Article citation information:
Gill, A.,
Smoczyński, P., Ławniczak, D. Measuring the
variability of the pedestrian crossing function in the socio-technical system
of urban road transport. Scientific
Journal of Silesian University of Technology. Series Transport. 2022, 117, 57-68. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.117.4.
Adrian GILL[1], Piotr SMOCZYŃSKI[2], Damian ŁAWNICZAK[3]
MEASURING THE VARIABILITY OF THE PEDESTRIAN CROSSING FUNCTION IN THE
SOCIO-TECHNICAL SYSTEM OF URBAN ROAD TRANSPORT
Summary. In some areas
of transportation systems, reduction of risk using typical safety engineering
tools can be difficult due to the relatively small number of events that can be
analysed to draw conclusions for the future. One way out of this situation is
to analyse systems in their normal operation when no adverse event occurs. It
can be done, inter alia, with the Functional Resonance Analysis Method. An
important research problem in this context is how to describe the variability
of system functions. In this article, we propose an original method, based on
the number of hazard sources present in a given analysis domain and apply it to
a real pedestrian crossing. The obtained results indicate that the quantitative
coincidence measures proposed by us are a convenient way to capture
‘functional vibrations’ in real socio-technical systems. This
allows the prediction of undesired states of such systems based on their normal
operation.
Keywords: pedestrian
crossing, hazard sources, public urban transport, Functional Resonance Analysis
Method
1. INTRODUCTION
Intuitively,
the traditional three-colour traffic lights remain the best form of crossing
protection that practically eliminates the possibility of activating hazards. A
similar phenomenon can be seen concerning railway level crossings equipped with
barriers [11], although in both cases –
despite advanced safety systems – there are still many hazard sources
left. One of the most important of these sources was indicated by Krukowicz et al. [10].
Road traffic observations conducted by them in a large city in Poland made it
possible to formulate an observation indicating that despite the improvement of
traffic organisation and modernisation of traffic lights at intersections, a
large number of road accidents and collisions are caused by inappropriate,
often illegal behaviour of road users. A detailed literature
review on the assessment of pedestrian-vehicle interaction on urban roads has
been presented by Thakur and Biswas [19].
Problems in
raising an already high level of safety are noticeable in many areas of human
activity, including in rail transport [2, 14]. This is an example of a
controller paradox [21],
quoted in [4]), whose task is to minimise
system variability; however, this variability is also the only way to measure
the effectiveness of this controller. In such situations, it is now proposed to
abandon the use of traditional methods of safety engineering (FTA, FMEA) for
the benefit of new ones, allowing a comprehensive description of the system
during its operation – both when everything goes fine as well as in the
event of hazard activation.
Examples of
new methods include the Systems-Theoretic Accident Model and Processes (STAMP),
proposed by Leveson [12] and used among others for
modelling maritime [8] or railway transport systems [20], where, however, its theoretical
character was pointed out. STAMP is also used as an enhancement of the Event
Analysis of Systemic Teamwork (EAST) method [16], which was used independently,
among others, in studying the behaviour of road traffic participants during
crossing intersections [15].
Another
popular method of the ‘new approach’ (often referred to as
‘Safety-II’) is the Functional Resonance Analysis Method (FRAM)
proposed by Hollnagel [5], and still being developed [4]. The use of the FRAM method is
shown in the example of air [18] or maritime transport [13]. However, there are no
applications in urban transport [17]. Furthermore, the existing
publications focus primarily on modelling using characteristic hexagons rather
than on the attempts to define how ‘functional vibrations’ manifest
themselves in real socio-technical systems.
This article
aims to propose an original understanding of functional vibrations for the
pedestrian crossing function, as well as to determine their waveform based on
our observation of a selected real pedestrian crossing in Poznan (Poland).
