=Paper=
{{Paper
|id=Vol-2061/paper1
|storemode=property
|title=Crossing Behaviour of the Elderly: Road Safety Assessment through Simulations
|pdfUrl=https://ceur-ws.org/Vol-2061/paper1.pdf
|volume=Vol-2061
|authors=Stefania Bandini,Luca Crociani,Andrea Gorrini,Giuseppe Vizzari
|dblpUrl=https://dblp.org/rec/conf/aiia/BandiniCGV17
}}
==Crossing Behaviour of the Elderly: Road Safety Assessment through Simulations==
https://ceur-ws.org/Vol-2061/paper1.pdf
Crossing Behaviour of the Elderly: Road Safety
Assessment through Simulations
Stefania Bandini1, 2 , Luca Crociani1 , Andrea Gorrini1 , and Giuseppe Vizzari1
1 Complex Systems and Artificial Intelligence research center,
Department of Informatics, Systems and Communication, University of Milano-Bicocca.
Viale Sarca 336 - Edificio U14, 20126 Milano (ITALY).
{name}.{surname}@disco.unimib.it
2 Research Center for Advance Science and Technology, The University of Tokyo.
4-6-1 Komaba, Meguro-ku, Tokyo 153-8904 (JAPAN).
Abstract. The assessment of the safety of road crossing facilities in urban sce-
narios can be supported by means of advanced computer-based simulations. Inte-
grated models considering the vehicular and pedestrian traffic, and their interac-
tions, still lack empirical evidences about the heterogeneous features of pedestri-
ans, with particular reference to age-driven crossing behaviour. Elderly pedestri-
ans are indeed one the most vulnerable road users, due to the progressive decline
of cognitive and motor ability linked to ageing. In this paper we introduce the re-
sults of an observation at a non-signalised intersection aimed at characterising the
crossing behaviour of the elderly. In particular, we compare the results about the
crossing speeds and accepted safety gap among two sample of adult and elderly
pedestrians while crossing. Then, the paper proposes an innovative approach for
modelling pedestrians and vehicles interactions in the area of a zebra crossing,
either signalized or not, considering the impact of age.
Keywords: Ageing, Pedestrian, Crossing, Modelling, Simulation
1 Introduction and Related Works
The Global Status Report on Road Safety by the WHO [23] showed that road accidents
represent the 8th leading cause of death in the world population: 1.2 million people are
killed on roads every year. Despite recent efforts, the measures currently in place to re-
duce road traffic deaths and injuries are mainly aimed at protecting car occupants. How-
ever, results showed that almost 50% of those dying on the world’s roads are vulnerable
road users (e.g., pedestrians, motorcyclists, cyclists). In particular, the percentage of
pedestrians fatalities corresponds to 26% of the overall traffic victims in EU (16% in
Italy, 14% in France, 14% in USA). This figure is even higher in low and middle-income
countries, due to the rapidly increased number of registered vehicles.
To effectively contrast the social cost of traffic accidents it is necessary to integrate
theoretical knowledge, analytical data and experience about pedestrian-vehicle interac-
tions in urban scenarios, within an evidenced-based approach. From a methodological
perspective, the complexity of such field of study requires a cross-disciplinary knowl-
edge (e.g., traffic engineering, traffic psychology, safety science, computer science) and
different techniques for data collection (e.g., on field observations, experiments in vir-
tual reality environments, computer-based simulations). The achieved empirical results
can support the development of advanced traffic management strategies and design so-
lutions, to enhance the safety of transportation infrastructures and to prevent the occur-
rence of road fatalities.
In this framework, several empirical contributions [19, 18, 16] investigated the im-
pact of the physical environment on pedestrian crossing behaviour (e.g., road width,
traffic volumes, type of intersection, cross-walk location). Other researches studied how
the demographical characteristics of pedestrians can impact their crossing behaviour,
taking into account also the specific needs of vulnerable pedestrians such as the el-
derlies. Aged pedestrians are indeed more likely to die or be seriously injured in road
traffic collisions than adult people due to their body fragility [1]. Moreover, the crossing
behaviour of the elderly is negatively affected by decline in a range of motor functions
and cognitive skills linked to ageing, as follows:
– locomotion limitations [15, 21], such as:
• reduced range of motion;
• loss of muscle strength and coordination;
• changes in posture;
• decreased walking speed.
