Article citation information:
Barchański,
A., Żochowska, R. Practical aspects of measuring critical gaps and
follow-up times at median uncontrolled T-intersections. Scientific Journal of Silesian University of Technology. Series
Transport. 2021, 113, 17-28.
ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2021.113.2.
Adrian BARCHAŃSKI[1],
Renata ŻOCHOWSKA[2]
PRACTICAL ASPECTS OF MEASURING CRITICAL GAPS AND FOLLOW-UP TIMES AT
MEDIAN UNCONTROLLED
T-INTERSECTIONS
Summary. Estimation of
critical gaps and follow-up times between vehicles at uncontrolled
intersections is an essential step in estimating the capacity of these objects
and assessment of traffic conditions. Therefore, measurements of these
parameters should be properly prepared and implemented. This paper presents
issues related to the performance of field tests at median uncontrolled
T-intersection. Measurements included both critical gaps and follow-up times.
Based on the collected material, the authors identified problems occurring
during traffic observation. Analyzed intersections were located both within and
outside built-up areas. Furthermore, this article discusses the influence of
selected factors on the accuracy of estimating the critical gaps and follow-up
times and formulates the principles of conducting traffic measurements at
selected types of intersections.
Keywords: uncontrolled
intersection, measurement of traffic characteristics, gap acceptance theory,
critical gap, follow-up time
1.
INTRODUCTION
Uncontrolled
intersections are common road infrastructure objects, which depending on their
location in the spatial structure of the area handle a very diverse traffic
flow. For decades, the behavior of traffic participants on such objects has
been the subject of empirical and theoretical research. The results obtained
allow increasing the accuracy of models describing the traffic flows. Nowadays,
analytical and simulation methods are used in this field [1-6].
One
of the most important purposes of the survey of traffic at uncontrolled
intersections and observation of driver behavior is to determine the capacity
of individual movements and assess traffic conditions [1, 7, 8]. The results of
the analyses form the basis for assessing whether a given infrastructure
solution meets the needs and expectations of users and whether it is sufficient
to handle the observed traffic. Based on this, decisions are made regarding the
need to upgrade or reconstruct individual intersections. The assessment of the
capacity of point and linear infrastructure elements also forms the basis for
spatial planning and management at the strategic and tactical level for
transport and road network. This confirms the important role of precise
estimation of parameters of individual road infrastructure elements in the
assessment of parameters of the entire road network of a city, area, or region.
Therefore, the results of the intersection field tests provide the basis for
the building of the model, its calibration, and constraint formulation.
Besides, they allow for the validation of the developed models and for allowing
their use in the analysis and description of the phenomena occurring in road
traffic [1, 9]. Thus, it is important to pay attention to the problems that may
occur when conducting field surveys and to define the rules of conduct when
performing traffic parameter measurements such that the error rate is minimized
much as possible.
In
practice, traffic measurement is a complex research process requiring
assumptions, reliable preparation, and conditions that the observed situations
must meet to be representative of the population due to the phenomenon under analysis
[1, 10, 11]. It is very difficult to meet the requirements of the methods used,
considering the random changes in traffic conditions and the individual
behavior of traffic participants [1, 9, 12-14]. In the world literature, much
attention has been devoted to the analysis of the results of these
measurements, the comparison of the efficiency and accuracy of the methods
used, and the identification and evaluation of the factors affecting the values
of the critical gaps and follow-up times [9, 11, 15-17]. However, there is a
lack of research on how to conduct measurements and the problems associated
with it, which are largely due to the specificity of the infrastructure element
under study.
Uncontrolled
median T-intersections with two two-lane one-way major road carriageways are
relatively rare in the road network. They are characterized by specific
geometric parameters and traffic organization. Therefore, the critical gap and
follow-up time values for these facilities may differ from the values set for the
typical uncontrolled intersections. In this situation, there is a need to
conduct a separate study of traffic participant behavior by considering the
specific characteristics of the intersection.
The
main purpose of this paper is to identify problems occurring during the
planning and implementation of tests conducted at uncontrolled median
T-intersection to estimate the value of critical gap and follow-up time.
This
article presents the results of research conducted on selected real objects.
The problem of estimating critical gaps and follow-up times at uncontrolled
intersections was discussed, with particular focus on the specificity of median
uncontrolled T-intersection. The process of conducting observations on selected
real objects was described. Finally, the most important recommendations for
researching for critical gaps and follow-up times were identified and
directions for further research were indicated.
