CC BY
10
In connection with the active development of information systems in transport, it becomes necessary to integrate vehicles, infrastructure and humans into a single information network. The V2I system of information analysis for monitoring and controlling vehicles in operating conditions is an organic combination of information and analytical components. The latter includes the analysis of information regarding changes in operating conditions. The article presents a study that has improved the processes of managing the operating conditions of vehicles in the V2I communication system by using simulation modelling. A simulation model for choosing the optimal operating conditions for vehicles is described. The model takes into account road, climatic, and transport conditions and culture of vehicle operation, as well as the peculiarities of public transport movement in a transport hub. The objective function with the appropriate restrictions and the problem of traffic optimization in the investigated transport hub were established. Diagrams of the processes of the simulation model were constructed for various input parameters, including the optimal ones, with the creation of corresponding agents and their populations. Models of public transport delays at stops using a triangular distribution were developed, and the corresponding hypotheses were confirmed by Pearson's test (x2). The developed models can be used in the process of rebuilding a transport hub, as well as for modeling traffic when the operating conditions of vehicles change and for predicting such changes. The simulation results can be used in the creation and design of intelligent transport systems
Keywords: simulation modelling, vehicle, transport hub, operating conditions, public transport, information system, intelligent transport system
UDC 656.1+004.94
pOI: 10.15587/1729-4061.2020.215006|
DEVELOPMENT OF THE ANALYTICAL SYSTEM FOR VEHICLE OPERATING CONDITIONS MANAGEMENT IN THE V2I INFORMATION COMPLEX USING SIMULATION MODELING
M. Volodarets
PhD
Department of Electric Power Complexes and Systems*
I. Gritsuk Doctor of Technical Sciences, Professor** Y. Ukrainskyi Senior Lecturer Department of Automobile Transport* E-mail: e.a.ukrainskyi@gmail.com V. Shein PhD
Department of Technology of Machinery Manufacturing and Machine Maintenance***
0. Stepanov Doctor of Technical Sciences, Associate Professor
Department of Traffic Management and Road Safety***
1. Khudiakov Senior Lecturer** M . A h i e i e v
PhD, Associate Professor** V. Vychuzhanin Doctor of Technical Sciences, Professor Department of Information Technologies Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044 O. Smyrnov Doctor of Technical Sciences, Associate Professor Department of Vehicle Electronics*** O. S ara i ev Doctor of Technical Sciences, Professor Department of Automobiles named after A. B. Hredeskul***
E-mail: sarayev9@gmail.com *Pryazovskyi State Technical University Universytetska str., 2, Mariupol, Ukraine, 87555 **Department of Vessel's Power Plants Operation Kherson State Maritime Academy Ushakova ave., 20, Kherson, Ukraine, 73000 ***Kharkiv National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002
Received date 18.09.2020 Accepted date 21.10.2020 Published date 30.10.2020
Copyright © 2020, M. Volodarets, I. Gritsuk, Y. Ukrainskyi, V. Shein, O. Stepanov, I. Khudiakov, M. Ahieiev, V. Vychuzhanin, O. Smyrnov, O. Saraiev This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0)
1. Introduction vehicles [1] in operating conditions is an effective combi-
nation of data and analytical components. The information The information analysis system of vehicle-to-infra- part of the system consists in a connection of the vehicle's structure (V2I) communication to manage and control onboard control components and information facilities with
the infrastructure's elements and systems of receiving and transmitting information, analysis, and control [1-10]. The analytical part includes software, logistical, and hardware components of the vehicle's board and infrastructure [1-4]. An obligatory element in this case is the place of the operator of the V2I communication network in the information analysis system for monitoring and controlling vehicles [1, 4, 5, 9] under the operating conditions. The components of the system as well as its general structure, operation and results of its information processing were described in detail in [1-10].
The operating conditions include climatic, road, and transport conditions and culture of vehicle operation [1].
The information part of the V2I system provides it with information from the vehicle and the infrastructure [1-10]. The analytical part of the V2I network processes information and controls the vehicle under operating conditions. One of the components of the analytical part is the analysis of information in terms of changes in the operating conditions, that is, in climatic, road, and transport conditions [1, 11]. To ensure the systemic interaction of operating conditions and the vehicle in the described V2I system, the authors of the article propose a method for adapting computational procedures for information processing and traffic management using simulation modelling. It is best suited for research and management of road and transport operating conditions. It can also be used to research and control vehicles when the atmospheric and climatic conditions of operation and the culture of operation change.
