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Available online at www.sciencedirect.com
Transportation Research Procedia 36 (2018) 252–259
2352-1465 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and Traffic Safety
Management in Large Cities (SPbOTSIC 2018).
10.1016/j.trpro.2018.12.077
www.elsevier.com/locate/procedia
10.1016/j.trpro.2018.12.077 2352-1465
© 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the scientic committee of the Thirteenth International Conference on Organization and
Trafc Safety Management in Large Cities (SPbOTSIC 2018).
Available online at
www.sciencedirect.com
ScienceDirect
Transportation Research Procedia
2352-1465© 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (
https://creativecommons.org/licenses/by
responsibilit y of t
he scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018).
Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018)
Methods for traffic management efficiency improvement in cities
Valeriy Kapitanov
a
,
Valentin Silyanov
a
Moscow Automobileand Road Construct
ion State Technical University
b
Scientific Research Center of Road Traffic Safety of the Ministry of the
Abstract
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
experience shows that traffic management in the
urban street and road network, first of all, requires a city
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
under rather severe restrictions. Therefore, most t
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
microlevel simulation models, are considered by the authors.
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
piecewise-
constant approximation of a traffic flow intensity function of t
actions (cycle shifts) to ensure coordinated control on highways is given. The suggested approach to modeling of traffic flow
cities is rather simple and efficient. Therefore, it can be of practical
actions in intelligent transportation systems, including in real time and for congested sections of the street
©2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-
ND license
Peer-
review under responsibility of the scientific committee of the Thirteenth International Confer
Traffic Safety Management in Large Cities (SPbOTSIC 2018)
Keywords:control actions; traffic flow; intensity.
* Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-
000
E-mail:a.b.chubukov@mail.ru
www.sciencedirect.com
ScienceDirect
Transportation Research Procedia
00 (2018) 000–000
www.elsevier.com/locate/procedia
https://creativecommons.org/licenses/by
-nc-nd/4.0/)Peer-review under
he scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in
Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018)
Methods for traffic management efficiency improvement in cities
Valentin Silyanov
a
, Olga Monina
b
, Aleksandr Chubukov
a
*
ion State Technical University
, 64 Leningradskiy Prosp.,Moscow, 125319, Russia
Scientific Research Center of Road Traffic Safety of the Ministry of the
Interior of the Russian Federation, 17 Poklonnaya St.,
Moscow, 121170
Russia
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
urban street and road network, first of all, requires a city
-
wide management
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
microlevel simulation models, are considered by the authors. Capabilities of various software tools that allow performing
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
constant approximation of a traffic flow intensity function of time, is suggested. An example of forecasting control
actions (cycle shifts) to ensure coordinated control on highways is given. The suggested approach to modeling of traffic flows in
cities is rather simple and efficient. Therefore, it can be of practical interest and can be used when forecasting network control
actions in intelligent transportation systems, including in real time and for congested sections of the street
-and-road network.
ND license
(https://creativecommons.org/licenses/by-nc-nd/4.0/)
review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and
Traffic Safety Management in Large Cities (SPbOTSIC 2018)
.
000
-0000 .
www.elsevier.com/locate/procedia
Methods for traffic management efficiency improvement in cities
Moscow, 121170
,
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
wide management
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
ed
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
Capabilities of various software tools that allow performing
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
ime, is suggested. An example of forecasting control
s in
interest and can be used when forecasting network control
ence on Organization and
Available online at
www.sciencedirect.com
ScienceDirect
Transportation Research Procedia
2352-1465© 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (
https://creativecommons.org/licenses/by
responsibilit y of t
he scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018).
Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018)
Methods for traffic management efficiency improvement in cities
Valeriy Kapitanov
a
,
Valentin Silyanov
a
Moscow Automobileand Road Construct
ion State Technical University
b
Scientific Research Center of Road Traffic Safety of the Ministry of the
Abstract
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
experience shows that traffic management in the
urban street and road network, first of all, requires a city
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
under rather severe restrictions. Therefore, most t
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
microlevel simulation models, are considered by the authors.
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
piecewise-
constant approximation of a traffic flow intensity function of t
actions (cycle shifts) to ensure coordinated control on highways is given. The suggested approach to modeling of traffic flow
cities is rather simple and efficient. Therefore, it can be of practical
actions in intelligent transportation systems, including in real time and for congested sections of the street
©2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-
ND license
Peer-
review under responsibility of the scientific committee of the Thirteenth International Confer
Traffic Safety Management in Large Cities (SPbOTSIC 2018)
Keywords:control actions; traffic flow; intensity.
* Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-
000
E-mail:a.b.chubukov@mail.ru
www.sciencedirect.com
ScienceDirect
Transportation Research Procedia
00 (2018) 000–000
www.elsevier.com/locate/procedia
https://creativecommons.org/licenses/by
-nc-nd/4.0/)Peer-review under
he scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in
Thirteenth International Conference on Organization and Traffic Safety Management in
Large Cities (SPbOTSIC 2018)
Methods for traffic management efficiency improvement in cities
Valentin Silyanov
a
, Olga Monina
b
, Aleksandr Chubukov
a
*
ion State Technical University
, 64 Leningradskiy Prosp.,Moscow, 125319, Russia
Scientific Research Center of Road Traffic Safety of the Ministry of the
Interior of the Russian Federation, 17 Poklonnaya St.,
Moscow, 121170
Russia
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
urban street and road network, first of all, requires a city
-
wide management
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
microlevel simulation models, are considered by the authors. Capabilities of various software tools that allow performing
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
constant approximation of a traffic flow intensity function of time, is suggested. An example of forecasting control
actions (cycle shifts) to ensure coordinated control on highways is given. The suggested approach to modeling of traffic flows in
cities is rather simple and efficient. Therefore, it can be of practical interest and can be used when forecasting network control
actions in intelligent transportation systems, including in real time and for congested sections of the street
-and-road network.
ND license
(https://creativecommons.org/licenses/by-nc-nd/4.0/)
review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and
Traffic Safety Management in Large Cities (SPbOTSIC 2018)
.
000
-0000 .
www.elsevier.com/locate/procedia
Methods for traffic management efficiency improvement in cities
Moscow, 121170
,
A methodology for traffic management in cities provides for extensive use of computer technologies. Modern international
wide management
system (intelligent transportation system, ITS). Development of a social process model is a complicated task that can be solv
ed
raffic management tasks are not formalized but solved empirically. Two basic
approaches to development of network mathematical models of traffic flows, based on a set of analytical models and on
Capabilities of various software tools that allow performing
modeling are reviewed. As a result, a method for forecasting network control actions affecting traffic flows, based on a
ime, is suggested. An example of forecasting control
s in
interest and can be used when forecasting network control
ence on Organization and
Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259 253
2 Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000
1. Introduction
Automation of traffic management has priority among actions aimed at the assurance of proper city functioning
under the conditions of intensive motorization.
Modern international experience shows that traffic management in the urban street and road network, first of all,
requires a city-wide management system (intelligent transportation system, ITS) including immediate
communication with municipal services, video surveillance devices, vehicle monitoring sensors, facilities for
assessment of traffic intensity and speed (vehicle detectors), electronic information boards and variable message
signs indicating possible bypass routes for complicated road sections, etc.
A methodology for traffic management in cities upon design and development of the systems provides for
extensive use of computer technologies. However, most traffic management tasks are not formalized but solved
empirically (intuitively).
The purpose of the study is to develop a method for forecasting network control actions impact on traffic flows.
2. Materials and methods
Vehicle traffic in modern urban conditions is interrelated with the behavior drivers. Each driver, when solving
his/her own optimization task to accomplish a trip during an acceptable time, conflicts with other drivers. This
interaction results in a collective strategy which can be simulated within the macro-approach most commonly used
in the field of traffic safety management (TSM).
The application area of micro-modeling, i.e. modeling of individual vehicles, is usually outside of the area of
multidimensional optimization management tasks, which is related to actual resource constraints.
Control actions in the street and road network (SRN) are addressed to the population of road users.
One of the main elements of managing transport and pedestrian flows in the urban SRN is traffic light control at
intersections, ensuring separation of conflicting flows.
Control actions affecting traffic flows represent a set of cycle shifts, duration of red and green lights at SRN
intersections with traffic lights(Plotnikov et al., 2017; Bekmagambetov and Kochetkov, 2012; Casas et al., 2010).
To ensure efficient control, complete data on the process, evaluation of its causes and conditions of their
occurrence are needed. An analysis of process trends makes it possible to evaluate its performance for the long run,
elaborate measures ensuring goal achievement and, thus, transition to a new state.
Development of a social process model is a complicated task that can be solved under rather severe restrictions.
Traffic flow shall be understood to mean a set of operated vehicles moving in the street and road network.