– perceptual-cognitive decline [20, 13, 5], such as:
• limited perception of light and colours;
• inability to tune out background noise;
• diminished attention and reaction time;
• spatial disorientation;
• slower and uncertain decision-making;
• scarce assertiveness in communicating their intention to cross.
The necessity to guarantee the safety of aged pedestrians at road crossing infras-
trictures has been highlighted by the World Health Organisation [22]: the concept of
Age-friendly Cities describes indeed a framework for the development of cities which
encourages the active ageing of the citizens by enhancing their mobility. This consists
of guidelines and policies for assessing and increasing the accessibility and safety of ur-
ban facilities for the elderly. The mobility of aged people represents indeed a key factor
for supporting them in maintaining an active and productive status, their social and civic
participation and access to community and health services, in spite of the progressive
social isolation linked to ageing [17].
In this context, the use of advanced computer-based simulation gives the possibil-
ity to test the safety of crossing intersections by testing alternative layouts and traffic
management solutions. Whereas separately simulation approaches about vehicular traf-
fic or pedestrian dynamics have produced a significant impact (see [14] for a review
of different approaches), efforts characterized by an integrated micro-simulation model
considering the simultaneous presence of vehicles and pedestrians are not as frequent
or advanced. With the notable exception of [12], most efforts in this direction are rel-
atively recent, such as [9], and they just analyse simple scenarios not even validated
Fig. 1. (a) A video frame of the analysed measurement area.
against real data. The most significant and recent work in this direction is represented
by [24] which adapt the social force model to this kind of scenario; while this work
considers real world data, the crossing behaviour of pedestrians is not thoroughly anal-
ysed.
The current work is aimed at producing an empirically validated model for the sim-
ulation of pedestrian-vehicles interactions at non-signalized crossings, considering the
crossing behaviors of elderlies. The research effort is, thus, driven by the necessity to
develop advanced and sustainable transportation strategies to contrast the social costs
of pedestrians’ injury and death due to car accidents [23].
Within this framework, this paper presents the results of an observation performed
at a non-signalised intersection in Milan, focusing on data regarding elderly pedestrian
while crossing (see Section 2). Then, it presents an example of integrated model for the
simulation of pedestrian and vehicular traffic flows, allowing the specific evaluation of
the level of efficiency and safety of the considered scenario (see Section 3). The paper
ends with a discussion on results.
2 Observation Results
The video-recorded observation has been performed on May 2015 in a particular area of
the city of Milan (the intersection between Via Padova, Via Cambini and Via Cavezzali).
The scenario (see Fig. 1) has been selected by means of a preliminary analysis which
was aimed at crossing the geo-referred information related to the socio-demographic
characteristics of the inhabitants of Milan and the localization of road traffic accidents.
Results showed that the chosen residential area is characterized by a significant presence
of elderly inhabitants and an high number of accidents involving pedestrians in the past
years1 . See [10] for a detailed description of the observation methodology.
2.1 Level of Service and Drivers’ Compliance
The bidirectional flows of vehicles and pedestrians passing through the observed zebra
crossing have been counted minute by minute to estimate the traffic volumes (1379 ve-
1 See http://aim.milano.it/en/pubblicazioni-en/archivio-pubblicazioni-en
Fig. 2. The work flow for selecting of crossing episodes from the video frames.
hicles, 18.89 vehicles per minute) and pedestrian flows (585 crossing pedestrians, 8.01
pedestrians per minute). The estimation of pedestrians’ age has been performed through
the visual inspection of the video by considering a set of locomotion and physical indi-
cators (e.g., walking pace, gait, posture, clothing, use of artefact for walking). Results
showed that elderlies were a significant portion of the total counted pedestrians (24%).