2. CONDITIONS
FOR CONDUCTING RESEARCH OF CRITICAL GAPS AND FOLLOW-UP TIMES AT UNCONTROLLED INTERSECTIONS
Models
to estimate capacity and assessment of traffic conditions are mainly based on
the gap acceptance theory. It singles out the most important parameters: the
critical gaps and follow-up times. Their values depend on the type of
intersection and allow the model to be calibrated to local conditions. They are
estimated using statistical analysis in a representative sample of recorded
traffic situations [16-19].
Critical
gaps and follow-up times generally characterize the average behavior in the
population of drivers of a given movement. The critical gap (tg)
corresponds to the minimum value of the time gap between the passage of two
consecutive vehicles of the major stream accepted by at least half of the
tested sample of drivers [1, 9, 14, 18, 20]. The follow-up time (tf),
on the other hand, is determined as the average time interval between the
crossing of the stop line by two consecutive minor stream vehicles in the
subordinate movement during the gap in the major stream. An extensive description
of the concepts used and the assumptions of the model used can be found in [14,
15].
To
guarantee the correctness of critical gap studies and standardize the results
obtained, the observed traffic must meet the assumptions adopted in the
construction of the models used to estimate the critical gaps and follow-up
times and correspond to the conditions and limitations of the methods for
capacity estimation and assessment of traffic conditions [17-19, 21]. They
define the ideal conditions for vehicle traffic at the intersection at the time
of the study, including [1, 9, 12-14]:
·
homogeneous traffic consisting only of passenger
cars in all streams,
·
the presence of only two conflicting movements:
the first rank stream and the studied subordinate movement,
·
free-flowing traffic with a steady first-order
stream passing the conflict zone straight through without impedance, delays, or
slowdown,
·
a permanent queue of vehicles of a given
subordinate movement waiting to continue their trip,
·
independent, random oncoming at the approach of
vehicles of the major stream without platoons,
·
the absence of other factors not mentioned above
such as pedestrian or bicycle traffic, impedance, bus stops, and the impact of
upstream signalized intersections.
A commonly used method of estimating the values of
critical gap and follow-up time is the observation of real traffic on objects
selected for the analysis, considering the time between the passage of
successive vehicles or by measuring the distance between individual, successive
vehicles. Many diverse models and ways of description have been developed in
this area [9, 10, 16, 19, 20, 22, 23].
Researching
real traffic conditions with the need to meet the assumptions of the method
used, involves the need to solve many practical problems resulting from the
variation of traffic conditions between the requirements of the model and
reality [17-19, 21]. It is most important to identify them early and take
corrective action before the actual analysis begins. On real objects, pilot
studies should be conducted before starting the analysis to be acquainted with
the drivers' behavior and to choose the most appropriate observation point
location. The field constraints [1, 12-14] should be considered.
It
is necessary to analyze the situation in the whole area of the intersection
during a single gap in the major stream. This approach is necessary to be able
to correctly interpret drivers' behavior and assess whether the observed
situation meets the requirements of [9, 16, 17, 20]. This creates some
difficulties in the process of automation of measurements and data analysis and
the need to playback the recorded footage at least twice.
The
problem of selecting an observation point equipped with a camera has received
little attention in the literature related to the estimation of critical gaps
and follow-up times [10]. Although, it is fundamental to ensure an accurate
measurement that is consistent with the actual duration of accepted or rejected
gaps as observed by drivers.
The
impact of the place of observation on the recording of the starting/ending time
of the gap is shown in Figure 1.
Fig.
1. A way of interpreting the road and traffic situation by two external
observers
[Authors’
research]
Gap
durations recorded from two different points will take different values.
Importantly, the magnitude of the gap duration estimation error depends on the
order of vehicle movement (labeled 1 and 2) in each lane of the major stream.
Equally
important is the choice of the observation point due to the temporarily reduced
visibility of the traffic situation at the intersection by vehicles moving on
the far lane, closest to the location of the recorder. It is advisable to seek
locations in the immediate area that minimize this effect. In addition, the
adverse effect of limiting visibility can be partially mitigated by delineating
certain virtual cross-sections perpendicular to the axis of the lanes, the
crossing of which by vehicles will determine the beginning or end of the gap.