There are two basic approaches to development of network mathematical models of traffic flows, based on a set
of analytical models and on microlevel simulation models.
Various software tools that allow performing modeling are known. Among those, the following can be
distinguished: PTV Vision® VISSIM, MXURBAN, DRACULA, TRANZIT, TSIS, Paramics, AIMSUN, Civil 3D,
Credo, Robur, SISTM and others.
AIMSUN2 (Advanced Interactive Microscopic Simulator for Urban and Non-urban Networks) is a software tool
based on microscopic simulation that is able to reproduce traffic of vehicles of various type with account for driver
behavior models (car following, lane changing, etc.) in the SRN with traffic lights. The state of traffic lights changes
discretely at specific points in time. AIMSUN2 is integrated into the GETRAM simulation environment (a network
graphical editor, a network database, a module for presenting results, etc.).
DRACULA (Dynamic Route Assignment Combining User Learning and Micro-simulation) is intended to solve a
wide range of tasks, including those during emergencies (road accidents, adverse weather conditions, etc.).
PARAMICS (PARAllel MICroscopic Simulation, Quandstone Ltd., United Kingdom) is intended to model
vehicles of various type in the SRN with traffic lights, public transport, specified routes, etc.
TRANZIT is a macroscopic model designed primarily for the use in automated traffic management systems
(ATMS), taking into account the following information: data on the network structure (a list of hubs and road
sections, lengths of road sections, trafficway geometry, etc.); data on traffic management in the network, traffic light
signaling, etc.; data on traffic flows in the network (composition, intensity and speed of traffic flows on roads
connecting the city with other populated localities).
254 Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259
Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000 3
Various target functions can be used in TRANZIT (e.g. delays, stops, fuel consumption, capacity, etc.) which are
aimed at the optimization of traffic lights operation (cycle and phase duration, cycle shifts).
VISSIM is one of the most state-of-the-art VISUM/VISSIM PTV Vision® software packages for micro-
modeling of traffic flows where parameters of the SRN (width of streets, number and width of lanes, allowed traffic
directions, etc.), characteristics of traffic flows within the network in all traffic directions represent the input data for
modeling. Besides, data on control signals of traffic lights, traffic routes, stops, types of vehicles and their number,
as well as the traffic schedule are required.
It should be noted that the main task of transport network design is to simulate passenger flows, form route
networks, and distribute trips along the routes.
Simulation of passenger flows within the traffic network is generally reduced to the formation of an
origin/destination matrix and network occupancy.
In order to evaluate correspondences, gravitational and entropy models are widely used. Development of the
model implies arrival/departure balance between two zones, besides, correspondences from one zone to another
should be proportional to the total volume of departures/arrivals and a function of distances between the centers of
those zones.
Occupancy models differ in their hypotheses for selection of routes, distribution criteria.
The above explains approaches to the design of transport systems; the relevant detailed information is available
in the works by Wilson (1978),Lopatin (1985).
During a traffic flow analysis, its characteristics as a complex object shall be taken into account. Some of those
characteristics are listed in works by Rastrigin (1980): stochastic behavior, resistance to control, non-stationarity,
non-repeatability, etc. Since synthesis and implementation of control take some time during which the object state
changes, traffic flow characteristics shall be determined, and control actions shall be forecast in advance.
Experts of various fields in Russia (earlier in the USSR), USA, Great Britain, Japan and other countries were
engaged in traffic flow modeling and management (Deng and Burghout, 2016; Jolovic et al., 2017; Plotnikov, 2017;
Vasconcelos et al., 2014; Djahel et al., 2015).
Essentially, management implies development and testing of actions affecting traffic flows through traffic light
signaling and multi-position road signs based on the information on traffic flows (delay duration, intensity, speed,
etc.).
To describe traffic flows at intersections, various deterministic and stochastic models are used which usually
consist of two components: a vehicle arrival model and a model of waiting and queue departing when the green light
is on.
3. Research and calculations
The task of managing traffic flows in the network is to assign control actions (schemes of traffic management and
control signals) providing the optimum value of an accepted quality criterion. Among other things, it is required to
determine the duration of the cycle and phases at each intersection, shifts in moments of turning-on of the same
lights.
Traffic flow intensity, saturation flows, time losses, permissible durations of the cycle and green light, a list of
"conflicting" flows at the intersection, etc. serve as the input data.