Section 2 presents the necessary theoretical information on functional
vibrations and functional resonance, as well as the applied research
methodology for determining the pedestrian crossing function vibrations. While
section 3 discusses the results of the observation study and shows how to apply
these results for determining functional vibrations. Finally, section 4 contains
conclusions and directions for further research.
2.
MATERIALS AND METHODS
2.1.
Functional vibrations
The concept of
functional vibration is a key element of the Functional Resonance Analysis
Method (FRAM) used for modelling socio-technical systems [5]. An important and sometimes
overlooked aspect of the theory behind FRAM is the mere phenomenon of
functional resonance, explaining the mechanism of activating hazards. According
to this theory, adverse events occur not as a result of breaking (intentional
or accidental) applicable procedures and specifications of the system operation
but as a result of the unfavourable superposition of the functions performed in
it. This is well illustrated by the diagram shown in Figure 1.
Fig. 1. Mechanism
of hazard activation according to
the functional resonance theory [17], based on
[6]
In the theory
of functional resonance (Figure 1), it is assumed that the result of the
system's operation is the composition (superposition) of its functions. The
superposition is variable over time but usually remains below a certain limit,
which exceeding results in the activation of a hazard (an adverse event, an
accident). Such a view on the work of socio-technical systems allows them to be
improved also when there are no adverse events. Thus, one should examine the
various ways of correct system operation – the variability, as Hollnagel
calls it – and undertake actions aimed at limiting this variability.
In this study,
we suggest that variability is described using the hazard sources that appear
during the implementation of a given function. A hazard source (also called 'a
risk source') is an element, which alone or in combination with other elements,
has the potential to give rise to (typically) undesirable consequences [1, 7]. A
broader discussion on the motivation to choose such a definition was presented
in [3]. The most important is that two
or more hazard sources may not be harmful; however, when combined they interact
to become dangerous [9]. This is graphically depicted in
Figure 2.
We, therefore,
propose that variability
where V
is the value of variability determined in the observation time interval
Fig. 2. Schematic representation of
the relation between the hazard source (HS)
and the hazard (H), as considered in this study
Describing
variability using Equation (1) allows differentiating between two levels of
superposition. First, there can be many hazard sources occurring during the
performing of one function of a socio-technical system, and their number is
variable over time. The variability of a particular function will therefore be
given by the superposition of the number of occurrences of individual hazard
sources. Second, in the context of performing all functions by a
socio-technical system, the superposition concerns variations coming from all
its functions – and this superposition, following the FRAM assumptions,
determines the possibility of having an adverse event.
2.2. Selection
of case study crossing
To carry out
the variation measurement, we have selected a pedestrian crossing equipped with
traffic lights located near two significant pedestrian traffic generators
(Figure 3). The first of them is the campus of the Poznan University of
Technology, used by approx. 20,000 students. In the immediate vicinity of the
crossing, both the most important didactic buildings and dormitories are
located. The second generator is Posnania, one of the largest shopping centres
in Poland. In addition, near the pedestrian crossing, there is an intersection
of two tram routes. This makes the tram stop located at the crossing to be
often used by passengers who make transfers.
The crossing
leads through two roadways and two tram tracks between them. The street is a
fragment of the second communication frame, that is, the bypass of the city
centre. The western roadway has two lanes, the eastern – four lanes,
including one for turning into the shopping centre. The maximum valid speed for
all roadways is 50 km/h. Three sets of traffic lights are installed at all
parts of the crossing: two on the roadway crossing, and one on the tram track
crossing. The condition of the roadway surface and tracks were assessed as
good, not interfering in any way with the movement of vehicles. Visibility is
very good, as there are no buildings or advertisements near the crossing that
could limit it. Within the crossing, there is street and tram stop lighting
that is sufficient to light the roadways as well.
To facilitate
the collection of observational data at the pedestrian crossing, it was divided
into two zones (Figure 4). Zone I includes the crossing through the tram track
and the adjacent tram stop Kórnicka. While Zone II covers the rest of
the pedestrian crossing, that is, the roadways in both directions.