A series of time stamping activities were aimed at measuring the Level of Service
(LOS) [11], as an important indicator of the efficiency and safety of an intersection. The
LOS has been estimated by time stamping the delay of vehicles due to vehicular and
pedestrian traffic conditions (time for deceleration, queue, stopped delay, acceleration),
and the delay of crossing pedestrians due to drivers’ non compliance to pedestrian right
of way (waiting, start-up delay). Results showed that both the average delay of vehicles
(3.20 s/vehicle ± 2.73 sd) and the average delay of pedestrians (1.29 s/pedestrian ± .21
sd) corresponded to LOS A. In conclusion, the results about LOS showed that nearly
all drivers found freedom of operation and that no pedestrians crossed irregularly, with
low risk-taking crossing behaviour.
Then, a sample of 812 crossing episodes have been selected (see Fig. 2) and anal-
ysed to evaluate the overall compliance of drivers with crossing pedestrians. The episodes
have been selected considering the direct interaction between one vehicle and one or
more crossing pedestrians, and then classified to the type of interaction: (i) pedestrian
approaching the cross-walk, (ii) pedestrian waiting to cross at the curb, (iii) pedestrian
crossing on the zebra-striped, (iv) pedestrian approaching or waiting or crossing from
the far lane. Results (see Tab. 1) showed that the 52% of drivers were compliant with
pedestrians, stopping or slowing down to give way to them. The 48% of drivers were
non compliant with the right of way of pedestrian; 6 episodes (1%) were characterized
by non compliant drivers with pedestrians already occupying the zebra-striped crossing,
with potentially risky interactions.
Table 1. Results about drivers’ compliance to pedestrians’ right of way at the observed non-
signalized intersection.
Typologies of interactions Compliant drivers Non-compliant drivers
Pedestrians from the near side-walk 191 (46.14%) 223 (53.86%)
Pedestrians from the far side-walk 230 (57.79%) 168 (42.21%)
Total (812 crossing episodes) 421 (51.85%) 391 (48.15%)
Fig. 3. An exemplification of the trend analysis performed on the time series of speeds. The
starting time of the appraising and crossing phases are highlighted with black dots.
2.2 Pedestrian Speeds and Crossing Phases
A video tracking analysis has been performed considering a sub-sample of 50 pedestri-
ans (27 adults, from about 18 y.o. until about 65 y.o.; 23 elderly, from about 65 y.o.),
which were selected avoiding situations influencing the direct interaction between the
pedestrian and the driver. Part of the selected episodes was characterised by the multiple
interaction between the pedestrian and two vehicles oncoming from the near and the far
lane. Moreover, the episodes have been sampled considering the impact of pedestrians’
age and the effect of the different spatial layout of crossing points A and B.
The speed of pedestrians has been analysed among the time series of video frames
(i.e. trend analysis). According to results, we defined a parametric description of cross-
ing behaviour as composed of three distinctive phases (see Figure 3):
1. Approaching phase: the pedestrian travels on the side-walk with a relatively stable
speed (Speed MA - CA ' 0);
2. Appraising phase: the pedestrian approaching the cross-walk decelerates to evalu-
ate the distance and speed of oncoming vehicles (decision making). We decided to
consider that this phase starts with the first value of a long-term deceleration trend
(Speed MA - CA < 0);
3. Crossing phase: the pedestrian decides to cross and speeds up. The crossing phase
starts from the frame following the one with the lowest value of speed before a
long-term acceleration trend (Speed min).
(a) Adult Pedestrians (b) Elderly Pedestrians
Fig. 4. The speed of adult and elderly pedestrians among the crossing phases. The Box and
Whisker plot reports: local maximum value, 75th percentile, mean, median (highlighted in red),
the 25th percentile and the local minimum value.
