Safety of a pedestrian facility depends on its features and on how it is used (i.e. pedestrian and vehicles traffic characteristics).
Models existing in literature are based both on traffic and pedestrian volumes information and on pedestrian crossing features, but in many cases traffic data are not available. The chosen approach focuses on safety of a pedestrian crossing, without taking into account existing traffic composition and volumes.
The risk is therefore not to select for intervention pedestrian crossings that show a high accident frequency due to higher traffic volumes. On the other hand the methodology permits to identify for intervention pedestrian crossings showing the worst characteristics.
A number of factors exist from literature that affect directly or indirectly pedestrian crossing safety. The relative weight of each factor can be defined through opinions by a panel of experts. The problem of finding the specific contribution of each factor to safety has been solved applying Analytic Hierarchy Process (AHP) method proposed by Saaty .
This method is generally used to compare different alternatives and evaluating which one is the best to satisfy a defined goal. For the purpose of the paper, AHP has been used to aggregate different experts’ opinions about contribution of every factor to safety.
A theoretical framework for safety has been defined including potential crossing safety related factors/features. Factors and features have been selected by a panel of experts on the basis of their relevance, perceived by the panel, and of results found in literature.
Due to significant differences in traffic rules and road users behaviour between signalized and not signalized pedestrian crossings, these two scenarios have been treated separately.
For each scenario the problem has been decomposed into three hierarchical levels. The first level represents the pedestrian crossing safety composite index.
The second level is defined by four macro-criteria contributing to safety of pedestrian crossings:
The third level contains the assessment criteria related to each of the four macro-criteria (see not signalized pedestrian crossings case in Fig. 1 and signalized pedestrian crossings case in Fig. 2).
Macro-criteria have been defined grouping identified criteria according to common objectives of good design principles [5, 16].
Spatial and Temporal Design macro-criterion takes into account pedestrian exposure to traffic, conflicts and timing factors to assess the functioning of the crossing for the pedestrian. Included criteria aim at minimizing waiting time needed to find a crossing opportunity and time needed to cross safely for all road users, including limitation of traffic exposure, through the reduction of conflict points and segmentation of crosswalk.
Day-time Visibility and Night-time Visibility criteria evaluate visibility of pedestrians at crossing for motorists, visibility of the pedestrian crossing for motorists, and visibility of oncoming vehicles for pedestrians.
Accessibility criteria account for ensuring proper access for all road users, with or without disabilities, to approach the pedestrian crossing free of obstacles and possible dangers.
For each criterion a specific indicator has been identified. Indicators can refer to quantitative measures (e.g. roadway width) or qualitative measures (e.g. visibility conditions of pavement markings).
As different measurement units are present, indicators have been re-scaled in order to have a common range (0, 1). A value near to 0 is associated to safer situations, while a value near 1 is associated to risky situations.
For quantitative measures, re-scaling consisted in giving a distance from a reference value or in definition of indicators above or below a threshold. For qualitative measures, categorical scales that assign a score to possible indicator values have been used. Engineering design handbooks and research studies provide conditions for safe and correct design of a pedestrian crossing [5, 7, 11, 16].
Selected criteria and related indicators are presented in Table 1.
Weighting of criteria
Once the problem has been defined, AHP has been used to find a weight for each criterion present in the theoretical framework.
According to this method, in case of a hierarchal structure with three levels defined by J criteria, M macro-criteria and a goal, it is necessary to evaluate:
All the weights are calculated by aggregating the results from a number of pairwise comparison square matrices, where the elements aij of a matrix (also called “dominance coefficients”) represent the prevalence of criterion Ai on criterion Aj in reference to the corresponding macro-criterion/goal. A comparison matrix (like that in Table 2) needs to be defined for each of the four macro -criteria and for the general goal.
The prevalence is measured qualitatively using a semantic scale  that links a numerical value (from 1 to 9) to a judgment expressing a possible result from the comparison (Table 3).
A focus group of 15 experts, with previous experience in infrastructure design, road safety planning and evaluation, has been set up to perform pairwise comparisons. Each expert assessed the relative importance of criteria individually to avoid possible influence on judgments.
Assuming ajk = wj/wk, with wj the weight associated to criterion j and wk the weight of criterion k, the following are valid:
The weights of each criterion have been obtained aggregating the dominance coefficients of resulting comparison matrices through the geometric mean, obtaining the “aggregated comparison matrix” A.
Matrix A should be square, positive, symmetric and consistent. Given w the vector of the weights wi, it can be demonstrated that:
From (1) it is possible to say that w is the eigenvector of matrix A associated with the eigenvalue n. If matrix A is consistent, it admits only one solution: the eigenvalue lmax, whose value is equal to n.
However in most cases, judgments given by experts need to be verified through the calculation of the Consistency Index proposed by Saaty.
According to AHP method a square matrix A can be considered consistent if the Consistence Ratio CR is lower than 0,1:
is called Consistency Index: in case of perfect consistence (lmax = n) CI = 0;
RI is called Random Index. It represents the average value of CI for a square, symmetric and positive matrix of order n random generated; values o f RI are known in function of n.
Finally, given a comparison matrix A, if CR <0,1, than the calculated weights w
can be considered equal to vector components w associated to the maximum eigenvalue l
If CR >0,1, the deviation of the matrix A from the condition of perfect consistence is judged not admissible, a revision of subjective judgments is needed. Results from the application of AHP method show that Night-time Visibility account for over 40% in both scenarios. Weights distributions among the four macro-criteria for the two scenarios are shown in Fig. 3. Night-time Visibility resulted to have the higher weight in both scenarios (about 41%), followed by Day-time Visibility, Spatial and Temporal Design and Accessibility.
In Table 4 the relative weights associated to each criterion and calculated Consistency Ratio for all aggregated matrices in both scenarios are reported. All values are smaller than 0,1, this indicates coherence of judgments provided by the experts.
In Fig. 4 global weights assigned to each criterion are presented. In both considered scenarios, Night-time Light conditions, Night-time Minimum approach sight distance and Day-time Minimum approach sight distance account for about 43% to crossing safety. For not signalized pedestrian crossings (NSPC) other important factors are: presence of pedestrian refuge islands, pedestrian- vehicles conflict points and obstacles in approaching crossing. For signalized pedestrian crossings (SPC) scenario, Night-time Pavement markings visibility, Presence of obstacles, Day-time Pavement markings visibility and Night-time PC signs/signal visibility are also important.
Composite safety index
A composite index for crossing safety and indexes for each macro-criterion have been developed. For the determination of indexes, the following assumptions have been made:
the safety level of a pedestrian crossing is calculated through a weighted mean;
relationship among criteria has not been taken into account (i.e. combination of effects from two or more criteria has not been considered).
The proposed index is defined by:
Additional indexes have been developed to evaluate safety of a pedestrian crossing in relation to a single macro-criterion. The index, for a generic macro- criterion m is defined by:
for criterion j can be also specified in order to identify features and characteristics to be enhanced.
A scale defined by five classes has been developed to classify pedestrian crossings in relation to the index value calculated with the proposed methodology.