1. Introduction

1.1. Litrature Review

1.1.1. Traffic Safety on Pedestrian Crossings

Pedestrian safety is regarded as one of the most challenging problems in urban transport [4], hence it should be jointly considered with the motorized transport system that plays a central role in the most societies. In many instances, commercial goods needed for everyday life are transported by road. In addition to this, residents of various places use motorized travel to reach their work or leisure destinations. While this advantage has been achieved, high levels of motorization contribute to serious consequences such as human and economic losses owed to road accidents [4].This being in mind, pedestrian safety has recently been recognized as a public health challenge worldwide [5].According to the [6] report on transportation considerations for the 2030 sustainable development goals, road safety remains an important development issue. [7] showed that pedestrian characteristics, is one of the factors that affect pedestrian crossing safety and [8] proposed the improvement measures in design of pedestrian crossing facilities, similar to Kigali pedestrians crossings [9]. Pedestrians accidents are very often resulting also from the infrastructure related factors of the crosswalks [8].

Contrary to the declining number of fatalities due to train–vehicle collisions at highway-rail grade crossings, the number of pedestrian and bicycle fatalities at highway- and pathway-rail grade crossings has increased in the last dozen years [10].A large number of deaths and injuries occur annually as a result of road crashes among pedestrians, especially in low-income countries, and unsafe crossing behaviors still exist [7] . Globally, about 400,000 pedestrians are killed due to road traffic accidents [11]. [8] showed that around 35% of all pedestrian fatalities happened at crosswalks and requires improvements.

To combat the issue of pedestrian deaths and injuries, engineers have come up with various ingenuity to address the issue. [12] suggested also that educating and training on safe crossing behavior in traffic can be a pedestrian protection measure. One of the most used pedestrian crossing type, a zebra crossing, was first designed and implemented in Slough, United Kingdom, in 1951 [13] Likewise, it’s the most popular pedestrian crossing in Rwanda.

1.1.2. Pedestrian Mobility in the City of Kigali

According to the 2018 Transport Master Plan, the population of Kigali stood at approximately 1.5 million. It was forecasted to grow to approximately 3.8 million in 2050. This is something that may raise the pressure on existing transport infrastructure, and thence on traffic safety measures that have been put in place [14].

According to this same survey, on average, the majority of employed citizens live within 2 km from their place of work. When comparing the mode of transport used to travel to work to the average monthly household income, it has been clear that the areas where people earn a higher income are also the areas where the usage of private car travel is more common. Since most urban citizen do not fall in this category, it was then concluded that the majority of employed citizens use walking as a mode of transport to their place of work [9]. The journey started by surveying Kigali major road networks, in its main corridors. High traffic and low traffic areas were purposively sampled. Safety risk is hypothetically present in either situation.

The Inspectorate General of Police (IGP) office set a tariff for violation of pedestrian crosswalk by the drivers excluding bike riders to an amount of 25$ since 2015 under serial number 24 [15].In addition to that; an annual "arrive safely/Gerayo Amahoro "weekly campaign is organized by the Rwanda National Police (RNP) together with the Ministry of Infrastructures in the Republic of Rwanda to sensitive drivers to carefully drive and give access to pedestrian for crossing at designated facilities. According to RNP data, road crash rates in Rwanda decreased by 17% [16]. This study was conducted as a measuring tool to cross check the drivers stopping behavior in order to investigate the prevailing situation in the City of Kigali and found that there is still a gap to fill as far as pedestrian safety is concerned at crosswalk based on the research output.

More so, on schooling and other motives of people movements, it has been noticed that walking is the most popular mode of transport for students travelling to school [9]. In addition to this, the time of day that people will likely use to travel to work in Kigali is between 06:00 and 09:00 in the morning [3].

Figure 1. Population concentration and potential mobility density in the City of Kigali [14]

Figure 1. Population concentration and potential mobility density in the City of Kigali [14]

1.1.3. Zebra Characteristics and Traffic Regulations

Pavement markings are an important means of traffic control on streets and roads. In some cases, the pavement markings are used to supplement general traffic regulations, or regulations and warnings given by signs and signals. In other cases, markings can be used without supplement by other devices [17]. The principal advantage of road markings is that they convey guidance or information to the driver without diverting attention from the roadway. Road crashes lead to huge social and economic losses and are often a result of unsafe road design and characteristics [18]. In bad weather conditions, this may be of vital importance to road safety [19].Pavement markings should therefore be given special attention with respect to both application and maintenance [17] .

