Simplification of Road Transport Infrastructure Layout for Better Self-Explanation

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With above Figure 1. author want to emphasize that Hungary needs further improvement in order to reach the EU target (50% decrease in the number of road fatalities between 2010 and 2020.). Regardless, the continuous improvement in road safety is evidenced by several indicators in Hungary ^{[1, 16, 21]}. This article focuses on general, large-scale problems that effect human behaviour and the solutions to which could aid prevention activities. To provide safer road infrastructure, the behaviour of road users needs to be known. „The road users - during their journey - unwillingly make mistakes: the task of road planners and operators to minimise that possibilities of mistakes and accidents. If errors still occur and the accident happens, it must be ensured that the consequences are minimized. The road infrastructure and its environment should be forgiving those who made mistakes and not penalizing them" ^[14]. In 1932, Sir Frederic Charles Bartlett, a British psychologist introduced the concept of schema in psychology. The schema contains all things a person knows. If new information could not be incorporated into a scheme then distortions will arise. The scheme represents an organized structure, which includes knowledge about our world and our expectations. People remember new things with the help of existing structures. In order to improve safety, the adequate scheme needs to be activated in drivers through infrastructure. This article aims to compare Hungarian rural road construction standards with the standards of the Germany by mathematical and statistical tools. The hypothesis of the author is that the scheme of rural Hungarian road network elements are diverse due to their design, making them more accident-prone ^[15] (e.g. through inappropriate choice of speed). This article aims to investigate improvement opportunities to have a simpler and more straightforward system such as the German one. As it can be seen from Figure 2. the number of registered motor vehicles are increased significantly in the recent years in Hungary. It has to be emphasized that parallel with this the number of fatal accident significantly decreased in Hungary.

Figure 2. Number of registered vehicles, number of accidents and people killed in road accidents in Hungary

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2. Methodology

This article investigates rural roads only. Cross-sectional conceptual designs of road infrastructure have been studied with the tools of mathematical statistics (quantitative multivariate data analysis, multidimensional scaling, hierarchical cluster analysis, principle factor analysis were used to prove the hypothesis - these mathematical methods are well known and have been used in several statistical analyses) extending to the following physical parameters:

● Maximum speed [km/h]

● Lane width [m]

● Rounding radius [m]

● Maximum slope [%]

● Curve radius [m]

The author considered these to be the major physical parameters of a rural road that influence the schemes in the driver’s mind. These are the physical parameters that influence the self-explaining roads.

A database had been built up by the described parameters in case of Hungarian and German rural roads. The parameters of Hungarian and German technical specification of rural roads had been used. The database includes the road type related physical parameters for each type of roads.

Quantitative multivariate data analysis was used for the empirical analysis of systematically collected data. Existing research indicates that these parameters determine speed choice ^{[5, 7, 11, 19]} and risk-taking behaviour ^{[4, 6]}. A comparative analysis of vectors generated from these parameters has been performed. A vector is a quantity that has a magnitude and a direction. In its simplest form, the vector is a directed line segment. The vector can also be considered as a special group of numbers. In this case, five-dimensional vectors have been compared. To do this, the length of five-dimensional vectors and the difference between each pair were calculated (1):

(1)

where:

x: one type of investigated infrastructure

y: other type of investigated infrastructure

i: parameter of investigation

The author assumed that if two vectors are different, then the two infrastructures are also different and activate different schemes in the driver - if the difference between the two vectors is greater than 5% of the smaller vector (5% tolerance is commonly accepted in engineering) (2):

(2)

where

ε: equivalence parameter [-], in this case 5%

β: binary coefficient {0,1} of reduction [-], 1 if two infrastructure types can be consolidated

Other statistical methods were also used to prove the hypothesis. The vectors created from physical parameters are five-dimensional; therefore the graphical representations are very difficult. This problem can be solved by multidimensional scaling. Multidimensional scaling (MDS) is a method of multivariate statistical analysis, a procedure by which geometric representations can be created on the basis of perceived similarities and differences ^{[2, 13, 18]}. In our case, the observed five dimensional similarities of the five-dimensional vectors were transformed into a two-dimensional "map" in which the observed differences and similarities remain.

A hierarchical cluster analysis - also a method of multivariate statistical analysis - was also performed to confirm the hypothesis, providing a dimension-reducing grouping for the vectors representing infrastructure elements so that similar elements in the reduced space are next to each other.

Factor analysis was also performed to verify the reduction hypothesis, since in the factor analysis models it is possible to explore relationships between variables. If there is a strong relationship between the components or there are dominant components present, then simplification is possible while retaining information contained by the vector components through the linear combination of smaller number of uncorrelated vectors. With this method, there is an opportunity to reveal the weights of combining factors and to discover hidden relationships between components. The dataset can be characterized by a linear function of several dominant factors. In this article, author has performed main factor analysis so the factor vectors will be eigenvectors of a correlation matrix. During the analysis, the varimax rotation strategy was chosen, where the number of explanatory variables are minimised.

3. Results

The vector reduction model described above (2) merged the initial 14 different road categories into seven categories. The generally accepted limit of 5% difference was used. Either some of these categories should be merged, or more significant differences should be introduced to separate them better so that drivers would be less likely to recall an inappropriate psychological schema. Similar results were found in the multidimensional scaling (Figure 3). The number of categories should be decreased as follows:

Figure 3. MDS based reduction*

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The MDS-based reduction (Figure 4.) yielded five groups.

The decreasing of eigenvalues of eigenvectors in the factor coefficient matrix can be seen in Figure 5. The figure shows that vector space made from the vectors of the cross-sectional design of the infrastructure elements can be simplified and the main components can be determined. Our analysis identified four main components, one of which was significantly different and determined the system. We believe that the four groups should be:

● Motorways (High-speed roads with an M prefix or (M) suffix. e.g. M1 or A1(M). The speed limit is generally 130 km/h. There is a physical separation between directions, no level crossing and one emergency lane per direction),

● Expressways (High-speed roads with an M prefix or (M) suffix. e.g. M1 or A1(M). The speed limit is generally 110 km/h. Does not necessarily exist a physical separation between directions or one emergency lane per direction)

● Main roads (roads with the speed limit of 90 km/h. There is no existing physical separation between directions, there could be level crossing and no emergency lane)

● Roads (all the other mainly regional roads in nature and used to connect areas of lesser importance. Usually shown as brown or yellow on maps.)

Figure 4. Hierarchical cluster analysis

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Figure 5. Decreasing the eigenvalues of eigenvectors in the factor coefficient matrix

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4. Analysis and Conclusion

As it can be seen from Table 1, 4 aggregated vectors determine the vector space, so the original 19 vectors (different infrastructure layout) could and should be reduced.

Table 1. Table of variance

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