Elsevier

Safety Science

Volume 38, Issue 1, June 2001, Pages 63-82
Safety Science

Analysis of pedestrians’ behavior at pedestrian crossings

https://doi.org/10.1016/S0925-7535(00)00058-8Get rights and content

Abstract

This paper presents a methodology for studying pedestrians’ behavior at pedestrian crossings. To help understand the behavior of pedestrians, separate models were developed and estimated for divided and undivided streets. Estimated models include waiting time at the curbside and the number of crossing attempts needed by the pedestrian to make a successful crossing. From a broad range of road user and roadway factors, the strongest and most significant predictors which influenced the pedestrian’s waiting time and the frequency of attempts to cross the streets were gender, age, number of children in household, crossing frequency, number of people in the group attempting to cross, access to private vehicle, destination, home location in relation to pedestrian crossing, and pedestrian past involvement in traffic accidents. In addition to these predictors, maximum likelihood estimates revealed that the pedestrian expected waiting time seems to profoundly influence the number of attempts needed to successfully cross the street (divided or undivided). Furthermore, results relating to pedestrian crossings on divided streets indicate that the pedestrian’s expected waiting time when crossing from one side of the street to the central refuge island seem to increase the risk to end the waiting time when crossing from the refuge island to the other side of the street. Finally, results seem to suggest that pedestrians behave differently or have different waiting times as they cross from one side of the street to the refuge and from the refuge to the other side of the street.

Introduction

Traffic accidents involving pedestrians have become a major safety problem all over the world, particularly in developing countries, due to high population density, rapid urbanization, and lack of adherence to traffic regulations by both drivers and pedestrians. Lack of adherence to traffic regulations at pedestrian crossings particularly by drivers create a paradigm in which pedestrians may become bold and force approaching vehicles in the traffic stream to brake in order to gain priority at the pedestrian crossing. On the other hand, pedestrian crossings with heavy pedestrian flow is likely to cause unacceptable vehicular delay (increased driver’s frustration).

Studies concerning accidents involving pedestrians have addressed a number of essential issues. These issues include delay at pedestrian crossings (Griffiths et al., 1984), drivers’ behavior and pedestrians interaction at pedestrian crossings (Katz et al., 1975, Griffiths et al., 1976, Fegan, 1978, Cresswell and Hunt, 1979, Landles, 1983, Himanen and Kulmala, 1988, Song et al., 1993, Varhelyi, 1998). A number of factors have been considered in these studies including: factors relating to physical environment (e.g. road width, existence of a central refuge at the crossing), road user variables (e.g. age, gender, socioeconomic characteristics, marital status), and the number of pedestrians in the group attempting to cross. Some of these factors turned out to influence the pedestrian’s decision to cross the roadway.

Griffiths et al. (1984) developed models that describe delays at sites without a central refuge and with effectively a single stream of vehicles in each direction. The paper addressed the issue of delay at pedestrian crossings where the major source of delay is attributed to the interaction between vehicles and pedestrians. The study reported that most drivers were prepared to stop when a pedestrian occupied or was approaching their part of the roadway. Young children and elderly pedestrians were likely to step onto the roadway when it was clear that a driver had yielded right of way or if the road was clear of approaching vehicles. The study indicated that as vehicle delay increases, drivers become more aggressive, taking advantage of very small gaps, in pedestrian flow across the pedestrian crossing. Katz et al. (1975) reported that drivers slowed down or gave the right-of-way more often for crossing pedestrians as a group, rather than as an individual.

Recent empirical results by Varhelyi (1998) indicated that drivers’ willingness to give the right of way to pedestrians at pedestrian crossings is low. Furthermore, drivers did not sufficiently lower their speeds to maintain a readiness to react to an unexpected dangerous situation. Moreover, drivers were willing to slow or stop when the speed of their vehicles was low. The study reported that three out of four drivers maintain the same speed and only one out of four slow down at crossing. The study concluded that drivers have to be influenced before they reached the decision zone (40–50 m before the pedestrian crossing) to prevent risky behavior.

Himanen and Kulmala (1988) specified and estimated a discrete choice model aiming to study the encounters between drivers and pedestrians at pedestrian crossings. The study addressed the problem by considering the choices of both drivers and pedestrians. Taking a variety of pedestrian’s, environmental, and traffic conditions into consideration, the probabilities of a driver braking or weaving and of a pedestrian continuing to cross in response to an encounter were identified. The data were collected through a video camera, as such, information relating to pedestrian’s type of trip in pursuit and socioeconomic characteristics were not gathered. The study reported that safety margins exists when the speed of the approaching vehicle is low. For example, if the speed of the vehicle 20 m prior to the pedestrian crossing is 50 km/h, there is no safety margin in the encounter. The study indicated that the most important explanatory variables were: number of pedestrians in the group, city size, vehicle speed, vehicle platoon size, and pedestrian distance from curb.