Let us specify the features of the processes of research and management of the operating conditions of vehicles in the V2I information analysis system using simulation modelling.
The transport network is a complex system characterized by stochasticity, namely: a random value of transport demand, atmospheric and climatic factors, changes in the characteristics of the road network, as well as emergency situations and wear of the road surface [1, 12]. Therefore, the most adequate means of describing and predicting the behaviour of the specified object is modelling, the essence of which is to replace the real control object with its simulation. Any object that reproduces the properties of a real system with sufficient accuracy for the user's purposes can act as a model. In recent years, information systems in transport have been actively developed. In this regard, it becomes necessary to integrate vehicles, infrastructure and humans into a single information system. One of the steps to solve this problem is to simulate the operating conditions of vehicles and their optimization. This will improve the control over vehicle operating conditions in the V2I communication system. This is especially useful in the context of the active development of intelligent transport systems.
2. Literature review and problem statement
Technical services for the operation of vehicles solve many problems in the process of improving the methods of operational management of vehicle performance. Most of the tasks have an information component of the assessment, such as to analyse road conditions of the vehicle operation; to predict possible emergency situations and transport conditions; to forecast atmospheric and climatic conditions, etc. [1, 13-19]. The tasks listed and similar to them are still mainly solved by outdated methods that no longer provide the required
quality, rational approach and efficiency [20-22]. Evaluation of operating conditions and analysis of road plans and profiles are usually performed manually; updates of maps and diagrams are extremely rare; data on the state of most objects are not systematized and thus difficult to access. This situation complicates the task of managing the classification of vehicle operating conditions in the information conditions of an ITS.
The process under consideration is complex; therefore, simulation modelling can be effective. Its main advantage is that, in contrast to analytical modelling, simulation modelling helps to repeatedly reproduce the studied complex system and determine its optimal performance.
Much research has been done in the field of transport modelling. Thus, in [1] an information system of interaction between the vehicle and the infrastructure was considered, but not enough attention was paid to modelling the transport and road conditions of the vehicle operation. In [2] a system of training for and safety of the vehicle in the conditions of intelligent transport systems was considered, but little attention was given to the influence of the operating conditions of the vehicle on its operation.
In [7] the general concept of developing intelligent transport systems was described but with little regard to the simulation modelling of the vehicle's operation under operating conditions. In [9] attention was paid only to the cyber-protection of vehicles in the context of intelligent transport systems, but the operating conditions of vehicles were poorly covered. Study [13] considered analytical models of urban transport, but it did not take into account the variety of operating conditions of the vehicles. In [19] methods for assessing the index of intelligent vehicles were considered, but without due attention to the influence of transport, road and atmospheric and climatic operating conditions of vehicles on their behaviour. In [23] modelling of road traffic of vehicles in the conditions of their operation was considered, but not enough attention was paid to the influence of the composition of vehicles on the adequacy of the traffic models. In [24] the issues of modelling the movement of intelligent vehicles were considered, but the influence of the culture of operating vehicles on their movement was not taken into account. In [25] the features of dynamic modelling and assessment of the state of an intelligent vehicle with several wheels and an engine were analysed, but the influence of climatic operating conditions and operating culture on the operation and behaviour of the vehicle was overlooked.
Therefore, it seems rational to conduct a study devoted to determining the mechanism for constructing a simulation model for choosing the optimal operating conditions for vehicles, taking into account the peculiarities of public transport. This will make it possible to use it for solving transport problems. In particular, the problem of optimizing the movement of vehicles can be solved. Moreover, it will be possible to predict the fuel consumption of vehicles with changing operating conditions.
3. Research goals and objectives
The aim of the work is to study the possibility of improving the processes of managing the operating conditions of vehicles in the information analysis system of the V2I communication network by using simulation modelling.
To achieve this aim, it is necessary to solve the following tasks:
- to build a dynamic model for determining the optimal operating conditions for vehicles in a transport hub;
- to analyse the operating conditions of vehicles in the hub for which simulation modelling will be performed; and
- to build a simulation model for choosing the optimal operating conditions for vehicles for a section of the transport network.
