Evaluation of Pedestrian Level of Service at Signalised Intersections from the Elderly Perspective

The crossing decisions and behaviour of elderly pedestrians are affected by the pedestrian level of service (PLOS). In this paper, an evaluation model was established to analyse the relationship between the traffic environment and the perceived evaluation of elderly pedes - trians. Firstly, the characteristic parameters of the selected intersections and the perceived evaluation data of elderly pedestrians at the synchronisation scenery were extracted using manual recording and questionnaire-based truncation methods. The correlation between the perceived evaluation data of elderly pedestrians and the traffic parameters were tested with respect to the dimensions of safety, convenience and efficiency. Then, the significant param - eters affecting PLOS were recognised. Based on the traffic characteristic parameters, the PLOS evaluation model from the elderly perspective was established using the fuzzy linear regression method. PLOS classification thresholds were obtained using the fuzzy C-means clustering algorithm. The data from two intersections were used to validate the model. The results show that the difference between the actual and the predicted PLOS values of the two crosswalks were 0.2 and 0.1, respectively. Thus, the proposed PLOS evaluation model in this paper can be used to accurately predict the PLOS from the elderly perspective using the traffic data of signalised intersections.


INTRODUCTION
By the end of 2021, the number of elderly people ≥ 60 years and ≥ 65 years accounted for 18.9% and 14.2% of the total population in China, respectively [1]. China has almost become a moderately aging society, with a gradually increasing degree of aging. The increase in the elderly population causes an annual increase in the proportion of elderly people in travel. Thus, lack of attention to elderly people's travel is set to bring about major hidden traffic hazards in China. Relevant data show that 24,000 elderly people died from traffic accidents in 2020. Particularly, elderly people who died in traffic accidents at urban road intersections accounted for 29.4%. Walking is the main travel mode for elderly people in China [2]. In walking travel, signalised intersections are the most complex nodes of traffic conditions faced by elderly pedestrians. With increasing age, the physical function of elderly people generally declines [3]. Thus, this can result in poorer body posture control, higher falling risk [4], more time spent looking at the ground [5], more focus on maintaining body posture stability and lack of attention to the surrounding traffic environment when elderly pedestrians cross streets [6]. When crossing streets with two-way traffic, elderly people tend to focus on the nearside lane and ignore traffic information in the farside lane [7]. Compared to young and middle-aged people, elderly people have lower traffic safety awareness [8], require longer decision-making time [9] and show a higher rate of making wrong crossing decisions [10]. In addition, elderly people have longer start-up time and lower walking speeds at signalised intersections [11]. Thus, they are subjected to higher exposure risks at intersections.
Pedestrians' crossing decisions and final crossing behaviour are influenced by their perceptions and judgments of the crossing environment. Pedestrian level of service (PLOS) is an important evaluation index re-flecting the operation of crosswalks at signalised intersections. PLOS can be evaluated from the perspective of users. Therefore, the study of PLOS evaluation methods has been an important research aspect worldwide. In terms of PLOS study at signalised intersections, HCM2000 first proposed a PLOS concept based on pedestrian crossing delays [12]. Since then, parameters such as average pedestrian occupied space, pedestrian flow rate, pedestrian walking speed and the ratio of pedestrian flow rate to traffic capacity at crosswalks have been included as the evaluation indexes based on pedestrian flow characteristics [13,14]. It is easy to obtain the data of single indicators that characterise pedestrian flow characteristics. However, they do not consider the effects of vehicles and traffic facilities on the PLOS [15]. Thus, studies based on single indicators still exhibit some limitations. Current studies on the impact of motor vehicle traffic flow on PLOS have focused on factors such as vehicle travel speed [16], vehicle traffic volume [17][18][19] and pedestrian-vehicle conflicts [20][21][22][23]. Studies on the impact of traffic facilities on PLOS have commonly used evaluation indicators, including crosswalk length or the number of lanes [21,24], pedestrian safety islands [22] and pavement conditions [25]. Thus, HCM2010 proposed an evaluation method for PLOS at signalised intersections by considering pedestrian delays, channelisation, traffic characteristics and control schemes [12]. HCM2016 followed the PLOS evaluation method presented by HCM2010 [26].
In summary, with the rapid increase of aging population in China, the PLOS evaluation at signalised intersections from the elderly perspective can provide a direct evaluation method of PLOS at signalised intersections for elderly pedestrians. Thus, this may facilitate the design of pedestrian crossing facilities and the adjustment of crossing measures at signalised intersections in an aging society. Therefore, this paper analysed the relationship between static/dynamic traffic characteristics data and the evaluation results of elderly people's perceptions. Then, based on the traffic facilities, traffic management and traffic flow operation conditions of signal intersections, important variables for the PLOS evaluation of elderly pedestrians were identified. A PLOS evaluation model was established. In addition, field surveys were conducted to obtain sample data in order to establish and solve the evaluation model. The thresholds for classifying PLOS were recommended. The PLOS evaluation model can provide a reference for studying traffic safety improvement strategies in the aging context.

