Application of the AHP Method to Analyze the Significance of the Factors Affecting Road Traffic Safety

Over the past twenty years, the number of vehicles registered in Poland has grown rapidly. At the same time, a...


INTRODUCTION
On the roads of the European Union about 26000 people die every year.Therefore road safety is an important issue.The lowest fatalities number is recorded in Great Britain, Sweden and the Netherlands, while most people die on roads of Romania, Latvia, Poland and Lithuania [6].Referring to the number of deaths to the population, Poland is one of the last countries among the EU and is well above the EU average.The fatalities number for selected EU countries with reference to population in 2013 is shown in Fig. 1 [6].The concern about road safety is important not only because of the value of human health and life.One has to take into account that the long term social losses also generate quantifiable financial losses in the economy.There are certain methods to estimate the cost of road accidents and collisions.The method used for Poland's needs is Pandora 2013, developed at the Road and Bridge Research Institute.Road accidents and collision costs calculated by this method for Poland for year 2012 are at the level of 34.5 billion zloty [4].This is almost 2% of GDP for the year 2012.However, due to traffic incidents, uncountable social costs are also incurred.These include the costs of: -a sense of grief after the loss of relatives, -physical and mental suffering of victims, -support and time dedicated to the victims by relatives, -decreasing the work effectiveness of relatives.
There is an urgent need to reduce the number and consequences of road accidents.To achieve this, it is necessary to identify the main factors affecting road traffic safety (RTS).The ranking of these factors in terms of their significance can be performed by using one of the multi-criteria analysis methods, which are widely used to solve decision problems.In this work, to analyse the influence of selected factors on RTS, the analytic hierarchy process method (AHP) was proposed [1].

STATING THE PROBLEM
The road safety problem is highly complex due to the large number of affecting factors.These can be put in order, by grouping them as DVE (driver -vehicle -environment) system components.Particular groups of the system are: -factors related to a road user and his condition in holistic (psycho -physical -emotional) meaning, further known as factors 'D', -factors related to a technical condition of the vehicle, further known as factors 'V', factors related to an environment of the road in the broad sense of the word (along with the geometrical features of the road, weather, traffic organization and surroundings), further known as factors 'E'.To analyse the importance of factors affecting the RTS for the purposes of this work, selected factors were decomposed in DVE system groups.
Analytic hierarchy process method enables us to rank factors influencing the RTS with reference to their importance.However, due to create a final rank, it is required to define the weight (level of importance) of each of the considered groups.For the purpose of the article, the importance of particular groups was based on accident statistics for Poland in 2013 [5].It was calculated as the share of each group in the total number of road accidents.
Factors that may be included in the driver's group are: -forcing the right-of-way, -inappropriate speed to traffic conditions, -incorrect overtaking, -driving after alcohol or drugs, -incorrect lane changing, -not keeping a safe distance between vehicles, -passing at a red light, -not granting priority to pedestrians, -failing to comply with other signs and signals, -hard braking, -tiredness, falling asleep, -incorrect turning, -driving without required lights, -incorrect reversing.
Factors related to the technical condition of the vehicle are: defects in lights, -defects in tires , -malfunction of the braking system, -malfunction of the steering system.With road environment, factors related to pedestrian traffic were linked.They are such as: -walking the wrong side of the road, -stepping onto the street at a red light, -crossing the road in front of a moving vehicle, -crossing the road from behind an obstacle, -crossing the road in an unauthorized location, and factors resulting from other causes: weather conditions such as sun blinding, fog, rain, snow, etc.
-improper condition of the road, -incorrect traffic management, -improperly secured roadworks, -objects / animal on the road, -being blinded by another vehicle.

J. Sordyl
The general form of a hierarchical structure, representing the issue discussed in the paper, is shown in Fig. 2. Factors presented in Fig. 2 are analysed due to the level of importance within the group to which they belong.The final ranking of particular factors affecting status of RTS in terms of their importance can be defined after assigning weights to the considered groups -'D', 'V, 'E.