4. Construction of a dynamic model for determining the optimal operating conditions for vehicles in a transport hub
A mathematical model for determining the optimal traffic parameters in a transport hub can be described as a correspondence between the elements of a set of inputs of the system X of 'possible values' x and a set T of 'time points' t, that is, in the form of the following mapping of T^X: x(t)eXT, teT.
Considering the output y(t) of the system as its reaction to inputs x(t), we can represent the model as a set of two processes: XT={x(t)} and YT={y(t)}, teT(Fig. 1).
( Àveh(t)
( Àpub(t)~
( Aped(t)~
ç p(t)
C i(t)
Ç Dpub(t)
x(t)
( Cr(t)
A MODEL FOR DETERMINING THE OPTIMAL OPERATING CONDITIONS FOR VEHICLES IN { A TRANSPORT HUB
-X pi(t) )
C TCi(t) ( Pr(t) Ç CD(t)
Ç cc(t) C Pi(t)
ç PS(t)
Fig. 1. A dynamic model for determining the optimal operating conditions for vehicles in a transport hub: setting the process at the inputs and outputs of the system
The set of input parameters x(t) is represented by the following parameters: Xveh(t) is the traffic intensity of vehicles, Xpub(t) is the traffic intensity of public transport, Xped(t) is the traffic intensity of pedestrians, p(t) is the matrix of transition probabilities, i(t) is the type of vehicles, Dpub(t) is the
delay time of public transport at stops, Cr(t) is the state of the roadway, TCi(t) is the technical condition of the vehicles, Pr(t) is the road parameters, CD(t) is the culture of vehicle operation, CC(t) is the atmospheric and climatic conditions, PI(t) is the infrastructure parameters, and PS(t) is the parameters of the regulation and control system.
The set of output parameters of the model is represented by the following parameters: p1(t), p2(t), pi(t), which are optimized parameters of vehicle operation.
The model can be used to develop a smart city transportation system to integrate the software into the infrastructure of the transport network.
5. Analysis of the researched transport hub and the operating conditions of its vehicles
Study [23] shows the cyphergram of the traffic flows in the transport hub (coordinates by Google Maps: 47°57'31.6"N 37°48'22.6"E). There, the traffic intensities were reduced. Based on the cyphergram, a graphical model of the movement of vehicles in the considered transport hub was built in the form of a graph of states with the probabilities of transitions from one state to another.
However, for modelling the movement of vehicles in the con-y(t) sidered hub, as close as possible to the real one, it is necessary to select from the total number of public transport those vehicles that move within a given section with stops. Moreover, the article considers optimization of road and transport operating conditions as the most significant strategy. Other operating conditions are assumed constant.
Fig. 2 shows the transformed cyphergram for vehicles moving through the hub without stopping.
Fig. 3 shows a model of the movement of public trans-
-X pi(t) ) -X p2(t) )
port with stops within the considered transport hub.
Fig. 2. The cyphergram of traffic flow intensities in the transport hub after the transformation
On the graph, the state-based transition displays the movement of public transport with stops within the considered hub in certain directions (Table 1), and states 5, 10 and 14 denote public transport stops.
Table 1
Transition through the graph states for public transport routes
Transition through the graph states Vehicle route
1-2-3-4-5-6 Trolleybus routes 17 and 21 Bus route 17
7-8-9-10-11-12 Trolleybus routes 17 and 21 (reverse direction) Bus route 17 (reverse direction)
12-14-15-2-3-16 Bus routes 37, 50, 79, 80, and 80A
12-14-15-2-3-4-5-6 Bus route 53
6. Construction of a simulation model for choosing the optimal operating conditions for vehicles for a section of the transport network
To model the movement of vehicles, a safe distance model based on Gibbs' reflective model was used [26, 27]. In this model of following the leader, vehicles are of two types: without restriction and with restriction by the vehicle in front (the leader). If a vehicle has a leader, it will adapt its speed to maintain a safe distance from the leader. In other words, the safe distance is determined so that the vehicle can avoid a collision with any adequate actions of its leader. If there is no restriction for the vehicle, then its speed is limited by the desired velocity and the maximum possible acceleration.