Adherence to traffic regulations by both pedestrians and drivers in developing countries are low in comparison with that of developed nations. In Jordan, drivers’ inclination to slow down and give way to pedestrians at pedestrian crossings is very low. Pedestrians usually wait at the curbside with the knowledge that drivers are not willing to stop and give them the right of way. As such, they try to force their way across hoping that drivers will slow or stop. If unsuccessful, they will return to the curbside and attempt again until successful. This crossing paradigm is likely to increase the pedestrians’ waiting time and therefore the potential increases in the rate of pedestrian accidents. In making recommendations to reduce pedestrian accidents it is essential to study behavioral aspects of pedestrians at pedestrian crossings. Previous research has made theoretical and methodological contribution to a practical understanding of pedestrian’s behavior and the interaction between the driver and the pedestrian at pedestrian crossings.

It is postulated in this paper that pedestrians arriving at the pedestrian crossing look for acceptable gaps between vehicles in the traffic stream. They either accept or reject such gaps. Rejection of prevailing gaps leads to longer waiting time at the curbside. The pedestrian’s waiting time at the curbside is modeled in this paper by the risk function. If a pedestrian attempted to cross the road and was successful then this means that the waiting time at the curbside has ceased (the pedestrian has accepted the available gap between vehicles). If on the other hand the attempt was not successful; then the waiting time has not ceased and the pedestrian has to make more attempt(s) to cross the road. It is hypothesized in this paper that as the number of crossing attempts increase, pedestrians in turn are likely to be bold and thereby force approaching vehicles to brake (i.e. increase the risk of crossing). As such, the pedestrian’s expected waiting time will enter the number of crossing attempts model as an exogenous variable.

In addition to the different approach adopted here, this paper will consider other predictors not considered in past research efforts. These predictors include origin and destination of the pedestrian, pedestrian’s past involvement (directly involved or witnessed) in traffic accidents, marital status, accessibility to private vehicle, and number of children in the household. In addition, this study will develop separate models (duration and count) to model the behavior of pedestrians on both divided and undivided streets. Moreover, separate models for each direction of divided streets will be estimated. Although models in this paper are calibrated with data gathered in Jordan, the methodology outlined here can be applied in any setting. Indeed, earlier studies that addressed the behavior of pedestrians at pedestrian crossings concluded large differences in crossing behavior among different countries.

Section snippets

Pedestrians’ waiting time at the curbside

The distribution of pedestrians’ waiting time (t) at the pedestrian crossing, considered as a random variable, is characterize in this paper by the risk function ξ(t). This function gives the instantaneous failure rate (ceasing the pedestrian’s waiting time at the curbside) assuming that the pedestrian has not crossed successfully (i.e. rejected available gaps) the street to time t. The notion of the risk function is a convenient theoretical construct that provides an index of the relative

Data collection

In Jordan, the inclination of drivers to give way to pedestrians at pedestrian crossings is very low. According to 1997 figures, pedestrian accidents accounted for 15% of the total accidents in Jordan. In addition, 35% of total traffic-related injuries and 42% of traffic-related fatalities involved pedestrians. In the capital city of Amman, 54% of fatalities (all fatalities resulting from all types of accidents) are attributed to pedestrian accidents. Moreover, 52% of pedestrians’ accidents

Undivided streets

Table 1 shows maximum likelihood estimation results of the pedestrians waiting time at pedestrian crossings. The likelihood ratio test clearly demonstrates the overall goodness-of-fit of the estimated waiting time model. The statistical significance of each individual variable is given by the t-ratio statistic. Most of the included variables are statistically significantly different from zero at the 10% level (one-tailed t-test).

Estimation results show that pedestrians who were involved or

Summary and conclusion

This paper introduces a methodology, combining duration and count models to study the behavior of pedestrians at pedestrian crossings located on divided and undivided urban streets. Findings from this paper are partly supplemented by those found in previous research that is based on other theoretical derived models, in particular, those with a specifically attitudinal focus.

Proportional hazard models are specified and estimated to identify the determinants of pedestrians waiting time on

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