Selection of influencing factors
The review studies of Bansal et al. [15] and Raad et al. [27] were taken as references. The questionnaire survey at the initial installation stage of crossing facilities for elderly pedestrians was analysed. Then, pedestrian characteristics, traffic characteristics, geometric characteristics and pedestrian-signal design at signalised intersections were selected as the influencing factors for the PLOS evaluation of elderly pedestrians at signalised intersections. The detailed characteristics are shown in Table 1.

Data acquisition
In order to analyse the influence of different factors on PLOS, the abovementioned influencing factors should have different parameter levels and incorporate a certain number of elderly pedestrians. Signalised intersections were selected according to the following requirements: 1) It is necessary to ensure that a certain number of elderly pedestrians pass through the crosswalk at the selected signal intersection; thus, they can complete the questionnaire about the pedestrian level of service.
2) The traffic data of each selected signal intersection crosswalk should be different, so as to ensure that the research is not limited to a certain type of pedestrian crossing scene, in order for the research results to have a certain applicability.
3) The selected survey sites can cover common and typical pedestrian crossing scenes at signalised intersections as far as possible, so as to ensure that the research conclusions have to be applied to other signal crosswalks. 4) The area around the signalised intersection is open and flat, which is convenient for setting up cameras to record video. Then, based on field pre-survey and screening, 12 crosswalks at six signalised intersections in Chongqing, China, were finally selected as data collection locations. For each of the selected crosswalks, dynamic parameters such as motor vehicle flow rate, pedestrian crossing flow rate and pedestrian crossing delay were recorded and extracted for 2-hour datasets. The selected 12 survey locations were arranged as follows: ten for constructing the evaluation model (i.e. the modelling group) and two for validating the evaluation model (i.e. the validation group). The location information of each crosswalk is shown in Table 2. All the intersections where the crosswalks are located have signal control for both straight and left-turning vehicles. For these 12 locations, information on intersection channelisation and timing schemes was recorded through on-site surveys. Data on motor vehicles, pedestrian flow and pedestrian delay were obtained by manually extracting recorded videos. The elderly pedestrians' perceptions of PLOS were investigated using an intercept survey method and synchronised with video shooting. Questionnaires were allocated to elderly pedestrians after they crossed the street. The questionnaire contained information on basic individual characteristics (such Figure 1 -Crossing video recording and the elderly pedestrian field questionnaire collection as gender and age) and three questions on elderly pedestrians' perceptions of the safety, convenience and efficiency of the crosswalks. A five-point positive scale was used to record the survey data (i.e. a score of 5 indicates "very safe"). During the survey, when the elderly respondents had difficulty reading and writing, trained surveyors were responsible for explaining the questionnaire and completing the survey. The survey method is shown in Figure 1.

Data analysis
Traffic data. Static and dynamic traffic data for ten crosswalks in the modelling group and two crosswalks in the validation group were obtained based on the field survey and manual data extraction, respectively. Table  3 shows the statistical description of these traffic data. Curb ramp setting Sample data. A questionnaire survey on the perception of PLOS was conducted for elderly pedestrians crossing the street. A total of 515 questionnaires were completed at the 12 crosswalks, with 457 valid questionnaires (369 for the modelling group and 88 for the validation group). Table 1, correlation analyses were conducted between the results of the perceived safety, convenience and efficiency ratings and the data of the corresponding variables at each dimension. This was aimed to identify the variables that elderly pedestrians consider important in influencing PLOS at signalised intersections among the possible influencing factors. Based on the sample data of the 12 crosswalks, Spearman's rank correlation test was applied to categorical variables (e.g. whether there were curb ramps at both ends of crosswalks), and the Pearson correlation test was applied to other variables. The correlation results show that the crosswalk length and the volume of right-turning traffic without signal control were strongly correlated with the safety dimension of PLOS. The pedestrian crossing speed and the existence of curb ramps at both ends of the crosswalks were strongly correlated with the convenience dimension of PLOS. The average pedestrian delay was strongly correlated with the efficiency dimension of PLOS. The results are shown in Table 4. Therefore, the above five variables were considered as important variables for evaluating PLOS perceived by elderly pedestrians at signalised intersections.