The speed of the n-th vehicle in the time interval [t, t+T] is determined as follows
,(t + T ) = min {va (t + T ), vb, (t + T )},
(2)
The matrix of transition probabilities for the reduced graph has the form
' 0 1 0 0 0 0 0 0 0 0 0 0 N
0 0 0.742 0 0 0 0 0 0 0 0.258 0
0 0 0 0 0 0 0 0 0 0.293 0 0.707
0 0 0 0 0.625 0 0 0 0 0 0 0.375
0 0 0 0 0 0.236 0 0 0 0 0.764 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0.651 0 0 0 0 0 0 0.349 0 0 0
0 0 0 0 0.755 0 0 0 0 0.245 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
, 0 0 0 0 0 0 0 0 0 0 0 0 ,
where T is the driver's reaction time, which is equal to one step of time simulation.
The maximum velocity V, that a vehicle can develop in a time step is determined by the following expression:
< (t + T ) = vn (t) + +2.5 ■ flmal T x
n
(t r
(1)
x
1 —
\
v.
des
x
/
x 0.025-
n (t)
(3)
max ln
The matrix of transition probabilities (1) was constructed for vehicles moving without stopping (i.e., for all vehicles except public transport) in the considered transport hub according to the model shown in Fig. 2.
value of acceleration of the n-th vehicle during its acceleration, and vds is the desired velocity of the n-th vehicle.
The safest velocity vbn of the n-th vehicle, taking into account the leading vehicle, is determined by the formula
-T)=dm- t+
r 2 [Xn-1 (t)- Vl - Xn (t)]-
\(dr T)2 - dr -vMT-^(t)2 [' d , n-1
(4)
where d™ is the maximum value of acceleration of the n-th vehicle during its braking, xn is the coordinate of the n-th vehicle, sn1 is the effective length of the (n-1)-th vehicle, which is determined by the length of the vehicle and the parameter that sets the minimum distance between vehicles, and d . is the estimate of the maxi-
n—1
mum acceleration of the (n-l)-th vehicle during its braking.
There are several approaches to assessing the acceleration of the leader when it is braking. First, it can be assumed that the driver can accurately estimate the leader's deceleration, thus assuming that
Fig. 7 shows the process diagram for public transport going in the direction 12-14-15-2-3-16 when simulating the traffic of route taxis on routes 37, 50, 79, 80, and 80A and buses on route 80.
The resulting process diagram of the simulation model to optimize the traffic in the transport hub is shown in Fig. 8.
c
Start
J
Statement of goals
0
Creation of agents and their populations
System formalization
Creation of a process
model
No Optimization
Re fi neme nt of the parameters
d ,= d
n-1 n-
(5)
where dn-1 is the acceleration of the (n-1)-th vehicle during braking. Second, the deceleration estimate of the lead vehicle can be calculated as the average between the acceleration of the lead and follower vehicles:
IM design
Specification of initial conditions
Input of initial data
d 1 = ^
n-1
Construction of a road network
Interpretation of the results
2
(6)
An algorithm is thus suggested for the development and verification of a simulation model for optimizing the operating conditions of vehicles in the transport hub, which is shown in Fig. 4.
At the next stage of developing the simulation model, a road network of the researched transport hub was created on the basis of a real scheme, and a process diagram of the simulation model was constructed according to [23].
Next, the process diagram was developed for the simulation model of the movement of public transport vehicles in the researched hub, running with stops according to the previously developed model shown in Fig. 3.
Thus, Fig. 5 shows the process diagram for public transport going in the following directions (Fig. 3): 12-14-15-2-3-4-5-6 to simulate the movement of route taxis on route 53; 1-2-3-4-5-6 to simulate the movement of trolleybuses on routes 17 and 21, as well as route taxis on route 17.
Fig. 6 shows the process diagram for public transport going in the direction 7-8-9-10-11-12 to simulate the reverse direction of trolleybuses on routes 17 and 21, as well as route taxis on route 17.