II I II
Fig.
3. Location of the case study crossing and indication of its zones
Due to the
lack of possibility to observe the entire tram stop, Zone I (Figure 3) only
includes a part of the stop adjacent to the crossing. Due to the fence mounted
along the tram stop between the tracks, people wanting to cross the tracks most
probably used the monitored pedestrian crossing for this purpose.
2.3.
Measurement procedure
Before
commencing the main observation study, a pilot study was carried out to develop
a catalogue of hazard sources appearing on the selected pedestrian crossing.
The catalogue developed in this way was the basis for the preparation of the
first version of the measurement card, supplemented during the main study with
further hazard sources identified in its course. On the measurement card, the
following were recorded:
·
Date and time of measurement.
·
Atmospheric conditions during measurement (for
intensive snow/rain, cloudy, sunny).
·
Traffic intensity of trams, cars and pedestrians
(Table 1).
·
The fraction of older people at the crossing (in
percents).
The card also
records information about the pedestrian's attitudes to identify hazard sources
(for example, looking around before entering the crossing); however, due to the
subjectivism of the assessment, it was not included in the subsequent
development of the research results.
Tab. 1
Taxonomy
of traffic intensity determined during this study
|
Key word |
Number
of trams [per
15 min] |
Number
of cars [per
15 min] |
Number
of pedestrians [per
15 min] |
|
Small |
<3 |
<400 |
<100 |
|
Medium |
3-7 |
400-700 |
100-400 |
|
Big |
>7 |
>700 |
>400 |
The basic type
of traffic violation, which is also a hazard source, is the use of crossing
when it is not allowed to do so. To better analyse the behaviour of pedestrians
and cyclists, the observed events were assigned to the following categories of
hazard sources:
·
Red light: traffic jam all lanes. These are events
when a pedestrian moves from the area of the tram stop between cars immobilised
in all lanes.
·
Red light: traffic jam one lane. In this type of
event, cars were immobilised only on a lane adjacent to the area of the tram
stop, and the remaining lanes were free.
·
Red light: entering in front of a tram. In case of
some events of this type, pedestrians took advantage of the fact that the tram
was staying at the stop with its door open (passenger exchange was ongoing).
·
Red light: entering in front of a car.
·
Red light: other cases.
·
Flashing green: pedestrian crossing.
·
Red light: bike crossing.
Each event was
qualified only to one of the above categories of hazard sources.
Some of the
observed pedestrians did not cross the roadway/track at the red light, but they
waited for the green light close enough to the edge that it was considered to
be a hazard source. There are two sources of this kind distinguished here: too
close to the roadway, and too close to the track. During the measurements, all
cases of using the wrong part of the crossing or going through roadway/tracks
outside the designated crossing were recorded. The following hazard sources
were distinguished in this regard: pedestrians on the bike side, bikes on the
pedestrian side, pedestrians outside the crossing, and slow motion on purpose.
Situations in which pedestrians passed through the part intended for cyclists
and completely left the designated crossing were not counted as the hazard
source ‘Pedestrians on the bike side’ but only as 'Pedestrians
outside the crossing'. In addition to events that are direct violations of the
current rules for the use of crossings, events that limit the situational
awareness of people on the crossing were also registered and are treated here
as hazard sources: using a mobile phone, using headphones, running through the
crossing. It should be noted that the behaviour of one person could generate
several hazard sources, for example, in a situation when a pedestrian with
headphones is running through the crossing.
3.
RESULTS
3.1.
Empirical results
This research
was carried out in two periods: autumn-winter and spring. Data registration
took place in 6.5-hour measuring sessions, carried out between 10:00 and 16:30
on selected days of the week. The hours included the evening communication
peak. Measuring sessions were divided into fifteen-minute time intervals. The
research was planned in such a way that the data registration took place at
least once in each observation time interval.
