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Transportation Research Procedia 20 ( 2017 ) 125 – 131
2352-1465 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 12th International Conference “Organization and Traffic Safety
Management in large cities”
doi: 10.1016/j.trpro.2017.01.032
Available online at www.sciencedirect.com
ScienceDirect
12th International Conference "Organization and Traffic Safety Management in large cities",
SPbOTSIC-2016, 28-30 September 2016, St. Petersburg, Russia
Calculation of Traffic Capacity of Signaled Intersections
Alexandr Chubukov 1a, Valeriy Kapitanov 2b, Olga Monina 2c, Valentin Silyanov 1d
*
,
Ulrich Brannolte 3e
1 Moscow Automobile and Road Construction State Technical University (MADI), 64 Leningradskiy prosp., Moscow, 125319, Russia
2 Scientific Research Center of Road Traffic Safety of the Ministry of the Interior of the Russian Federation, 17 Poklonnaya str., Moscow,
121170, Russia
3 Bauhaus-Universität, 13d Marienstr, Weimar, 99423, Germany
Abstract
In order to calculate traffic capacity of signaled intersections, it was suggested to apply an approach based on the concept of
congestions. The paper states examples of traffic capacity calculation.
© 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the organizing committee of the 12th International Conference "Organization and Traffic
Safety Management in large cities".
Keywords: signaled intersections; traffic capacity; congestion
1. Introduction
Increase of traffic intensity leads to situations when it becomes impossible to provide a satisfactory level of traffic
servicing with the help of only traffic light signaling means. Congestion at a section of the road traffic network with
traffic signals is a situation when the average duration of the vehicle delay exceeds the length of the traffic signaling
cycle [Kapitanov and Khilazhev (1986), Federal Road Agency (Rosavtodor) (2012)]. In this case, the queue length
can increase, reaching the length of the road intersection. Further development of the road blocking paralyzes larger
parts of the road network and disorganizes the traffic in whole.
* Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 .
E-mail address: a.b.chubukov@mail.rua, valerij47-k@yandex.rub, monina612@yandex.ruc, silyanov@bk.rud*, ulrich.brannolte@bauing.uni-
weimar.dee
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 12th International Conference “Organization and Traffic Safety
Management in large cities”
126 Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
Congestions can be divided into systematic (stable) and occasional. The cause of occasional congestions can be
different random factors, such as accidents or emergency situations. Systematic congestions are characterized by
periodic repetition in time and stability in space. Such congestions occur in certain directions of movement at the same
sections of the road traffic networks, during “rush hours”, as a rule.
Basically, optimization of traffic control implies challenging of forecasting, recognition and elimination of pre-
congestion situations, preventing road blocks, which requires exclusion of causes of traffic overloading by means of
redistributing of traffic flows onto alternative routes. The traffic control system should promptly inform the drivers
on possible traffic congestions and recommend bypass routes [Kravchenko (2013)].
2. Main text
2.1. Methods
Methods of traffic flows control in the situation of congestions can be divided into methods of on-line control and
methods which are based on the input data on parameters of traffic flows referring to the time prior to the moment for
which the impact is calculated. Input data of the latter methods can apply to any other “standard” situations. The
method of control based on the analogue of the “library” of free traffic flows control applications can serve as an
example [Kapitanov and Khilazhev (1986), Plotnikov (2010), Transportation Research Board, National Research
Council (2000)]. For example, M-number of standard situations for the object was revealed in the result of field
observations. Corresponding exposure is calculated for each such situation. The system measures different traffic flow
parameters, and if these parameters are close to those of some standard set out of M-number situations, the system
completes appropriate actions.
2.2. Examples
Let us consider an example of a simple intersection of two-way roads and multi-phase control of actions and
characteristics of traffic flows.
Let us introduce the following variables: qik (intensity of ith flow in the kth phase), Сik (congestion flow
corresponding to the ith flow), gk (duration of enabling traffic signal k), lik (time loss per a cycle related to the traffic
flow with the intensity qik), n (the number of control phases) (Fig. 1).
In accordance with the diagram of the queue relieving (Fig. 1), the driver spends some time on starting and
acceleration under fully intensive enabling period after the green signal starts. After a few seconds, the intensity of
queue relieving reaches its peak value and stabilizes (the flow of loading). Fig. 1 shows time interval revealing the
effective duration of the green signal g, which is defined as the time interval during which cars move across the stop
line (under piecewise-constant approximation of the output flow intensity).
127
Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
Fig. 1. A picture of controlling traffic signals of the intersection.