Evaluation model
The perceived PLOS evaluation data of signalised intersections obtained from the questionnaire-based survey were subjective. These data were based on personal judgments of elderly pedestrians via linguistic description. Thus, these data were fuzzy, while the static and dynamic traffic parameters of intersections were quantitative. The fuzzy liner regression (FLR) method based on the likelihood distribution is more suitable for dealing with such subjective qualitative data [28]. Thus, the FLR model was adopted for modelling in this paper.
The evaluation model is expressed as where  y is the composite score of pedestrian level of service perceived by elderly pedestrians expressed as LR-type fuzzy numbers in the FLR model; x n is the n th independent variable, which is the traffic characteristics of signalised intersections verified by significance tests, i.e. crosswalk length (L c ), the volume of right-turning traffic without signal control (Q r ), pedestrian crossing speed (V p ), curb ramp setting (R c ) and the average pedestrian delay (D p );  n a is the regression coefficient of the n th independent variable expressed as LR-type fuzzy numbers in the FLR model.
If the score is lower, the PLOS is better [12], so the five-point positive scale score data of the sample were backward processing (i.e., a score of 5 indicates "very unsafe"). And according to the questionnaire results of perceived evaluation by elderly pedestrians, the data of ten crosswalks in the modelling group were used to demonstrate the score distribution in each dimension, as shown in Figure 2.
To solve such FLR models by referring to the relevant literature [29], let the regression coefficients be , where s is the mean value of the perceived sample data of the modelling group; p is the left extension; q is the right extension. The regression coefficients and dependent variable matrices can be expressed as   The mean value, the left extension and the right extension for the perceived sample data of elderly pedestrians are written as: where ( ) d ij y is the perceived evaluation score of the j th respondent at the i th crosswalk in the d th dimension; N 1 is the total amount of data on the perceived evaluation values at the i th crosswalk; N 2 is the amount of data smaller than s; N 3 is the amount of data larger than s.
The regression coefficients of the FLR model are solved by The LR-type fuzzy number addition algorithm shown in Equation 7 was used to sum the scores  ( )  Based on Figure 2, the FLR model was used to obtain the scores in each dimension and the composite scores from elderly pedestrians. The score results are shown in Table 5. The five significant variables of the ten crosswalks in the modelling groups in Table 3 and the composite PLOS score data in Table 5 were extracted to obtain the matrices X, S and P of the perceived PLOS evaluation. The parameter estimates of the FLR model were calculated. Then, the composite evaluation model of PLOS at signalised intersections was obtained: The evaluation data can be obtained using Equation 8. However, the general PLOS evaluation value is one score. Thus, the data can be solved using the centroid method: where ŷ i denotes the score of pedestrian level of service for the i th crosswalk;  are the lower, middle and upper value, respectively. Thus, the data of the perceived PLOS evaluation by the elderly pedestrians at the corresponding static and dynamic characteristic parameters of the signalised intersections can be obtained.

Determination of level threshold
Considering the fuzzy nature of the collected evaluation sample data, the fuzzy C-means (FCM) clustering algorithm was used to perform clustering and classify the PLOS. The FCM algorithm has natural and non-probabilistic characteristics. More sample data were obtained for clustering to make the classification results more accurate. With reference to relevant literature [30][31][32][33][34], different value ranges and linear intervals are determined for each independent variable. The ranges and intervals were assigned to the crosswalk length, the volume of right-turning traffic without signal control, pedestrian crossing speed, whether to set a curb ramp and pedestrian delay. The details are shown in Table 6.
where c i is the cluster centre of the i th level of PLOS; m is the weighted index to control the fuzzy degree of the membership matrix, taken as 2; u ij is the membership degree of the j th sample data to the i th level of PLOS. The Lagrangian operators were introduced to transform the extreme value problem with membership constraints into the unconstrained condition problem.
The input parameters in the objective function (u ij and c i ) were derived to obtain the necessary conditions for the objective function to reach the minimum value: where c l is the cluster centre of the l th level of PLOS. When i = l, Equation 11 can be used to solve for c l .
The iterative computation process of the FCM algorithm includes the following three steps: Step 1: Parameter initialisation. The following parameters are initialised: the fuzzy weighted index m, the error threshold ε and the number of clusters k of the membership matrix U. The error threshold is used as the condition to determine the iteration termination, taken as 5 1 e − × . The PLOS is classified as A~F in this paper; thus, the number of clusters was taken as 6.
Step 2: Using Equation 11 to calculate the membership matrix U of PLOS evaluation data and the clustering centre vector C of each PLOS.
Step 3: Determining whether the iteration is terminated. The termination conditions of the iteration are expressed as Equation 12 holds, the objective function is minimised, and the iteration is terminated. Then, the membership matrix U and the cluster centre vector C are obtained. If Equation 12 does not hold, then k=k+1 and return to Step 2 for iterations.
According to the iterative calculation process of the FCM algorithm, the ten sample datasets of PLOS evaluation values were clustered and solved in turn. The average PLOS classification boundary values in the ten clustering results were taken to obtain the recommended PLOS classification thresholds ( Table 7).