A summary of
the results of this study carried out in the autumn-winter and spring periods
is shown in Table 2. In the case of hazard sources for which it could have been
significant, the zone of occurrence of the hazard source was also registered
(following Figure 3). This has an impact on the number of occurrences of hazard
sources because the behaviour of one pedestrian crossing in the wrong way was
recorded three times: once in Zone I (crossing the track) and twice in Zone II
(crossing the eastern and western roadway).
Sources of the
hazard that generates the largest losses – that is, ‘Possibility of
incurring losses/damage because of a pedestrian being hit by a car or
tram’ – is the presence of a pedestrian at the crossing in a
situation where the red light is on. Based on the observation results (Table
2), it can be stated that this is a relatively frequent situation. For example,
in the spring period, 653 cases of the occurrence of this hazard source were
recorded on the entire crossing followed by 402 more situations of entry onto
the roadway or the track at a flashing green light. However, it was also
possible to observe various pedestrian motivations for such behaviour (Figure
4).
Tab.
2
Observed number of
hazard source occurrences in the autumn-winter
and spring measurement sessions
|
No. |
Hazard source |
Zone |
Number of occurrences |
|
|
Autumn-winter |
Spring |
|||
|
1 |
Red light: traffic jam all lanes |
II |
7 |
27 |
|
2 |
Red light: traffic jam one lane |
II |
21 |
27 |
|
3 |
Red light: entering in front of a tram |
I |
60 |
46 |
|
4 |
Red light: entering in front of a car |
II |
24 |
35 |
|
5 |
Red
light: other cases |
I |
276 |
239 |
|
II |
230 |
220 |
||
|
6 |
Flashing
green: pedestrian crossing |
I |
211 |
199 |
|
II |
200 |
203 |
||
|
7 |
Red
light: bike crossing |
I / II |
16 |
59 |
|
8 |
Too close to the roadway |
II |
79 |
80 |
|
9 |
Too close to the track |
I |
132 |
136 |
|
10 |
Pedestrians on the bike side |
I |
125 |
137 |
|
II |
183 |
188 |
||
|
11 |
Bikes on the pedestrian side |
I |
111 |
147 |
|
II |
81 |
110 |
||
|
12 |
Pedestrians
outside the crossing |
II |
554 |
593 |
|
13 |
Using
mobile phone |
I |
100 |
104 |
|
II |
138 |
135 |
||
|
14 |
Using
headphones |
I |
111 |
122 |
|
II |
146 |
146 |
||
|
15 |
Running
through crossing |
I |
75 |
81 |
|
II |
101 |
111 |
||
|
18 |
Slow
motion on purpose |
I |
99 |
88 |
|
II |
120 |
113 |
||
The data
presented in Figure 4 indicate a relatively small proportion of situations in
which pedestrians would enter directly before an oncoming vehicle – a
tram or a car. The share of this type of hazard source in the group of all
sources related to the crossing on a red light is within 5-10%, depending on
the season and part of the analysed crossing. The percentage share is higher in
the case of crossing the tram tracks; however, it should be noted that entering
in front of a tram also means the situation in which the pedestrian passes in
front of the tram in which the exchange of passengers is ongoing. If there are
no other sources, such as the fall of a pedestrian who lying on the ground is
not in the driver's view, the activation of the hazard is relatively unlikely.
Fig. 4. Share
of different types of red-light crossing, distinguished during this study
During the
tests, it was also noticed that pedestrians were confused over the light
signals and intended to pass through the track and across the roadways, thus
starting to cross the road when the green light in the signalling device for
tram tracks was lit. There were also situations in which pedestrians entered
the crossing between cars standing in a traffic jam, which – just like in
the case of trams with open doors – can lead to losses only when other,
rarely occurring hazard sources are present at the same time.