The time of the vehicle waiting in the queue does not exceed the duration of the cycle (no congestions), if the
following conditions are satisfied:
k: qik T
d
Cik gk
¦
k
(gk + lik) = T (1)
gmin
d
gk
d
gmax,
Tmin
d
T
d
Tmax,
where gmax, gmin, Tmin, Tmax are restrictions laid by the road traffic rules.
This system of inequalities (constraints) connects movement parameters (q, C) and control signals (T, gk).
If an objective function is added and the optimization problem is solved under the above stated restrictions, then
the values of control signals can be obtained.
If T and gk are excluded from the system (1), we can get such a condition when there is no congestions at the
intersection (if we want to find a condition under which there is no congestions, without solving the optimization
problem every time, at that):
128 Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
¦
¦
d
!
¦
d
kkmk,
A1 kmk
l
m
B
kmk,
Ckmk,
q
kmk,
A
max
g
m
B
kmk,
Ckmk,
q
0
kkmk,
A1
max
T
m
B
(2)
where mk is the number of flows (m) in the phase k, which corresponds to
Ckik,
qkik,
i
max
Akmk,
Violation of any condition means that the period of the vehicle stay in the queue exceeds the duration of the cycle,
i.e. there is congestion at the intersection. An example:
Fig. 2. A scheme of the intersection.
129
Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
A condition of congestion absence at the intersection with traffic light signaling is defined as follows (Fig. 2).
Phase 1 (traffic flows 1, 2)
C
q
C
q
2
2
1
1
d
2
1
m
2
2
1,21
C
q
A
Phase 2 (traffic flow 3)
C
q
3
3
3
2 m
3
3
2,32 C
q
A
Phase 3 (traffic flows 4, 5)
C
q
C
q
5
5
4
4
t
4
3
m
4
4
3,43
C
q
A
Conditions determining traffic congestions are as follows:
A21,1 + A32,2 + A43,3 t 1 — congestion at the intersection
A21,1 + A32,2 + A43,3 1 — no congestions.
The system (2) can be applied to define the concept of "traffic capacity of a signaled intersection”.
A traffic capacity of the intersection implies a set of vectors with the physical dimension k (a number of phases);
their projections onto coordinate axes equal the intensity
kmk
q
,
and satisfy the following condition at the same time:
max
2,
o
¦
kkmk
q
.
An example:
Fig. 3. A scheme of a simple intersection.
Let us consider an intersection with two-phase signaling control shown in Fig. 3. Let us assume that, in this case,
130 Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
there are no restrictions on duration of the cycle and no limits on effective duration of enabling signals, i.e.:
f
f
max
max
,
T
g
In this case, the traffic capacity of the intersection, i.e. the vector
),(
21
qqq
, is determined by the following
equation (to simplify the task, the loading flows are assumed to equal 1):
max
01
2
2
2
1
21
o
!
qq
qq
Fig. 4 states solution of this task:
Fig. 4. Graphic illustration of intersection traffic capacity.
The traffic capacity of the considered intersection is summed up of a set of vectors with the beginning at the zero
point and the ending on the line connecting the points with unit coordinates on the axes.
3. Conclusion
Thus, it is proposed to use the above stated approach based on the concept of congestions to calculate the traffic
capacity of intersections and roads with traffic light regulation.
References
Transportation Research Board, National Research Council (2000). Highway Capacity Manual 2000.. Washington, D.C., USA, 1134 p.
131
Alexandr Chubukov et al. / Transportation Research Procedia 20 ( 2017 ) 125 – 131
Federal Road Agency (Rosavtodor) (2012). ODM (Industry-specific road guidance document) 218.2.020-2012. Methodological recommendation
on the assessment of road capacity [ODM 218.2.020-2012. Metodicheskie rekomendacii po ocenke propusknoj sposobnosti avtomobil'nyh
dorog]. Moscow: Federal State Unitary Enterprise INFORMAVTODOR, 143 p. (in Russian).
Kapitanov, V. T., Khilazhev, Ye. B. (1986). Traffic flow control in cities [Upravlenie transportnymi potokami v gorodah]. Moscow: Transport (in
Russian).
Kravchenko, P. A. (2013). Traffic organization and safety in large cities [Organizacija i bezopasnost' dvizhenija v bol'shih gorodah]. Science and
Engineering for Highways, (1): 1–2 (in Russian).
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[Razrabotka shem organizacii dvizhenija transportnyh i peshehodnyh potokov na reguliruemyh perekrestkah: Uchebnoe posobie dlja vuzov].
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