A two-factors analysis of variance (two-way ANOVA) showed a significant dif-
ference among the speeds of pedestrians while approaching, appraising and crossing
[F(2,144) = 61.944, p < 0.0001], and a significant effect of pedestrian’ age on results
[F(1,144) = 63.751, p < 0.0001] (see Tab. 2). A series of post hoc Tukey test showed
a non significant difference between the speeds of pedestrians while approaching and
crossing, considering both adults and elderlies (p > 0.05). The difference between the
speed of adults and elderlies was significant among all the three crossing phases (p <
0.0001). A one-factor analysis of variance (one-way ANOVA) showed that there was
no a significant effect of gender on the speeds of pedestrians while approaching (p >
0.05), appraising (p > 0.05) and crossing (p > 0.05) (see Tab. 2).
In conclusion, results (see Fig. 4) demonstrated that pedestrian crossing behaviour
is based on a significant deceleration in proximity of the curb (appraising phase) to eval-
uate the distance and speed of oncoming vehicles and safely cross. A further considera-
tion, concerns the need to embed heterogeneous features of pedestrians into computer-
based simulation about crossing phenomenon: results showed also that elderlies walked
in average 22% slower than adults among the three crossing phases, and they deceler-
ated 6% more than adults while appraising. This demonstrated the impact of ageing on
crossing behaviour in terms of motor skills decline.
2.3 Crossing Decision and Accepted Time Gap
Now we use the term accepted time gap to denote the ratio between the pedestrians’s
evaluation of the distance of an approaching vehicle and its average speed (not taking
into account acceleration/deceleration trends) to decide to pass safely avoiding colli-
sion. Results are based on the estimation of the distance and speed of vehicles when
pedestrians decide to cross and speed up (i.e. starting time of crossing phase, from
Table 2. The speeds of adult and elderly pedestrians among the three phases: approaching, ap-
praising, crossing.
Phases Speed of adult pedestrians Speed of elderly pedestrians
Approaching phase 1.28 m/s ± 0.18 sd 1.03 m/s ± 0.18 sd
Appraising phase 0.94 m/s ± 0.21 sd 0.69 m/s ± 0.23 sd
Crossing phase 1.35 m/s ± 0.18 sd 1.09 m/s ± 0.17 sd
the frame after the one with the lowest value of speed before a long-term acceleration
trend).
Results take into account the impact of several factors potentially influencing pedes-
trians’ crossing decision. First of all, we compared results considering the lane occupied
by the oncoming vehicle (oncoming from near lane or far lane). Then, focused on single
and multiple pedestrian/vehicle interactions (one pedestrian interacting with only one
vehicle or two vehicles oncoming from the near and the far lanes). Finally, we tested
the impact of pedestrians’ age on results.
A series of independent samples t-tests showed that crossing pedestrians did not
discriminate between the distances and speeds of vehicles oncoming from the near (ac-
cepted time gap = 4.10 s ± 2.43 sd) and the far lanes (accepted time gap = 4.39 s ±
1.92 sd). Data analysis showed also that there was not a significant difference (p >
0.05) between the accepted time gaps in a situation comprising one vehicle approach-
ing from the near lane (4.12 s ± 2.45 sd) or two vehicles respectively oncoming from
the near and far lane (4.20 s ± 2.24 sd). A series of two-way ANOVA showed the non
significant impact of the factors age (p > 0.05) and gender (p > 0.05) on results. The
accepted time gaps of adult (3.98 s ± 2.55 sd) and elderly pedestrians (4.49 s ± 1.77
sd) did not differ significantly in any of the tested crossing typologies.
In conclusion, data analysis showed the average time gap accepted by pedestri-
ans corresponded to 4.20 s ± 2.24 sd (average distance of vehicle = 16.83 ± 8.71 sd;
average speed of vehicles = 15.93 ± 7.02 km/h). However, further data analysis on
age-driven crossing decision have been performed, showing a significant difference be-
tween the time duration of the appraising phase among elderly (4.12 s ± 2.54 sd) and
adult pedestrians (2.79 s ± 1.47 sd), t(48) = 2.40658, p = 0.012. Although pedestrians
have the right of way on zebra-striped, elderly were found to be more cautious than
adults: 57% of them gave way to at least one approaching vehicle, compared to 30% of
adults. This result suggested that, when elderly pedestrians decided to cross, they were
able to regulate their behaviour by adapting the accepted time gap to their own crossing
capacities (lower walking speed).