Same philosophy is used to convey guidance toward pedestrian crossings roads and it is very well known that the most crucial factors in road construction is the safety of road users [20]. Various markings, as shown later in this report, are drawn to guide drivers and pedestrians. At some special intersections, traffic lights are used to guide both drivers and pedestrians, while at most places, it’s only road markings. In Rwanda, it’s a traffic offense to violate pedestrian crossings such as a Zebra crossing. Since 2019, when the Government of Rwanda launched the safety week, it is in that regard that for the best practices, the pedestrian has a right of way of a vehicle, when the pedestrian has reached the crossing relatively as the first [21]. In such cases, the vehicle is supposed to stop, preferably somewhere in the deceleration zone, before the stop-line marking.

The government has continued to implement safer road programs through other government institutions to educate road users on effective and safe usage of the road. In 2017 the government reviewed laws on road safety to toughen penalties against traffic offenders. They have also committed to implementing all possible strategies to enhance road safety measures as evident by a campaign launched by the Rwanda National Police (RNP) and Ministry of Infrastructure (MININFRA) in 2017 to curb road accidents and promote road users respect so as to abide by road safety standards [22]. The vulnerable road user population, mainly pedestrian’s users [23] need a strong government road safety program for safe usage of roads.

2. Materials and Methods

2.6. Statistical Tests

To begin with, all data was stored in a central dataset to perform cleaning and critical joins. Using spatial dimensions attached to each entry, a spatial analysis was made. Using Tableau (Version 2021.4), spatial visualizations have been built to compare population densities, traffic densities and pedestrian crossing compliance on each surveyed site. Descriptive statistics have been used to portray safety challenges caused by vehicles. Cross tabulations and Pearson Chi-square tests have been used to evaluate probable dependencies of subject variables. To wind up the analysis part, Binary logistic regression models were built and have been used to evaluate driver’s stopping behaviors against traffic flow characteristics.

2.6.1. Chi-Square

Chi-square tests of independence test whether two qualitative variables are independent, that is, whether there exists a relationship between two categorical variables [32]. If the test shows no association between the two variables (i.e., the variables are independent), it means that knowing the value of one variable gives no information about the value of the other variable [31].

The Chi-square test of independence is a hypothesis test so it has a null (H₀) and an alternative hypothesis (H₁):

H₀: the variables are independent, there is no relationship between the two categorical variables. Knowing the value of one variable does not help to predict the value of the other variable

H₁: the variables are dependent, there is a relationship between the two categorical variables. Knowing the value of one variable helps to predict the value of the other variable

The calculation aspects of this test stems from the logic of Mathematical Probability. For two independents events A and B, the following probability equation should always hold true:

$$P\left(A\cap B\right)=P\left(A\right)\ast P\left(B\right)$$

Therefore, the Chi-square test of independence works by comparing the observed frequencies (so the frequencies observed in your sample) to the expected frequencies if there was no relationship between the two categorical variables (so the expected frequencies if the null hypothesis was true). This difference, referred as the test statistic (or t-stat) and denoted by χ2, and is computed as follows:

$$\mathsf{\chi }2=\sum _{\mathrm{i},\mathrm{j}}^{}\frac{{({\mathrm{O}}_{\mathrm{i}\mathrm{j}}-{\mathrm{E}}_{\mathrm{i}\mathrm{j}})}^2}{{\mathrm{E}}_{\mathrm{i}\mathrm{j}}}$$

O represents the observed frequencies and E the expected frequencies.

The test statistic alone is not enough to conclude for independence or dependence between the two variables. As previously mentioned, this test statistic (which in some sense is the difference between the observed and expected frequencies) must be compared to a critical value to determine whether the difference is large or small.

The critical value can be found in the statistical table of the Chi-square distribution and depends on the significance level, denoted α, and the degrees of freedom, denoted $df=(rows-1)(columns-1)$. The significance level is usually set equal to 5%.

Figure 2. Chi-square Distribution.

Figure 2. Chi-square Distribution.