3.2. Variability function
Number of
occurrences of the
From the standpoint
of the superposition of occurrences of individual hazard sources, the most
important is the maximum value that can be taken by a random variable
In the theory
of functional resonance, it is assumed that the result of the system's
operation is the composition (superposition) of its functions. The presented
examples allows determining the form of the function f (Eq. (1)) given by the following formula:
Given the
assumptions made previously (Eq. (3)) and dependencies (1) and (4), the
variability over time
The method of
determining the value of function variation
10:45
– 11:00 Observation time intervals ∆t(j-1,j) ... ... Hazard sources (j = 4) ... HS1 ... HS2 ... HS11 (i = 1) (i = 2) (i =11) Number of hazard sources present on the observation day: ... 4 ... 6 ... 0 Day
1 (k = 1) ... 13 ... 4 ... 1 Day
2 (k = 2) ... 4 ... 2 ... 0 Day
3 (k = 3) ... 13 ... 6 ... 1 Number of HS in the interval qHSi
= ... ... Value of the function variability
V(tj) = 13
+ 6 + … + 1 = 58
Performed
empirical studies describe the state of the pedestrian crossing during the day
(from 10:00 to 16:30), that is, the number of hazard sources occurring in
individual observation time intervals (according to Equation (1)). To determine
the waveform of variability of the pedestrian crossing function, it is
necessary to assign the identified sources to a specific zone, according to the
information contained in Table 2, column 3.
The recorded
number of individual hazard sources allows to draw a waveform of variability of
the crossing function through the considered part of the crossing according to
the dependence (4). Figure 6 shows the waveform of variability as the sum of
all occurrence numbers of hazard sources in each observation time interval.
Fig. 6.
Superposition of hazard source quantities at the tram part of the crossing in
spring
4. CONCLUSIONS
The concept of
functional resonance is so mature that now it is worth taking action at the
stage of its application. There is a lack of such activities in urban rail
transport, and the existing ones (in other domains) do not give a precise
answer on how to understand ‘functional vibrations’ in real
socio-technical systems. In our opinion, the problem consists in the lack of adequate
models and quantitative measures describing functional resonance. For this
reason, we proposed a proper understanding of functional vibrations for the
pedestrian crossing function. We also showed how to determine the variability
values of this function based on our observation study of the selected real
pedestrian crossing.
We, therefore,
propose that variability of the function performed by the socio-technical
system in time would depend on the number of occurrences of hazard sources
identified in the analysis domain in subsequent observation time intervals. As
part of the work on how to describe the variability of the system's functions,
we also considered other possibilities for its implementation. First, we
considered the fact that adverse events are usually caused by the coincidence
of hazard sources and not the activity of a single source. In such a case, an
interesting group of models and measures of variability of the system's
functions may be the measures of diversity.
Implementation
of the description of the system's functions variability using the presented
models and measures is a relatively simple task. However, the interpretation of
the mathematical dependences used for this may be troublesome. With this in
mind, we have prepared appropriate diagrams showing how to determine the value
of variability of the socio-technical system function (pedestrian crossing) in
practical applications.
To develop the
models proposed by us and measure the variability of a system function, we
planned and performed appropriate observations. On this basis, we have shown
that the quantitative coincidence measures proposed by us are a convenient way
to capture ‘functional vibrations’ in real socio-technical systems.
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Scientific Journal of Silesian University of Technology. Series
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[1] Poznan University of Technology, Pl. Skłodowskiej-Curie 5, 60-695 Poznań, Poland. Email: adrian.gill@put.poznan.pl. ORCID: https://orcid.org/0000-0002-2655-4584
[2] Poznan University of Technology, Pl. Skłodowskiej-Curie 5, 60-695 Poznań, Poland. Email: piotr.smoczynski@put.poznan.pl. ORCID: https://orcid.org/0000-0003-3824-3764
[3] Poznan University of Technology,
Pl. Skłodowskiej-Curie 5, 60-695 Poznań, Poland. Email: damian.lawniczak@student.put.poznan.pl.
ORCID: https://orcid.org/0000-0002-5686-9034