentrate on trips with occasional use of toll roads. Respon- dents made 247 trips with vignettes valid for a week or four days. The shortest distance travelled by those who had a choice of travelling on a toll road, was 11 km while the longest one was 535 km. The shortest distance travelled by those who occasionally use toll roads was 18 km; while the longest one was 505 km. The average distance travelled by occasional toll road users was 128.4 km, while for those who did not travel on toll roads it was 78.6 km (half of those who used toll roads travelled more than 130 km, while half of those not travelling on toll roads travelled less than 44 km). Figure 1 presents the graph of the empirical probability density function by travel distance of non-toll road users and occasional toll road users based on our sample.
NUMBER Of TRIPs PERcENTAGE Of ALL cAR TRIPs
MOTORWAY UsE POTENTIAL AcTUAL
NON-LOcAL
cAR TRIPs 19,410 100.0%
Of WHIcH: NON-
TOLL ROAd UsERs 18,784 96.8%
POTENTIAL
TOLL ROAd UsERs 2,533 13.0% 100.0%
AcTUAL
TOLL ROAd UsERs 626 3.2% 24.7% 100.0%
Of WHIcH :
REGULAR UsER 379 2.0% 15.0% 60.5%
OccAsIONAL
Figure 1: proportion of toll road users by travel distance bands
The empirical probability density functions show that there is a considerable difference in travel distance depending on the use of toll roads. The frequencies indicate remarkable differences. There- fore, we examined the probability of choosing toll roads in relation to travel distance in order to establish if there is any quantifiable relationship between travel distance and the use of toll roads. The proportion of toll road use was analysed as a function of the travel distance measured in kilome- tres. For this, we used the distances contained in the model created for the national origin-destin- ation matrix. Then, using data presented in Figure 1, the proportion of trips occasionally using toll roads to the number of people travelling to a certain distance was calculated for each travel distance using the following formula:
where:
yi is the proportion of toll road users to the number of travellers travelling to the
given distance band;
x1i is the total number of toll road users to the number of travellers travelling to the given distance band;
x2i is the total number of non-toll road users to the number of travellers travelling to the given distance band.
Only the origin-destination pairs were considered in our calculations that had both non-toll road user and toll road user trips. The rest of the origin-destination pairs were excluded so that we can examine the choice of using or not using a toll road in comparative conditions.
Considering that travel distance itself can largely explain the decision made about using a toll road, the influence of other factors (income, economic status, education, place of residence, etc.) was not studied. It is obvious, however, that there may be other relevant influencing factors as presumably the higher level of comfort and safety offered by toll motorways also affects decisions. The impact of non-monetary benefits on decision making is probably linked to the social status of the traveller.
y
i= x
1i/ (x
1i+ x
2i)
60% 50% 40% 30% 20% 10% 0% 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 360 420 520 non-toll road useroccasional toll road user
In the next phase, we tried to create a function that can reliably describe the relationship between travel distance and the use of toll roads. This function determined which trips must or need not use toll roads fully or partially during the subsequent modelling process. It was also expected to reveal what proportion of all trips needs to be assigned to toll roads.
During our calculations, we examined the relationship among the frequency of choosing toll roads, travel distance and time as well as transformed forms of time and distance savings (reci- procal, logarithm, etc.). Further analysis showed that the strongest correlation can be observed between the reciprocal of travel distance and the choice of toll roads. The correlation coefficient is as high as 90.9%.
After this, we determined the function that could best describe the relationship. Besides linear re- gression models we considered best fitting exponential and logarithmic functions and polynoms. An exponential equation was found to provide the best function to reflect the relationship studied:
where:
y: is the proportion of toll road users;
x: is the reciprocal of travel distance in kilometres. The value of the curve-fit is: R2 = 0.830
Since the function is not bounded, we had to carry out a transformation to ensure that the values of our curve fitted to the observed values fall between 0 and 1, as the probability of choosing a toll road needs to be estimated in relation to travel distance.
The distribution function that defines the probability of choosing a toll road is as follows:
where:
y: is the probability of choosing a toll road; x: is the travel distance in kilometres;;
a & b are constant parameters of the function (a = 0.8588, b = 14.6467). The value of the curve fit is: R2 = 0.921.
Figures 2 and 3 show the function curve based on the two different methods of calculation.
y=b*(-1/(x+1)
a)+1
Figure 2: probability of choosing motorways as a function of the reciprocal of travel distance in kilometres
Figure 3: probability of choosing toll roads occasionally
120% 100% 80% 60% 40% 20% 0% 0.000 0.005 0.010 0.015 0.020 0.025
Expon. (Probablilty of choosing motorways, %) Probablilty of choosing motorways, %
120% 100% 80% 60% 40% 20% 0% -20% 100 200 300 400 500 km Trend Probability of choosing toll roads
After establishing the functions, we examined how the curve behaves and how logical its behaviour appears.
a. At the beginning, as travel distance increases the probability of choosing a toll road, it is steep. It is understandable, since the toll paid per each kilometre of distance travelled becomes lower and the advantages of a motorway are more important on a longer trip. In addition, toll roads usually run farther away from settlements or access to them requires extra travel, which would mean a disproportionately long extra detour just to reach a motorway for shorter trips. Hence, it is more likely that main and secondary roads are preferred for shorter trips.
b. With the further increase of the travel distance the probability of choosing a toll road approaches its maximum so the rate of increase becomes smaller. On the one hand, this can be explained by the fact that there are fewer drivers who still have not chosen to pay the toll as the travel distance becomes greater, so it is a mathematical law that the rate of growth decreases. On the other hand, our survey revealed that some drivers are unwilling to pay road tolls irrespective of the extent of the charge, which also limits the rate of growth on the curve.
It can be concluded that the behaviour described by the curve that best fits the data from our survey is also in accord with previous findings regarding the price elasticity of the willingness to pay for road tolls. In addition, it also confirms analytic results.