DETEMINING RELATIVE RATINGS MATRIX
Ranking of particular factors influencing the RTS in terms of their importance in AHP requires to determine the matrix of relative importance ratings of each of the considered factors.These ratings are made by direct comparison in pairs of all the factors regarding the criterion of importance within the equivalence, when level of importance of both compared factors is identical, -weak preference, when level of importance of one of the factors is only slightly larger than the other, -significant preference, when level of importance of one of the factors is noticeably greater than the other, -clear preference, when level of importance of one of the factors is significantly larger than the other, -absolute preference, when level of importance of one of the factors is much higher than the other.
An adequate numerical value is assigned to each of the five situations.If a pair of factors for which the comparison is performed is denoted as {e 1 , e 2 }, the numerical values as in Table 1 are used, to quantify particular ratio.The intermediate numerical values may be also used to quantify the rate.Based on pairwise comparisons of the factors determining the state of RTS the matrixes of relative ratings are made, as described in the next section.

Relative ratings matrix for the group of factors relevant to the driver
The pairwise comparison of the 'D' factors was made on the basis of the survey.The respondents indicated how often each of these factors is the cause of road accidents, committed by the driver.Numerical values were assigned to responses.It allowed to calculate the percentage of the response indications.The value of indications of particular factors is presented in Table 2.

Relative ratings matrix for the group of factors referring to technical condition of the vehicle
The evaluation of the next group of factors was performed on the basis of statistical data which define the ratio of particular factor in the total number of road accidents caused within the group [5].Among the factors related to the technical condition of a vehicle: -defects in lighting are responsible for 53% of accidents, -defects in tires are responsible for 22% of accidents, -malfunction of the braking system is responsible for 18% of accidents, -malfunction of the steering system is responsible for 4% of accidents.The analysis omitted other causes which in total represent about 3% of accidents among the considered group of factors.
The most important factors in RTS within this group are defects in the lighting of the vehicle.The next two factors -defects in tires and malfunction of the braking system -are almost equivalent to each other.The least important factor is malfunction of the steering system.The matrix determined on the basis of statistical data is shown in Table 4.

Relative ratings matrix for the group of factors referring to the environment of the road
The pairwise comparison of the 'E' factors was also made on the basis of the survey.The respondents indicated how often each of these factors is the cause of road accidents.Again, numerical values were assigned to the responses.The value of indications of the particular factors is presented in Table 5.The value of matrix indications, determined on these basis, is shown in Table 6.

COHERENCE ANALYSIS OF THE MATRIXES OF RELATIVE RATINGS
In the next step, the local priority vectors were determined (vectors for each matrix of relative ratings) and the consistency of the evaluations for each obtained matrix was checked.
Assuming that the    () is a relative rating of i-th step in comparison to the step j according to the criterion k, created matrix of relative ratings R (k) for k = 1, 2, 3 are square matrixes as: ⋯  , where: n -matrix dimension.
Each element of the matrix R (k) corresponds to the quotient of the absolute ratings of steps regarded to the k-th criterion, i.e. the element    () can be represented as: where: w i (k) , w j (k) are the unknown absolute evaluation of steps i and j with respect to criterion k.To determine an absolute ratings vector W (k), it is required to solve such matrix equation as: where:  () = � 1 () , . .,   () �  and ∑ Determined local priorities vectors W (k) allow us to rank the factors affecting RTS due to their significance.In this paper local priorities vectors were calculated in iteration steps [ 3 ], with permissible error not greater than ε = 10 -4 .
The next step was a verification of coherence.For each matrix the relative consistency ratio CR was calculated according to the equation: ) where: RI -random consistency index, CI -consistency index calculated as: where: λ max is the maximum value of the matrix.
For this purpose, after determining local priorities vectors W (k) , λ max and the consistency ratio were calculated for each matrix.The obtained values for each matrix of relative ratings are shown in Table 7. Analysis of coherence of each matrix of relative ratings shows that the acceptable value of CR is not exceeded.It means that the matrixes fulfil the formal criterion of the AHP method [1] Therefore, local priorities were used to determine a final ranking of factors affecting RTS with regard to their importance.