3 Model Description
The model presented here extends the work proposed in [4]. In this paper we will pro-
vide a brief description of its core components, supporting the evaluation of results
presented in the next section. For a complete and thorough discussion, we refer to [7].
(a)
(b)
Fig. 5. (a) Schematic representation of the environments and agents. (b) Example of a floor field
spread in the simulated scenario of the crossing.
The model supports the simulation of non-signalized pedestrian crossing by means
of heterogeneous agents, namely pedestrians and vehicles. The two types are hosted in
different environments, which grant an effective reproduction of the two different but
coupled dynamics considered in the simulation.
As shown in Figure 5(a), the model is based on the integration of two indepen-
dent models for the simulation of vehicles, moving in continuous lanes, and pedestri-
ans, moving in a 2-dimensional discrete environment. The two environments are su-
perimposed, and car-agents perceive pedestrian-agents while they are crossing or in the
nearby of the curb (grey cells in Fig. 5(a)) and vice-versa. The interactions between
them are described in Figure 5(b). Pedestrian-agents consider the speed and distance
of cars to avoid collisions, giving way to non-compliant vehicles. The compliance of
car-agents is mainly influenced by the necessary braking distance. On the other hand,
according to a fixed probability that will be set on the collected data on compliance, car-
agents can deliberately avoid to stop even if the braking distance is sufficient, requiring
pedestrian-agents to yield.
3.1 The Behaviour of Car and Pedestrian-Agents
The motion of cars is based on the car-following model by Gipps [8], in which the
speed of each vehicle is updated considering, firstly, internal parameters of the agent:
(i) maximum acceleration for each time-step of the simulation; (ii) maximum breaking
capabilities; (iii) speed limit of the road. The presence of a vehicle ahead of the updating
one affects its next speed according to a safe speed vsafe . vsafe is calculated based on the
distance between the two vehicles and their breaking capabilities. In this way, possible
collisions between cars are simply avoided in this model since they are not subject of
investigation.
If the car-agent perceives a pedestrian, which is already crossing, then vsafe is calcu-
lated in order to let the car stop in correspondence of the zebra cross. Given the rules of
the interaction also on the pedestrian-agent side, in this case the car-agent will always
be able to stop before the crossing. On the other hand, if the pedestrian is approaching
or waiting to cross the street, the car-agent will yield to the pedestrian if both there is
enough space, according to its current speed, and the car-agent chooses to be compliant.
The behaviour pedestrian-agents is modelled on the basis of the classic floor field
model [3]. When activated, pedestrian agents can move in the 8 cells surrounding their
position in the grid (i.e. Moore neighbourhood). By considering the assumed side of
cells and the time-step duration of the car model, the instantaneous speed of the agent
is computable as 0.4/0.1 = 4.0 m/s, which is rather high for pedestrian walking. A
different time-step duration of 0.3s is then assumed to simulate the pedestrian motion,
in order to get a maximum speed of pedestrians of about 1.3 m/s.
To simulate the three phases of crossing behaviour, as well as the observed dif-
ferences in the speeds of adult and elderly pedestrians (see Sec. 2), the activation of
pedestrian-agents for movement at the beginning of the time-step is managed in a prob-
abilistic fashion, similar to [2]. In order to trigger a specific behaviour for the appraising
phase, we exploited the intrinsic nature of the floor field generated by the curb close to
the zebra crossing: since it indicates the distance from the cells generating it, its low
value will trigger a specific set of actions to decide about crossing timing. In particular,
when the pedestrian agent is nearby the curb, it will evaluate the safety gap from on-
coming vehicles, which describes the time needed by the incoming car-agent ci to reach
the pedestrian-agent position, considering the current speed vci .