Like for many other statistical tests, when the test statistic is larger than the critical value, the null hypothesis is rejected at the specified significance level.

2.6.2. Binary Logistic Regression

Collected data was also analyzed using binary logistic regression. This one can predict the probability (P) of a specific event when the dependent variable is dichotomous [35] . In this study, the occurrence of a specific stopping behavior can be considered as a binary response variable. The driver will either stop or continue driving during a pedestrian crossing event. The log odds (logit) of P equals the natural logarithm of P/(1-P). Therefore, Binary logistic regression estimates the log odds of the independent variables as a linear combination as shown in the equation below:

$$\mathrm{L}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}\left(\mathrm{P}\right)=\mathrm{L}\mathrm{n}\left(\frac{\mathrm{P}}{1-\mathrm{P}}\right)={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{X}}_1+{\mathsf{\beta }}_2{\mathrm{X}}_2+\dots {\mathsf{\beta }}_{\mathrm{n}}{\mathrm{X}}_{\mathrm{n}}$$

In this equation, P is the probability of the behavior occurrence; X_n is the independent variable; and β_n is the logistic regression coefficient. For each research question, the significance value of 0.05 was accepted as an influential predictor variable. For each model, the odds ratio was calculated to determine if there is an increase (>1) or decrease (0–1) in the probability of the behavior when the independent variables increase with one unit [36]. The Cox & Snell R Squared and Nagelkerke R Squared tests have been used to assess each model’s goodness of fit. The test determines the percentage of variance caused by independent variables in the equation [33] . SPSS 25.0 has been used for all statistical computations.

3. Results

3.1. Zebra Characteristics

According to the Figure 3, using satellite imagery, it is easy to track subject zebra crossings. Using remote sensing, on the 6m scale, on precise coordinates, it’s possible to estimate zebra crossing characteristics and track asymmetries. Generally, in road design, it’s normal to get non-uniform dimensions depending on terrain nature. The focus of this research is on investigating the relationship between zebra characteristics and vehicle’s (un)stopping behaviors. Stopping behaviors of vehicles are subject of pedestrian safety.

Figure 3. Research Flowchart.

Figure 3. Research Flowchart.

A pedestrian crossing can be characterized by various aspects. Some are inherently due to the way the road infrastructure has been set up. Other factors may depend of how markings have been drawn. In both cases, data collectors have collected important information using tape measures.

While sites have been trimmed down to granular uniformity details, recorded measurements still show that there are clear inconsistencies in Zebra characteristics in the City of Kigali. For instance, one site (Site 9) did not have a stop line one side of the lane. Zebra lines lengths also greatly vary in measure with μ=3.7m (mean) and σ=0.96m (standard deviation). Zebra lines lengths are arguably designed depending on pedestrian traffic on both ends of the road facility.

Table 1. Zebra characteristics for selected sites. Quick analyses involving spark lines and bars have been done. Additional columns to show average measurements and standard deviations is shown as well. All are measured in meters.

Table 1. Zebra characteristics for selected sites. Quick analyses involving spark lines and bars have been done. Additional columns to show average measurements and standard deviations is shown as well. All are measured in meters.

One other major characteristic with variability is the distance between stopping lines and zebra lines themselves. They were measured, on both lanes with maximum μ=2.9m and σ=1.25m. Zebra lines markings vary from country to country. Like all other road markings, there is no fixed or correct length. Most markings are adapted to the traffic situation, to address factors like overtaking possibility, design speed, and more. Therefore, design standards suggest acceptable ranges. Nonetheless, it is of great interests, to investigate whether zebra characteristics have any, or, are in anyway associated to drivers stopping behaviors in cases of pedestrian crossings. According to our observations, most measurements fell into acceptable ranges with some exceptions. This was partly due to the fact that data collection sites were hand-picked upon various factors.

Pedestrian walkways may affect pedestrian safety at pedestrian crossings. According to collected data, at least 3 out of 10 sites, did not have a pedestrian walkway on either of its lanes. It’s unknown whether this characteristic has a positive or negative stopping behavior toward drivers, but it’s arguably a non-ignorable safety risk for pedestrians. In most cases, when pedestrians are crossing, they tend to feel safer when the crossing destination is safer. The lack of pedestrian walkways in some roads therefore poses a significant hazard toward pedestrian safety. At worst cases, the lack of walkways was associated with existence of non-covered water canals and drenches. It’s therefore undeniably risky to cross over such a facility.