Model error check
The accuracy of the FLR-based PLOS evaluation model was checked using mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) and goodness of fit (R 2 ). The model error check results (Table 8) show that the error between the questionnaire-based true PLOS and the FLR-based predicted PLOS was insignificant. The model generally exhibited high goodness of fit (R 2 =0.9794).

Clustering performance analysis
The standard FCM clustering algorithm can only guarantee that the solution is locally optimal but not the overall optimal solution. Thus, it is necessary to evaluate the clustering performance of the FCM algorithm. Three evaluation indicators are commonly used, including classification coefficient F, average fuzzy entropy H and standard FCM classification success rate v: where u ij denotes the membership degree of the j th sample data to the i th level of PLOS; w denotes the number of times the cluster centres are successfully obtained by running the standard FCM ten times.
The arithmetic mean of each clustering performance evaluation index was obtained using the results of ten runs of the standard FCM algorithm. The results show that the FCM algorithm has good clustering performance, with F=0.75, H=0.51 and v=100%.

MODEL VALIDATION
The traffic data of the two crosswalks in the validation group were used to validate the established evaluation model. The actual PLOS scores obtained from the questionnaire and predicted PLOS scores were compared and analysed. The results are shown in Figure 3.

Validation group crosswalk
Actual PLOS score Predicted PLOS score

Figure 3 -Model validation results
From Figure 3, the actual and predicted PLOS score for Crosswalks G (4.9 and 4.7) and H (4.9 and 4.8) were classified as Level A according to the recommended threshold for classification of pedestrian service level in Table 7. The differences between the actual and predicted PLOS scores for Crosswalks G and H were 0.2 and 0.1, indicating smaller errors and good consistency. So, the divided threshold in the paper can be used to classify the group. In addition, the evaluation model for pedestrian level of service at signalised intersections from the elderly perspective can be used to predict the evaluation conditions from the viewpoint of elderly pedestrians according to signalised intersection traffic data.

CONCLUSIONS
In this paper, the perceived evaluation of elderly pedestrians was obtained using a questionnaire survey. The static traffic facilities and dynamic traffic parameters of signalised intersections were collected. A PLOS evaluation model was established, with the intersection traffic characteristics parameters as input and the perceived PLOS evaluation of elderly pedestrians at signal intersections as output. The main findings are as follows: 1) Analysis of significant factors affecting the PLOS evaluation of elderly pedestrians. The subjective evaluation of elderly pedestrians with respect to three dimensions (safety, convenience and efficiency) of signalised intersections was correlated with pedestrian crossing characteristics, traffic characteristics, intersection geometric design and pedestrian-signal design at the intersection, respectively. The results show that the perceived PLOS evaluation of elderly pedestrians was mainly related to the crosswalk length, the volume of right-turning traffic without signal control, pedestrian crossing speed, the presence of curb ramps at both ends of the crosswalks and average pedestrian delay at the intersection. 2) Establishment of the PLOS evaluation model based on elderly pedestrians' perceptions. The traffic characteristic parameters significantly affecting the PLOS evaluation by the elderly at signalised intersections were used as inputs. Based on the fuzzy linear regression model, the PLOS evaluation model from the elderly perspective was established. The model parameters were calibrated using the traffic environment data collected from ten crosswalks and the perceived evaluation results of elderly pedestrians. 3) Analysis and validation of model thresholds. The elderly pedestrians' evaluation and objective traffic parameters in the modelling group were collected. Based on the fuzzy C-means clustering algorithm, the thresholds for PLOS classification were recommended. Then, the evaluation and classification of the mod- el were validated using the data of the two crosswalks in the validation group. The results show insignificant differences between the predicted and actual (perceived) PLOS values at the two crosswalks. The proposed model exhibited good prediction performance.