4 Discussion about Simulation Results
The present paper has introduced a model for the simulation of pedestrian-vehicles in-
teractions at non-signalized road crossings. The model is based on already existing ap-
proaches extended to grant the different actors the possibility to interact and coordinate
their behaviours. The model has been defined according to the results of an observa-
tion, which was focused on studying the crossing behaviour of elderly pedestrians. The
results of the observation have been employed to calibrate and perform an initial vali-
dation of the model in a reference scenario.
Simulation results are based on the arrival rate empirically observed for both pedes-
trian and vehicle traffic flows: 5.52 pedestrians per min; 16.53 vehicles/km. The speed
limit was set to 35 km/h, based on the empirically observed velocities: despite the speed
limit of 50 km/h, drivers were not able to approach this velocity due to the presence of
additional intersections roughly 150 m before and after the modelled crossing.
Table 3. Assignment of the calibration parameters regarding the operational level model.
Pedestrian features Value
Adult walking speed (mean) 1.30 m/s
Adult walking speed (variance) 0.20 m/s
Elderly walking speed (mean) 1.05 m/s
Elderly walking speed (variance) 0.20 m/s
Acceleration 0.30 m/s2
Deceleration 0.50 m/s2
Crossing behaviour Value
Appraising distance 3.0 m
Accepted gap adult (mean) 4.0 s
Accepted gap adult (variance) 2.5 s
Accepted gap elderly (mean) 4.5 s
Accepted gap elderly (variance) 1.8 s
Minimum accepted gap 1.0 s
The model improves the results of previous works in this area, with reference to the
introduction of: (i) the non-compliance of drivers to pedestrians’ right of way at zebra
crossing; (ii) the observed appraising phase of pedestrians to evaluate the safety gap
from oncoming vehicles to safely cross; (iii) the heterogeneous speeds of pedestrian-
agents comparing adults and elderlies. With these features we introduced the hetero-
geneity among adult and elderly pedestrians, as described by the parameters shown in
Table 3.
The compliance of drivers has been modelled in a static way: car-agents are con-
figured as either compliant or not at their generation and they will keep this behaviour
for all the simulation run. The probability of generating a compliant car-agent is then
assigned to 0.5, in accordance to the observation. Moreover, since the results of the ob-
servation showed that there was no significant difference between the average time gap
of adult and elderly pedestrians, the accepted time gap for all pedestrian agents in the
simulation has been normally distributed with µ = 4s and σ = 2s.
The results achieved through the simulation campaign are in tune with the empirical
evidences of the presented observation, highlighting the validity of the model. Simula-
tions can be already used to test the effects of different traffic conditions on the perfor-
mance of the road infrastructure (e.g., travel time, LOS). In particular, the simulation
results presented in [6] are based on an experimental evaluation of the risk of the cross-
ing by considering: (i) different proportions between adult / elderly pedestrians; (ii)
different traffic conditions; (iii) the possibility of distraction for both crossing people
and drivers. On the other hand, the model currently allows few modifications to the
tested environment, which now defines the surrounding –of configurable width– of a
pedestrian intersection in a two-lanes road. It is already possible to simulate a longer
road with more crossings by linking the borders of multiple environments with respect
to this definition, but what is now lacking in the model and that will be part of future
works is a component to manage arbitrary road intersections and more complex ge-
(a) (b)
Fig. 6. (a) Schematic representation of the observed cross-walk and possible alternative layout
which could guarantee to pedestrians enough room for evaluating distance and speed of oncoming
vehicles and take decision to cross in a more safe manner.
ometries of the setting. This would allow to enlarge the analysis to a larger area (e.g.,
a neighbourhood of a city), verifying possible propagations of jams due to mixed car-
pedestrian traffic conditions, but also to test alternative spatial layout to avoid pedestrian
jaywalking (see Fig. 6).
Acknowledgement The authors thank Claudio Feliciani for his valuable contribution.
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