3.3. Descriptive Analysis

The collection of data was long and interesting. Over 22,000 vehicles were identified in 10,259 stopping occasions. Across 10 sites; drivers, vehicles, pedestrians and road characteristics were different. This variety of situations came to interesting findings summarized in the following table:

Table 2. Cross tabulation of major frequencies.

Table 2. Cross tabulation of major frequencies.

Variable Name	Evening		Morning		Totals
	N	%	N	%	N	%
	11,354	(51.5)	10,704	(48.5)	22,058	(100)
Did the vehicle stop?
No	9,124	(41.4)	9,049	(41.0)	18,173	(82.4)
Yes	2,230	(10.1)	1,655	(7.5)	3,885	(17.6)
Vehicle Type
Bicycle	95	(0.4)	245	(1.1)	340	(1.5)
Motorbike	7,499	(34.0)	7,366	(33.4)	14,865	(67.4)
Bus	89	(0.4)	116	(0.5)	205	(0.9)
Car	3,428	(15.5)	2,401	(10.9)	5,829	(26.4)
Stopping Distance
Breached	9,124	(41.4)	9,049	(41.0)	18,173	(82.4)
< 0.5 Meters	142	(0.6)	109	(0.5)	251	(1.1)
< 1.0 Meters	120	(0.5)	48	(0.2)	168	(0.8)
< 1.5 Meters	147	(0.7)	110	(0.5)	257	(1.2)
< 2.0 Meters	344	(1.6)	148	(0.7)	492	(2.2)
< 2.5 Meters	296	(1.3)	162	(0.7)	458	(2.1)
< 3.0 Meters	429	(1.9)	299	(1.4)	728	(3.3)
< 3.5 Meters	265	(1.2)	370	(1.7)	635	(2.9)
Greater than 4m	487	(2.2)	409	(1.9)	896	(4.1)
Week Day
Monday	1,230	(5.6)	1,175	(5.3)	2,405	(10.9)
Tuesday	1,400	(6.3)	1,690	(7.7)	3,090	(14.0)
Wednesday	1,536	(7.0)	2,064	(9.4)	3,600	(16.3)
Thursday	2,020	(9.2)	1,937	(8.8)	3,957	(17.9)
Friday	1,327	(6.0)	1,863	(8.4)	3,190	(14.5)
Saturday	2,241	(10.2)	1,224	(5.5)	3,465	(15.7)
Sunday	1,600	(7.3)	751	(3.4)	2,351	(10.7)

At a glance, zebra compliance is arguably in a bad shape and safety at pedestrian crossings is not the best. In all observed occasions, from Monday to Sunday, in morning and evening peak hours, only 17.6% of drivers stopped to allow pedestrian to cross. Everyone else just continued to drive while pedestrians are crossing, not to mention that those who stopped didn’t necessary stop far away from pedestrians. According to recorded observations, only 896 vehicles (4.1%) stopped at least 4m away from the Zebra center line.

In this study, researchers tried to visualize four variables of traffic flow and pedestrian crossing events in one graph. These include: vehicle types, days of the week, peak hour periods (hours, minutes and seconds) and stopping distances. Advanced statistical and data computational tools have been used to come up with such a graphs

Figure 4 shown above, is a clear and integral visualization of pedestrian safety on zebra crossings in Kigali. From the left, on the upper axis, there are consecutive days of the week when the survey was carried. On the bottom x-axis, there are stopping distances per zebra crossings. Distance 0 is recorded for every vehicle which crossed the center line of the zebra, thence breaching safety regulations and putting pedestrians lives at risk.

Figure 4. From left to right, satellite visualization of data collection sites: 15, 14 and 12. The last mockup shows various dimensions that were measured using a tape measure. It’s already obvious that stopping line are not uniform on each zebra crossing.

Figure 4. From left to right, satellite visualization of data collection sites: 15, 14 and 12. The last mockup shows various dimensions that were measured using a tape measure. It’s already obvious that stopping line are not uniform on each zebra crossing.