Let us consider an intersection with a traffic flow arriving. This flow is characterized by changes in the intensity
q (t) in time (at constant average characteristics). According to the results of experimental studies, in case of high
occupancy of the road network, intensity can be approximated by a piecewise-constant function, as shown in Figure
1, where ' is a time interval from the start (the moment of green light turning-on) of the cycle to the moment when
the first vehicle that has left the adjacent intersection at the moment of green light turning-on appears in this cycle
(T) (Kapitanov and Khilazhev, 1985).
Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259 255
4 Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000
Fig. 1. Approximation of an intensity function of time.
During intersection departing, the traffic flow is determined by duration p and average intensity '
q. In such case:
''' ppp ,
where '
p is the effective duration of the green light;
'
qis the average flow intensity during the effective duration of the green light.
The value ''
p is determined by flows from minor directions on a road section and calculated according to the
following equation:
'
''
q
Tq
p (1)
where ''
q is the total intensity of turning traffic flows. The value '
q is related to the average intensity q by the
following ratio:
g
qT
q
' (2)
where
g
is the effective duration of the green light;
At a distance from the intersection, (model) characteristics of the flow change. If t is the average travel time
(from the intersection) to the point of the route under consideration,
p
and '
q can be determined by the following
equations (Kapitanov and Khilazhev, 1985):
'
' ''
008.0
)0(
)0(
)(/)0()0()(
],)0(min[)(
qq
ppp
tppqtq
Teptp t
(3)
The delay duration z and the number of vehicle stops N per cycle can be determined as follows. In this case, as
mentioned above, it is considered that when the green light is on and until the moment when the queue disappears,
the intensity of the decreasing flow is equal to the constant value C equal to the saturation flow.
)(
)0,max( );,0max(
),min( );,min(
2
)1()1(
2
22
qN
Tpx
C
qx
r
qC
C
p
qC
Cr
x
C
q
qq
C
qq
qrz
(4)
256 Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259
Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000 5
The value of the moment (Figure 2) when a leader appears in the cycle is calculated by the following equation:
Tnrt )1( 8.0 221
,
where t is travel time along the road section.
Fig. 2. Interrelation of control signals.
The value n (n = 0, 1, ...) is selected in such a way that the following inequality is true:
T
0.
The delay duration (per cycle) can be determined more precisely (taking into account the Poisson nature of the
flow) by the following equations:
(5)
The average delay duration 1
z and the average number of vehicle stops 1
N are determined as:
(6)
The obtained calculated ratios allow determining a delay related to vehicle stops. The value of the total delay
z
,
with account for a decrease in speed in the intersection area, is approximately determined by the following equation
(Kapitanov and Khilazhev, 1985):
43.604.1 zz
Example.
It is required to calculate the shifts 321 ,,
in the cycle of the traffic lights on the main road, a layout and main
characteristics of which are shown in Figure 3. It is assumed that all durations of the cycle and other signals have
already been determined.
)(
1
4.0
2
)1()1(
2
1
1
2
1
22
rTC
qT
x
x
x
C
q
qq
C
qq
qrz
qT
N
N
qT
z
z 11 ;
Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259 257
6 Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000
Fig. 3. A layout of the main road.
q1’ = 0.25, q2’ = 0.2, q3’ = 0.2, q1 = 0.25, q2 = 0.35, q3 = 0.35, q1” = 0.1, q2” = 0.05, T = 65.
Phase 1: main directions; phase 2: entry directions.
To perform calculations, the following is necessary:
1. To determine model characteristics at the departure from the first intersection in the forward direction and at
the arrival to the second intersection.
36.0
14.63
56406.0
)(
)0()0(
)(
36.0
14.63
56406.0
)(
)0()0(
)(
56
406.0
651.0
2565
)0(
)0(
406.0
2565
6525.0
)0(
1
11
1
1
11
1
1
'
1
11
1
1
1
tp
pq
tq
tp
pq
tp
q
Tq
rTp
rT
Tq
q
(7)
2. To determine a dependence of the vehicle delay in the forward direction at the second intersection on the cycle
shift. The cycle shift at the first intersection is taken to be zero. The following equations are used:
2112
22
2
2
)1(
2/)1(2/)1(
);,min(
);,0max(
);,min(
rTnt
C
q
qq
C
q
qqrz
qC
C
p
C
qx
r
qC
Cr
x
(8)
The sequence is as follows:
;0
2
(9)
258 Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259
Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000 7
Thus, the duration of the vehicle delay at the second intersection in the forward direction is 247.8 s per cycle at
the zero shift 2
= 0.