To keep the adoption of these cross-sections unambiguous and constant, they
should be based on fixed elements in the intersection area. Given the need to
ensure continuous visibility of the characteristic points when the traffic
situation and the momentary position of vehicles changes, it is important to
have them located as close as possible to the collision points.
For
accurate results, it is advantageous to conduct observations from high
altitudes, where the object becomes approximately two-dimensional and a single
camera is sufficient to record the entire face of the intersection and all
movements. It is worth mentioning that it would be good practice to locate the
observation point in a manner which in addition to monitoring the most
important elements from the point of view of the analysis purpose, fragments of
road sections of the subordinate and major approach are also visible so that it
is possible to observe the queue of waiting vehicles and oncoming traffic as
well.
Example
combinations of the passage of subsequent vehicles of the first rank stream
influencing the acceptance of the available gap in relation CL1 (Class 1) are
shown in Figure 2, presenting the relevant part of the intersection for a
given relation.
a) b)
Fig.
2. Influence of the major stream's vehicle passing sequence on the decisions
made by drivers of vehicles waiting at the subordinate approach:
a)
accepted gap; (b) rejected gap; G – gap duration
[Authors’
research]
The
hatched area marked on the diagrams (Figure 2), denotes the conflicting portion
of their traffic corridors on the intersection face shared by the superior and
subordinate streams. Due to the different size of the conflict zone required by
the vehicle of the subordinate relation in both situations, the crossing time
will be different, that is, shorter in situation a than in situation b.
Although the measured duration of G-gaps according to the definition will be
comparable in both situations, the probability of their use by drivers will differ.
3.
CHARACTERISTICS OF MEDIAN UNCONTROLLED T-INTERSECTIONS
The
subject of the analysis was the time intervals between vehicles at the median
uncontrolled T-intersections and two two-lane one-way major roadways. In
manuals, these intersections are treated similarly to 1x2 road crossings or
four-way intersections with a wide median strip, and capacity analyses are
conducted using commonly used methods such as MOP SBS, HBS, or HCM [12-14].
However, the specific characteristics of these facilities require a different
approach to the planning and implementation of field traffic measurements [1].
The dissimilarity of these types of objects is confirmed by the results of the
analyses of the hierarchy of movement, the influence of impedance, and how the different
movements are performed [1, 12-14, 16, 17, 19]. Therefore, the values of the
critical gaps and follow-up times contained in the indicated instructions do
not apply to this type of intersection.
Fig.
3. General diagram of a median uncontrolled T-intersection with
the indication of traffic flows
[Authors’
research]
Both
the geometric layout of the examined type of intersection and the traffic
organization is shown in Figure 3. The most characteristic feature of the
studied type of facilities is the presence of a wide dividing median strip.
This element, together with the two two-lane carriageways of the major road,
determines how the vehicles of the subordinate movements make their maneuvers,
the amount of superior conflicting stream, the number, and how the superior
streams are observed. The presence of a wide dividing median strip
accommodating one vehicle makes the left turn maneuver executed in two stages.
Thus, to estimate the values of the critical gap and follow-up times, it has
been divided into two separately considered maneuvers, CL1 and CL2 (Class 2)
[1, 9, 19, 24, 25].
Some
of the maneuvers of the subordinate movements, that is, turning right from the
subordinate approach (CR) and turning left from the major road (BL- Back left),
are similar to the corresponding maneuvers at the 1x2 type road intersection.
Minor differences may only be due to the number of lanes of superior movements
and their traffic flow [1, 12-14, 25].
4. DESCRIPTION
OF SURVEYS CONDUCTED ON SELECTED REAL SUBJECT INTERSECTIONS IN A SPECIFIC
LOCATION
Problems
occurring during measurements for estimating critical gaps and follow-up times
were identified based on the experience gathered from the survey conducted in
2018 at two selected intersections located in the Metropolis GZM (in Polish:
Górnośląsko Zagłębiowska Metropolia) – the
metropolitan area in the Silesian Voivodeship. Figure 4 shows the location of
the study intersections.
Fig.
4. Location of the tested objects with the indication of the measurement sites:
a)
the location of the subject intersections in the background of the
administrative division of the country and the GZM metropolis, b) View of
object No. 1 (within the built-up area),
c) View of object No. 2 (outside built-up area)
[Authors’
research]
The
first object is located in one of Katowice's downtown districts and handles
through, inbound and outbound traffic in the city. The southern alignment of
the major road provides one of the few connections between the southern and
northern districts and the city center. The minor road is of local
significance, although a significant increase in traffic volume is observed
throughout the object during peak hours. The immediate environment has diverse
socio-economic functions. Commercial and service facilities, low-rise
residential buildings, production plants, and warehouses are located here.