Figure 5. From the left: Data collection sites on Kigali Map, Vehicle frequencies by type on stopping occasions, Vehicle activity when pedestrian are crossing on each site.

Figure 5. From the left: Data collection sites on Kigali Map, Vehicle frequencies by type on stopping occasions, Vehicle activity when pedestrian are crossing on each site.

Figure 6. Integral visualization of vehicle stopping behavior on all sites throughout the week.

Figure 6. Integral visualization of vehicle stopping behavior on all sites throughout the week.

On the Y-axis, the graph portrays traffic peak hours in a continuous fashion. By trimming out outliers and other edge observations, the graph shows data from the morning at 6:00 AM till 7:00 PM in the evening. A 4 – semi-transparent color legend variable has been used to portray vehicle type, while circle radii were used to showcase the density of the same.

On the granular level, there are obvious observations that can be noted. For instance, on the traffic flow aspect, there are a few vehicles in weekend mornings. Same is for a Wednesday evening, nevertheless this could have been an anomaly since it rained heavily in that evening halting pedestrian mobility and data collection altogether.

In addition, on the first day of recording data, observers and data analysts were at first agnostic of vehicle type, until when they realized that vehicles behave differently upon various crossing events. As shows the videos, two wheeled vehicles are likely to continue moving while pedestrian are crossing, even when four-wheeled (or more) ones have stopped to allow safe passage of pedestrians. From this point forward, vehicle types were recorded as part of the survey.

3.4. Stopping Behaviors

To compute various equation elements of the Chi-Square equation, the following table has been made:

Table 3. Cross Tabulation and Chi-Square Values (Expected values in Bold).

Table 3. Cross Tabulation and Chi-Square Values (Expected values in Bold).

Did the vehicle stop?	No			Yes			Totals
	N	%		N	%		N	%
	18173	(82.4)		3885	(17.6)		22058	(100.0)
1.Peak Hour Period – X2 (1) =66.3, p<.001
Evening	9124	(41.4)	(42.4)	2230	(10.1)	(9.1)	11354	(51.5)
Morning	9049	(41.0)	(40.0)	1655	(7.5)	(8.5)	10704	(48.5)
2.Vehicle Type – X2 (4) =2774, p<.001
Bicycles	323	(1.5)	(1.3)	17	(0.1)	(0.3)	340	(1.5)
Motorcycles	13519	(61.3)	(55.5)	1346	(6.1)	(11.9)	14865	(67.4)
Buses	131	(0.6)	(0.8)	74	(0.3)	(0.2)	205	(0.9)
Cars	3522	(16.0)	(21.8)	2307	(10.5)	(4.7)	5829	(26.4)
Null	678	(3.1)	(3.1)	141	(0.6)	(0.7)	819	(3.7)
3.Day of the Week – X2 (6) =259.2, p<.001
Monday	1897	(8.6)	(9.0)	508	(2.3)	(1.9)	2405	(10.9)
Tuesday	2391	(10.8)	(11.5)	699	(3.2)	(2.5)	3090	(14.0)
Wednesday	2898	(13.1)	(13.4)	702	(3.2)	(2.9)	3600	(16.3)
Thursday	3197	(14.5)	(14.8)	760	(3.4)	(3.2)	3957	(17.9)
Friday	2625	(11.9)	(11.9)	565	(2.6)	(2.5)	3190	(14.5)
Saturday	3107	(14.1)	(12.9)	358	(1.6)	(2.8)	3465	(15.7)
Sunday	2058	(9.3)	(8.8)	293	(1.3)	(1.9)	2351	(10.7)
4.Vehicle Density – X2 (2) =181.3, p<.001
Low	3039	(13.8)	(14.3)	788	(3.6)	(3.1)	3827	(17.3)
Medium	4426	(20.1)	(18.6)	564	(2.6)	(4.0)	4990	(22.6)
High	10708	(48.5)	(49.5)	2533	(11.5)	(10.6)	13241	(60.0)
5.Pedestrian Density – X2 (3) =138.4, p<.001
Less Dense	6327	(28.7)	(27.6)	1061	(4.8)	(5.9)	7388	(33.5)
Dense	1138	(5.2)	(5.3)	291	(1.3)	(1.1)	1429	(6.5)
Very Dense	4863	(22.0)	(23.2)	1353	(6.1)	(5.0)	6216	(28.2)
Extremely Dense	5845	(26.5)	(26.2)	1180	(5.3)	(5.6)	7025	(31.8)

Model Fit

A logistic regression was conducted to determine if five traffic flow variables (Vehicle type, peak hour period, day of the week, vehicle density and pedestrian density) are able to predict stopping behaviors of drivers to allow pedestrian use zebra crossings in safety. The results of the logistic regression were highly statistically significant, with X (13) =2954.6, p<.001, using the Omnibus Test.