c
The end
I)
Fig. 4. The flowchart of the algorithm of the simulation model for choosing the optimal operating conditions for vehicles in the transport hub
CMT bSl CS mb53
CMT bS3 mb53
~D bS3 mb53
Fig. 5. The process diagram of the simulation model for public
transport running on routes 12—14—151-2-3-4-5-6
■2-3-4-5-6 and
CS_tbl7_2 (3—
CS 1b21 2
CMT bS2 tbl 7
CMT bS2 tb21
CS mbl 7 2
CMT bS2 mbl 7
D bS2_tbl7 -IS-
D_bS2_tb21 -0-
D_bS2_mbl 7
—ra-
CMT 9
Fig. 6. The process diagram of the simulation model for public transport running on routes 7—8—9—10—11 — 12
CS_mb37 ©-
CS_mb50 ©-
CS_mb79 Q—
CS_mb80 Q—
CS_mb80A
CS_b8~ Q—
CMT bSl mb37
ib37
CMT bSl mb50
CMT_bS 1 _mb79 -ffl-
sFsii
CMT bSTmb80
D_bSl n
D b^mb50 -0-
D_bS1_mb79
—n-
D_bSl_mb80
-sj-0-
CMT bSl mb80AD_bS 1 _mb80A
CMT bSl
D bSl b80
CMT 12
Fig. 7. The process diagram of the simulation model for public transport running on routes 12—14—15—2—3—16
CS_7 CS_1
Q-
SO 7
CMT 9
I
SO_2 —
CS_8
Q—
SO_8
CS_4
S-
SO 4
t:
SO 5 t
CMT bS1 mb53 CMT bS3 mb53
CS mb53 CS_tb17_1 CS tb21 1
D bSl
fc]
mb53
D bS3 mb53
CMT bS3 tb17
D_bS3_tb17
-E3-
CMT bS3 tb21
CS mb17 1
D_bS3_tb21 —!@{-
CMT bS3 mb
D_bS3 mb17
—1St-
CS_tb17_2 Q—
CS_tb21_2
<3—
CS mb17 2
CMT bS2 tb17
D bS2 tb17
CMT bS2 tb21
D bS2 tb21
CMT bS2 mb17
-EE-
D_bS2_mb17
—151-
CMT 11
SO 3
CMT 10
r
CS mb37 CS mb50
O—
CS mb79
<3—
CS mb80
CS_mb80A
a—
CS b80
CMT_bS1 mb37 --
CMT bS1 mb50
D bS1 mb37 -0-
D bS1 mb50
—n-
CMT bSl mb79 D bSl mb79
CMT bS1 mb80
D bS1 -
mb80
CMT bS1 mb80A D bS1 mb80A
CMT bS1 b80
D bS1 -fêt
b80
CD
Fig. 8. The process diagram of the simulation model to optimize the traffic in the transport hub
In the process of constructing the process diagrams of the simulation model, the following blocks were used:
- CS_1, CS_4, CS_7, and CS_8 are the incoming streams for the model of the considered transport hub for the graph points 1, 4, 7, and 8, respectively;
- SO_2, SO_3, SO_4, SO_5, SO_7, and SO_8 are the blocks intended for dividing the flows entering them into two streams for the model of the considered transport hub for the graph points 2, 3, 4, 5, 7, and 8, respectively;
- CMT_9, CMT_10, CMT_11, and CMT_12 are the blocks displaying outgoing flows for the model of the con-
sidered transport hub for the graph points 9, 10, 11, and 12, respectively;
- CS_mb53, CS_mb17_1, CS_mb17_2, CS_mb37, CS_mb50, CS_mb79, CS_mb80, and CS_mb80A are the incoming flows for the model according to Fig. 3 for point 13 of the graph for route taxis on routes 53, 17, 17 (reverse direction), 37, 50, 79, 80, and 80A, respectively;
- CS_tb17_1, CS_tb21_1, CS_tb17_2, and CS_ tb21_2 are the incoming flows for the model according to Fig. 3 for points 1 and 7 of the graph for trolleybuses on routes 17, 21, 17 (reverse direction), and 21 (reverse direction), respectively;
- CS_b80 shows the incoming flows for the model according to Fig. 3 for point 13 of the graph for the bus on route 80;
- CMT_bS1_mb53, CMT_bS1_mb37, CMT_bS1_mb50, CMT_bS1_mb79, CMT_ bS1_mb80, CMT_bS1_mb80A, and CMT_ bS1_b80 are the blocks leading to a stop corresponding to point 14 of the graph according to the model shown in Fig. 3 for such vehicles: route taxis on routes 53, 37, 50, 79, 80, and 80A and buses on route 80, respectively;
- CMT_bS2_tb17, CMT_bS2_tb21, and CMT_bS2_mb17 are the blocks leading to the stop corresponding to point 5 of the graph according to the model shown in Fig. 3 for such vehicles: trolleybuses on routes 17 and 21 and route taxi on route 17, respectively;
- CMT_bS3_mb53, CMT_bS3_mb17, CMT_bS3_tb17, and CMT_bS3_tb21 are the blocks leading to a stop corresponding to point 10 of the graph according to the model shown in Fig. 3 for such vehicles: route taxis on routes 53 and 17 and trolleybuses on route 17 and 21, respectively;