Research
object No. 2 is located outside the built-up areas; however, in the area of
influence of large agglomerations, in the administrative area of the city of Mikołów
(Silesian voivodeship). The major road is a regionally important connection of
urban centers, running to the borders of the voivodeship. The minor road
provides access for city residents to important thoroughfares in the area and
runs through the entire urban area of the city. The intersection serves the
through traffic characterized by a significant size of traffic streams in all
movements. The proximity of large agglomerations generates trips in many
motivations and directions. In the immediate vicinity, there are homogenous,
dense low-rise buildings, service and commercial points, and forest areas.
Both
facilities are effectively separated from their immediate surroundings, and
there is no influence from pedestrians or other factors that could interfere
with the traffic conditions necessary to determine the critical gaps and
follow-up times.
As
part of the pilot survey and analysis of the immediate surroundings of the
objects in a specific location to find the best available observation points,
while aiming to minimize the number of cameras required, attempts were made to
record from several potentially attractive locations. The locations in the area
of intersections are shown in Figure 4. White squares indicate the location of
the observation point in the surroundings of the intersection face and the
segments coming out of them in the direction of registration in the axis of the
camera. The view of the intersection face from cameras placed at all surveyed
measurement locations is shown in Figure 5.
In
Figure 5, the view from the places selected for the main surveys shows the
location of the virtual cross-sections used to determine the start and end
times of the gaps - the dotted lines are used to study the major streams, while
the lines of the "dot-dash" type - the subordinate movement. A study
of the CL2 movement was conducted from point 6. The virtual cross-section for
the superior stream was determined based on the presence of a vertical sign
located at the edge of the wide dividing strip, while for the subordinate
stream - based on a dashed line separating the major road lanes from the entry
slip road. The same principles were applied when analyzing the CR[3] movement
using observation point 8. The CL1 and BL movements were examined from
observation point 7. The virtual cross-section for the superior stream
identical for both maneuvers was determined based on the vertical sign
remaining in line with the apex of the excluded surface separating the
carriageway on the subordinate road. However, for subordinate streams, these
are the unconditional stop lines and the wide dividing strip limit line.
Before
conducting the main research, it is necessary to analyze the driver behavior
occurring at the intersection, its proper classification, and aggregation. It is
necessary to make assumptions, defining which situations will be used for
research and which will be rejected. Although it may seem that the law
regulates the way of moving in the intersection area, practice shows that each
situation is different, and sometimes inconsistent with generally accepted
rules, which for the studied objects is presented in Figure 6.
Fig.
5. View of the studied intersections with potential observation points
[Authors’
research]
a) b)
Fig.
6. Examples of different ways of creating a queue of vehicles in CL2 movement:
a) parallel stops of vehicles; b) a queue built under the assumptions for
1x2 road intersections
[Authors’
research]
The
most diverse situations were observed in the traffic of vehicles of CL2
movement. Different queuing methods determine the response time required to
join the traffic, and thus, causes the resulting critical gaps and follow-up
times to vary.
5. IDENTIFICATION OF PROBLEMS OCCURRING DURING
SURVEYS OF CRITICAL GAPS AND FOLLOW-UP TIMES AT UNCONTROLLED T‑INTERSECTIONS
During
the theoretical analysis, the preparation of measurements, and the conduct of
research, were identified a set of conditions and problems specific to each
subordinate movement. They were formulated independently for the estimation of
critical gap and follow-up time. The results are presented in Table 1.