Effect size

The variance in driver’s stopping behaviors predicted by traffic flow variables in the model ranges from 12.5% to 20.7% based on the Cox & Snell R Square or Nagelkerke R Square, respectively.

Classification Table

Without any predictor, the model would have predicted 82.4% of the stopping behavior correctly. On the flipside, with independent variables included, this number increases slightly with 0.50 basis points to 82.9%. Some statisticians refer this to percentage accuracy(PAC) in classification too.

Sensitivity

Percentage of cases in which Stopping at a Zebra crossing was observed ("yes") and were correctly predicted by the model. 9.5% of drivers who stopped were predicted by the model to have stopped. The positive predictive value is the percentage of correctly predicted cases with the observed characteristic (those who stopped) compared to the total number of cases that were predicted to stop. That is, of all cases predicted to stop, 93.7% were correctly predicted.

Specificity

Percentage of cases in which Stopping at a Zebra crossing was observed ("no") and were correctly predicted by the model. 98.6% of drivers who breached the zebra crossing were predicted by the model to have violated. The negative predictive value is the percentage of correctly predicted cases with the observed characteristic (those who breached) compared to the total number of cases that were predicted to breach. That is, of all cases predicted to violate, 99.9% were correctly predicted.

Model Summary

The model (traffic variables name them) explained between 12.5% (Cox & Snell R²) and 20.7% (Nagelkerke R²) of the variance in Driver’s stopping behaviors and correctly classified 82.9% of cases. Sensitivity was 9.5% and Specificity was 98.6%. The positive predictive value was 93.7%. and the negative predictive value was 99.9%.

4. Discussion

4.1. Effect of Peak Hour Period

As per the statistical raw data in Table 3 the peak hour period plays a minor role under descriptive statistics. Driver’s behaviors to give access to pedestrians to cross is better and more during evening times than mornings rated at. This may due to the fact that the evening period people are no longer stressed by the duty reporting delay but going at home. Hence still the probability of giving access to pedestrians is below 1 as per the odds ratio of 0.733 from Table 4.

Table 4. Logistic regression equation variables and their statistical significance.

Table 4. Logistic regression equation variables and their statistical significance.

							Lower	Upper
Variable	B	S.E.	Wald	df	Sig.	Exp(B)	95% C.I. - Exp(B)
Intercept	-3.390	0.266	162.468	1	.000	0.034
1. Peak Hour Period	-0.311	0.040	59.095	1	.000	0.733	0.677	0.793
2.Vehicle Type
Bicycle (1)			2289.644	4	.000
Moto	0.415	0.252	2.704	1	.100	1.514	0.924	2.481
Bus	2.208	0.290	57.838	1	.000	9.094	5.148	16.064
Car	2.341	0.252	86.486	1	.000	10.389	6.343	17.014
Null	0.992	0.273	13.157	1	.000	2.696	1.578	4.609
3.Day of the Week
Monday (1)			168.105	6	.000
Tuesday	-0.078	0.081	0.923	1	.337	0.925	0.789	1.085
Wednesday	-0.162	0.080	4.061	1	.044	0.851	0.727	0.996
Thursday	-0.269	0.079	11.601	1	.001	0.764	0.655	0.892
Friday	-0.276	0.083	10.936	1	.001	0.759	0.645	0.894
Saturday	-0.884	0.088	100.973	1	.000	0.413	0.348	0.491
Sunday	-0.599	0.093	41.426	1	.000	0.549	0.458	0.659
4.Vehicle Density*	0.671	0.044	233.313	1	.000	1.956	1.795	2.132
5.Pedestrian Density*	-0.494	0.056	77.360	1	.000	0.610	0.547	0.681

5. Conclusions

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