FINAL RANKING OF THE FACTORS DETERMINING RTS
The next step is to determine the absolute ratings referring to the relevance of each of the three criteria considered in the paper.Weights assigned to each criterion are based on statistical data [5].Weights of the criteria are shown in Table 8.The final ranking of factors affecting status of RTS requires the aggregation of rating factors (weight of local priorities) with respect to the relevance of particular groups of factors (weight of J. Sordyl criteria).Global priorities for factors influencing RTS and determined by using AHP method are shown in Table 9. defects in lighting 0,003 defects in tires 0,001 malfunction of the braking system 0,001 malfunction of the steering system 0,000 factors 'E' crossing the road in front of a moving vehicle 0,035 improper condition of the road 0,035 crossing the road from behind an obstacle 0,023 weather conditions such as sun blinding, fog, rain, snow, etc. 0,023 stepping onto the street at a red light 0,023 crossing the road in an unauthorized location 0,015 incorrect traffic management 0,008 objects / animal on the road 0,005 walking the wrong side of the road 0,005 being blinded by another vehicle 0,004 improperly secured roadworks 0,003

CONCLUSIONS
As a result of procedure described in the work, the ranking of factors determining the road traffic safety was made.Analysis of global priorities shows that the most significant factors having impact on RTS are: forcing the-right-of-way, inappropriate speed to traffic conditions, incorrect overtaking, driving after alcohol or drugs, incorrect lane changing and not keeping a safe distance between vehicles.All these most important factors are from 'D' group of factors.Within this group there is 82% of global priorities value.We can conclude that this group is the most important of the three considered.
All factors related to the environment of the road are in the middle of the rank therefore we can conclude that they have moderate importance.It is worth noticing that all factors related to the technical condition of the vehicle, are not considered as significant in relation to other factors.A comparison of the value of global priorities for each group of factors is shown in Fig. 3.In conclusion, it is worth emphasizing that the presented ranking depends not only on an assessment of the relative ratings of factors, but also on the assumed importance criteria (for groups of factors).The main objective was to show one of the possible approaches to assess factors affecting road safety by using the AHP method.

Fig. 2 .
Fig. 2. Scheme of decomposition of ranking factors influencing the RTS referring to their importance Rys. 2. Schemat dekompozycji zadania szeregowania czynników wpływających na stan BRD w odniesieniu do ich istotności Ranking of factors influencing the RTS with reference to their importance 'D' factors -related to the driver forcing the right-of-way inappropriate speed to traffic conditions incorrect overtaking driving after alcohol or drugs incorrect lane changing not keeping a safe distance between vehicles passing at a red light not granting priority to pedestrians failing to comply with other signs and signals hard braking tiredness, falling asleep incorrect turning driving without a required lighting incorect reversing 'V' factors -related to the technical condition of the vehicle defects in lights defects in tires malfunction of the braking system malfunction of the steering system 'E' factors -related to environment of the road walking the wrong side of the road stepping onto the street at a red light crossing the road in front of a moving vehicle crossing the road from behind an obstacle crossing the road in an unauthorized location weather conditions such as sun blinding, fog, rain, snow, etc. improper condition of the road incorrect traffic management improperly secured roadworks objects/animals on the road being blinded by another vehicle groups.To quantify the relative ratings the Saaty's scale was used.It leads to the distinction of five basic situations:

Fig. 3 .
Fig. 3.The ranking of the factors determining the RTS with regard to the level of importance Rys. 3. Uszeregowanie czynników determinujących stan BRD w odniesieniu do poziomu istotności

Table 1
The numerical values corresponding each of the situation for the basic Saaty's scale

Table 2
The values of indications of factors related to road userThe value of matrix indications, determined on these basis, is shown in Table3.Table3The matrix of relative ratings for factors referring to the driver

Table 4
The matrix of relative ratings of factors referring to the technical condition of the vehicle

Table 5
The values of indications of factors related to the environment of the road

Table 6
The matrix of relative ratings of factors relevant to the environment of the road

Table 7
The obtained values for matrixes of relative ratings