- D_bS1_mb53, D_bS1_mb37, DTo_ bS1_mb50, D_bS1_mb79, D_bS1_mb80, D_ bS1_mb80A, and D_bS1_b80 are the blocks that set the delay time at the stop corresponding to point 14 of the graph according to the model shown in Fig. 3 for such vehicles: route taxis on route 53, 37, 50, 79, 80, and 80A and buses on route 80, respectively;
- D_bS2_tb17, D_bS2_tb21, and D_ bS2_mb17 are the blocks that set the delay time at the stop corresponding to point 5 of the graph according to the model shown in Fig. 3 for such vehicles: trolleybuses on routes 17 and 21 and route taxis on route 17, respectively;
- D_bS3_mb53, D_bS3_mb17, D_bS3_tb17, and D_ bS3_tb21 are the blocks that set the delay time at the stop corresponding to point 10 of the graph according to the model shown in Fig. 3 for such vehicles: route taxis on route 53 and 17 and trolley buses on routes 17 and 21, respectively;
- CD is the block that removes vehicles from the system. While implementing the model, new types of agents were
created for a vehicle (Car), a route taxi (MBus), a bus (Bus) and a trolleybus (TBus) with parameters reflecting the time spent by each agent in the system, t_bs_c, t_bs_mb, t bs b, t_tb, respectively, and also the corresponding populations
of the agents (cars, mBuses, Buses, and tBuses) that were added to blocks of the carSource (CS) type.
To collect data on the travel time of the agents of the transport hub, the travel_time element was created, which estimates the difference between the current time () and the time when the agents appear in the system, that is,
travel _ time =
main.travel _ time.add (time () - t _bs_ ) main.travel _ time.add (time () - t _bs_mb) main.travel _ time.add (time () - t _bs_ b) main.travel _ time.add (time () - t _bs_ tb)
(7)
The duration of the traffic light phases was set by the parameters pi and p2 with default values of 37 and 25, respectively.
To display traffic light regulation, four Traffic Light blocks were added to the system. In the Properties of these blocks, the operation modes of the traffic light objects for the specified stop lines were set. The blocks were divided into groups of directions of movement (Fig. 9). The modes of operation of the traffic light objects were expressed in general terms through the parameters of the duration of the phases of the traffic light objects pi and p2, taking into account the transient modes for the possibility of further optimization of road traffic in the hub under consideration.
^Duration, \sec Stop line\ p1-10 3 3 p2+1 3
Stop line 1
Stop line 6
Stop line 2
Stop line 5
To optimize traffic in the transport hub, an experiment 'Optimization' was created based on the model in Fig. 1. The optimization problem was reduced to minimizing the objective function travel_time (pi, p2), that is,
travel _ time (p1, p2) = ^^ Atj =
i j
k
= £ [t _ bs _ Cj (pi, p2) - tOij ] +
j
+Z[t _ bs _ mbj (pi, p2) - to2 j ] +
j
k
+£[t _ bs _ bj (pi, p2) - to3j ] +
j
+£ [t _ bs _tbj (pi, p2) - to4j ] ^ min, (8)
j
where i is the parameter characterizing the type of agent in the simulation model, j is the parameter characterizing the number of the i-th agent in the population of the model agents, and ki is the number of i-th agents in the population of the agents.
Car MBus Bus TBus
(9)
The restrictions imposed on the model are reduced to the system:
1 < i < n, 0 < j < ki, p1mln < j < p1mi P2min < j < P2n
X ki = ko
(10)
^^Quration,
^-xsec p1-3 3 p2-10 3 3 4
Stop lm_\
Stop line 2
Stop lines 5
b
NQuration,
\,sec p1-10 3 3 p2+4 3
Stop) line\
Stop line 3
c
^Duration,
\sec p1-10 3 3 p2+1 3
Stop lmè\
Stop line_4
d
Fig. 9. Operation modes of traffic light objects for specified stop lines: a — trafficLight_1_2_5_6; b — trafficLight_7_8; c - trafficLight_3; d - trafficLight_4
where pimin, p2min, p+max, and p2max are, respectively, the minimum and ma ximum values of the parameters pi and p2, and ko is the total number of agents in the model.