The corresponding delay values at other cycle shift values are presented in Table 1.
3. To determine a dependence of the vehicle delay at the first intersection (opposite direction) on the cycle shift.
The equations are similar to those given in paragraph 2. It should be noted that the moment
when a leader appears
is calculated as follows:
Model characteristics at the departure from the second intersection (opposite direction) and at the arrival to the
first intersection:
(10)
The results of calculating the delay duration at the first intersection in the opposite direction at various cycle
shifts are presented in Table 2.
4. According to the analysis of the data in the tables, the cycle shift at the second intersection which is equal to 0
s ensures the minimum vehicle delay of 247.8 s with account for the selected increment.
Changes in the cycle shifts 3
at the third intersection do not affect the delay. Therefore, the value 3
can be
taken arbitrarily.
Table 1. Results of calculating the delay duration at the second intersection in the forward directionat various cycle shifts.
x Cr/(c-q) R+qx/c- qr q2/2(q/c-1) q q(q/c-1)2/2 z
0 39.6 37.74 46.88 37.74 3.99 3.99 6.23 407.59 -164.08 8.95 -4.66 247.8
10 49.6 47.74 46.88 46.88 -2.41 0 0 506.3 -253.18 0 0 253.1
20 59.6 57.74 46.88 46.88 -8.81 0 0 506.3 -253.18 0 0 253.1
30 4.6 2.74 46.88 2.74 26.39 26.39 41.96 29.59 -0.86 398.6 -211.3 216.1
40 14.6 12.74 46.88 12.74 20 20 31.8 137.59 -18.7 22.96 -121.4 226.5
50 24.6 22.74 46.88 22.74 13.59 13.59 21.61 249.59 -59.57 105.7 -56.04 235.7
60 34.6 32.74 46.88 32.74 7.19 7.19 11.43 353.59 -123.48 29.59 -15.68 244.0
.8.247
2
23.6
)1
1
36.0
(36.023.699.336.0)1
1
36.0
(
2
74.372.0
74.37302.02/)1(2/)1(
;74.37)
36.01
301
,74.37min(),min(
;23.0)
36.01
99.31
,14.63min(),min(
;99.3)6.39
1
74.3736.0
30,0max(),0max(
;74.37)6514.636.39,0max(),0max(
;6.39030128.000)1(
2
2
22
2
2112
C
q
qq
C
q
qqrz
qC
Cr
x
qC
C
p
C
qx
Tpx
TrTnt
1
'
112 )1( rTnt
'
1
'
2
1
2
"
2
12
1
0.008
'
11
'
1
0.2 65
(0) 0.37;
65 30
0.05 65
(0) 35 35.78;
(0) 0.37
( ) (0) 35.78;
( ) 0.37.
t
qT
qTr
qT
p Tr q
pt p e
qt
Valeriy Kapitanov et al. / Transportation Research Procedia 36 (2018) 252–259 259
8 Valeriy Kapitanov, Valentin Silyanov, Olga Monina, Aleksandr Chubukov / Transportation Research Procedia 00 (2018) 000–000
Table 2. Results of calculating the delay duration at the first intersection in the opposite direction at various cycle shifts.
x Cr/(c-q) R+qx/c- qr q2/2(q/c-1) q q(q/c-1)2/2 z
0 25 0 39.68 0 0 0 0 0 0 0 0 0
10 15 39.68 0 10 10 1.6 0 0 5.92 -0.3 5.62
20 5 0 39.68 0 20 20 3.2 0 0 23.68 -1.2 22.48
30 60 30.78 39.68 30.78 -26.75 0 0 284.7 -110.85 0 0 173.87
40 50 20.78 39.68 20.78 -18.75 0 0 192.22 -50.5 0 0 141.72
50 40 8 39.68 10.78 -10.75 0 0 99.72 -13.6 0 0 86.12
60 30 8 39.68 0.78 -2.75 0 0 7.22 -0.07 0 0 7.15
4. Conclusions
As a result of the works conducted, based on the analysis of the existing approaches and application of methods
of mathematical modeling, the method for forecasting network control actions affecting traffic flows, based on a
piecewise-constant approximation of a traffic flow intensity function of time, was suggested. The provided example
of forecasting control actions (cycle shifts) to ensure coordinated control on highways demonstrates that the
suggested method is simple and efficient. It is assumed, that the method can be of practical interest and can be used
when forecasting network control actions in intelligent transportation systems, including in real time and for
congested sections of the street-and-road network.
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