Tab. 1
List
of problems identified during the survey of the tg and tf
times independently for each subordinate movement [Authors’ research]
|
Movement |
Problems
with estimation of: |
|
|
tg |
tf |
|
|
BL |
The
limitation of the visibility of the superior stream by the CL2 movement
vehicles in a wide dividing median strip. |
The
limitation of the visibility of the superior stream by the CL2 relation
vehicles on a wide dividing median strip. In extreme situations, they
prevent the movement of BL relations. Diversified
trajectories of the movement of subsequent vehicles depending on the place of
starting and stopping. |
|
CR |
Visibility
limitation by a parallel-created queue of vehicles of the CL1 movement. |
Two
lanes of the major road as destination lane. |
|
CL1 |
The
acceptance of the gap depends on the occupation of the wide dividing median
strip. The
impact of AR[4]
vehicles on the available gaps. |
Strong
dependence on traffic conditions in relation CL2. The
decision to execute the maneuver and the trajectory of movement depend on the
individual characteristics of the drivers and the occupation of the wide
dividing median strip. The
impact of AR vehicles on the available gaps. |
|
CL2 |
The
limitation of the visibility of the superior stream by the vehicles of the BL
movement. Influence
of BL movement vehicles on the gap distribution in the BS[5]
stream. |
Dependence
of the entry of subsequent vehicles from the queue on the traffic conditions
in CL1 movement. Variation in how more vehicles join and the queue created in
the dividing median strip, limiting visibility and maneuverability. Two
lanes of the superior carriageway selected as the target line. Impact
of BL vehicles. |
For each of the subordinate movements, it is possible
to estimate the values of the critical gap and follow-up times. The observed
traffic must meet the conditions defined in the methods. In practice, however,
driver behavior varies widely and it is impossible to draw a clear line between
compatible and incompatible situations with the assumptions of the method used.
For BL movement, the problem of varying trajectories through the intersection
is most relevant. In contrast, drivers moving in the CR movement choose one of
the two lanes of the major road as their destination lane. When analyzing the
CL1 relation, the most significant is the effect of the wide dividing median
strip on the variation in the driving behavior of both the first and subsequent
vehicles in the subordinate movement. The CL2 maneuver is unlike any other
maneuver observed at other types of uncontrolled intersections. This considers
both the target lane into which the vehicles will merge and the differentiated
entry of subsequent queuing vehicles.
Therefore, it is necessary to make additional
assumptions and rules to interpret driver behavior and the extent to which
observed traffic situations are used. It is first necessary to identify the
traffic situations occurring on a given site and attempt to aggregate them into
internally homogeneous groups differentiated from each other to classify
driving behavior in the same way during analysis. The last important factor is
to clearly define the purpose of the test and the scope of validity of the
determined values of the critical gaps and follow-up times, that is, for a
specific real object or for a type of object as a whole.
6. CONCLUSIONS
Summarizing
the analysis carried out, it should be emphasized that the study of traffic at
uncontrolled intersections is aimed at collecting as much information and
traffic characteristics as possible to build an accurate model on the studied
type of objects to obtain the real behavior of most drivers. This paper points
out the necessity of rational planning of critical gaps studies and the
preparation for their implementation at median uncontrolled intersections.
Nowadays, many different methods are known for testing the values of critical
gaps and follow-up times, but in each of them, the observed motion must meet a
certain set of strictly defined and rigorous requirements. The selected
research object should be analyzed in terms of the existing movements,
geometry, trajectory and traffic conditions, technical possibilities of traffic
registration, and drivers' behavior. The pilot study allows verifying the made
assumptions and refining of the way of measuring and setting of the cameras.
The final step is to gather a sufficient research sample size.
To
ensure high accuracy of the results and precision of the measurements, it is
very important to make a proper selection of the observation points, reflecting
the traffic situation on the objects exactly as it is in reality and as it is
seen by the drivers waiting to crossing or merging the traffic. Observation
conducted from a distance, at non-standard angles may falsify the image,
introducing distortions in the perception of mutual position of vehicles, and
thus, lead to significant errors.
The
information contained in this article will be useful for those preparing and
planning the implementation of research and traffic observation, especially in
the area of intersections, estimation of critical gaps and follow-up times, and
those seeking information on traffic conditions and the diversity of real
traffic situations.
Furthermore,
it is necessary to conduct further in-depth research, although the presented
results of the authors' work in an unambiguous, precise, and natural way
complements the existing research gap in terms of defining the practical
principles and conditions for analyzing critical gaps and follow-up times. In
their scope remains the analysis of drivers' behaviors on uncontrolled median
T-intersection and the influence of diversified behaviors on the determined
values of critical gaps and follow-up times. The biggest challenge will be to
develop an apparatus that allows fully automatic determination of the critical
gaps and follow-up times. The software should intelligently interpret the
traffic situation, select the situations that meet the assumptions of the
method used and properly respond to the problems occurring during the
measurements, including those identified in this paper.
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978-3-030-34069-8.
Received 11.09.2021; accepted in
revised form 30.10.2021
Scientific Journal of Silesian University of Technology. Series
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