Optimization of the model consists in the sequential performance of several runs of the model with different values of the parameters and finding the optimal values of the parameters for the given task. It is necessary to estimate the best values of the model parameters taking into account the given constraints. By combining heuristics, neural networks and mathematical optimization, the values of the model parameters corresponding to the maximum or minimum of the objective function were found, both under uncertainty and under constraints.
The interface of the optimization window of the simulation model was created, in which its number, functionality and parameters pi and p2 were displayed in the form of a table for the current and best values of the iteration.
7. Results of modelling and optimizing vehicle operating conditions for the researched section of the transport network
In the optimization process, a triangular distribution was used to model public transport delays at stops. A tri-
angular distribution is a continuous distribution bounded on both sides. It is often used when there is little or no information available and can rarely accurately represent a set of values. Despite this, due to its ease of use, it is applied as a functional form of representing areas with fuzzy logic.
The function of the distribution density of the triangular distribution (Fig. 10, a) is
Table 3
f ( - ) =
0
2( x - Xmin )
( Xma x - xmin )( Xmod - Xmin )
2(X max - X )
( -ma x - Xmin )( Xmax - Xmod )
0
for X < Xmin
for Xmin < X < Xmod ' f0r Xmod < X < Xmax'
for X > X „.
F ( X ) = 0
(X - Xmin )2
1 —
„in )( Xmod - X
(Xmax - X)2
n)(X
for X < Xmin, for X • < X < X„
for Xmod < X < Xm
1
for X > X„
Parameters of the triangular distributions for the delay blocks (D)
(11)
The distribution function of the triangular distribution (Fig. 10, b) is
Block D Delay time distribution function
D bS1 mb53 triangular(0, 8, 20)
D bS3 mb53 triangular(5, 8, 15)
D bS3 tb17 triangular(7, 12, 20)
D bS3 tb21 triangular(5, 10, 19)
D bS3 mb17 triangular(0, 9, 12)
D bS2 tb17 triangular(7, 13, 15)
D bS2 tb21 triangular(6, 13, 16)
D bS2 mb17 triangular(5, 8, 15)
D bS1 mb37 triangular(5, 7, 14)
D bS1 mb50 triangular(7, 9, 14)
D bS1 mb79 triangular(0, 7, 10)
D bS1 mb80 triangular(6, 9, 11)
D bS1 mb80A triangular(0, 6, 10)
D_bS1_b80 triangular(5, 12, 16)
(12)
The triangular distribution was specified by the triangular (double min, double mode, and double max) function, which generated the x value according to the triangular distribution (Table 2). For the delay (D) blocks, the corresponding parameters of the triangular distributions are given in Table 3.
During the optimization experiment, the parameters p1 and p2 were varied in the range from 20 s to 40s with a step of 1 s.
Table 4 and Fig. 11a show the results of the simple experiment 'Simulation1', which simulated traffic in the considered transport hub with the current values of p1=37 s and p2=25 s with the given vehicles according to the model in [23].
Table 4 and Figs. 11, b, 12, a show the results of the simple experiment 'Simulation2', which simulated traffic in the considered transport hub with the current values of p1=37 s and p2=25 s. However, it takes into account public transport stops according to the model in Fig. 3 and the matrix of the transition probabilities p* (1).
The results of traffic optimization in the considered transport hub are shown in Fig. 13.
It was found that for a given objective function (7), the optimal phase values were p1=37 s and p2=20 s, which were obtained for the sixth iteration. In this case, the average travel time of a vehicle through the hub under consideration was about 117 s, and the average relative error of real tests with the simulation modelling results was 3.2 %. The maximum error value was 4.3 %.
Table 4
Results of simulating travel_time
0 xm
xmod xmmx
xmod xmox x
a b
Fig. 10. The function of the triangular distribution: a — the function of the distribution density; b — the distribution function
Table 2
Description of the parameters and result of the triangular (double min, double mode, and double max) function
Name Type Description
Parameters
min Double the minimum value of x
max Double the maximum value of x
mode Double the most likely value of x
Result
Z Double generated value
Parameter Duration for "Simula-tionl" Duration for "Simula-tion2" Duration for "Simula-tion3"
Number of vehicles passing through the hub 1,160 1,147 1,096
Average travel time, s 136.846 131.283 117.088
Minimum travel time, s 15.766 15.66 15.66
Maximum travel time, s 1,182.576 646.449 612.859
Standard deviation of travel time, s 148.766 106.978 105.796
Confidence interval of travel time, s 8.561 6.191 6.264
Total travel time, s 158,741.588 150,581.158 128,326.621
0 x
90 80 o 70
^50 |40 £ 30 20 10 0
i i -T---ri i
-t---1--
i i --I----1--
i i - +---
i i - +---
i i - +----hi i
- +---4--
I I
--I----4--
I I
0 200 4000 600 800 1000 1200 1400 Duration of travel time, s
80 70 60
b' 50
H 40
2 30
Ph
20
10 0
0 100 204 30a 400 500 6000 700 800 Duvation of travel time, s
b
80 70
xc 60
050 0 40
030 £ 20 10 0
"T---r---
i i
-i-----i----
i i _ -L___J____
I
I
0 100 200 300 4400 500 600 700 800 Duration of travel time, s
Fig. 11. The histogram of the probable travel_time distribution for the experiments: a — 'Simulationl'; b — 'Simulation2':
c — 'Simulation3'
a b
Fig. 12. The map of traffic jams in the simulation model for the experiments: a — 'Simulation2'; b — 'Simulation3'
Fig. 13. The results of traffic optimization in the transport hub
a
c
Table 4 and Figs. 11, c, 12, b show the results of the simple experiment 'Simulation3', which simulated road traffic in the considered transport hub with the optimal values of p1=37 s and p2=20 s and taking into account public transport stops according to the model in Fig. 3 and the matrix of transition probabilities p* (1).
Fig. 11-13 show that the selection of public transport vehicles from the total number, taking into account their stops at stopping points, affects the modelling of traffic in the hub.
8. Discussion of the results of modelling and optimizing the vehicle operating conditions
Based on the comparison of the average relative error of real tests with the simulation modelling results, it can be concluded that the simulation model adequately describes real processes. At the same time, the maximum error value of 4.3 % is due to the fact that, as a result of simulation modelling, the selected vehicle movement model slightly differs from the real one. This is due, inter alia, to the culture of operating the vehicles. As a measured parameter, we took the average travel_time of the vehicles in the transport hub. The measurements were performed at the same points at which the vehicles entered and left the transport hub according to the simulation model.
Thus, as the optimization result, the average travel time through the considered transport hub was reduced by 10.8 % (Table 4), and the number of vehicles in traffic jams was reduced by 11.5 % (Fig. 12), which shows the effectiveness of the developed models.
The developed simulation models can be used in the process of rebuilding a transport hub to simulate traffic under changing operation conditions for its vehicles and to predict them. They can also be effective in the process of managing the operating conditions of vehicles in the information analysis system V2I of monitoring and control proposed by the authors.
The implementation of the described method for managing vehicles with changes in the atmospheric and climatic
conditions of operation and the culture of operation requires further research.
The study took into account changes in transport and road conditions for the operation of vehicles. The influence of public transport on the results of the simulation modelling presented in the work was also researched. At the same time, the atmospheric and climatic conditions of operation and the culture of operation of vehicles were taken constant, although they had been included in the model. In the future, it is planned to take into account the influence of these factors in dynamics.
9. Conclusions
1. A dynamic model has been built for determining the optimal parameters of the operation of vehicles in a transport hub, which takes into account a large number of factors affecting the process of movement. The model can be used in the formation of an intelligent transport system of a city to integrate the software in the infrastructure of the transport network.
2. The operating conditions for vehicles in the researched transport hub were analysed. Graphic models of the movement of the vehicles in it were built and the influence of public transport on the process of movement in the hub was considered. The obtained models and the values of the vehicle operation parameters were taken into account when performing the simulation modelling.
3. A simulation model has been created for choosing the optimal operating conditions for vehicles, taking into account the peculiarities of public transport, which can be used to solve the problems of optimizing the movement of vehicles. The model was tested on a section of a transport network. Its adequacy was confirmed by appropriate calculations. As a result of the optimization, the average travel time through the considered transport hub and the number of vehicles in traffic congestion were reduced. The developed simulation models can be used in the process of rebuilding a transport hub to simulate traffic under changing operation conditions for its vehicles and to predict them.
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