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Eastern-European Journal of Enterprise Technologies ISSN 1729-3774 3/3 ( 99 ) 2019
30
A. Prokhorchenko, A. Panchenko, L. Parkhomenko, G. Nesterenko, M. Muzykin, G. Prokhorchenko, A. Kolisnyk, 2019
1. Introduction
Under current economic conditions, railroad compa-
nies-carriers must solve complex tasks on adapting an
operating model of railroad freight transportation to the
requirements of consignees. The market of transport services
increasingly faces the need for personalized mobility and
logistics solutions that ensure lower risks in the transporta-
tion process. As practice shows, the technological process of
cargo transportation by railroads has a lot of serious draw-
backs, the main of which is the lack of predictability of the
duration of operations execution in the process of transpor-
tation [1]. The high degree of uncertainty in the execution of
a transportation process is particularly characteristic of the
railroad system of Ukraine (AT “Ukrzaliznytsya”), which
belongs to railroads with a system of trains traffic not com-
plying with a departure schedule. The lack of information
about the traffic time of a cargo dispatch included in the
composition of trains leads to a mismatch between the plan
of transportations and actual operational conditions. There
are failures to meet the terms of unloading wagons and to
supply empty wagons for loading, which are due to errors in
determining a timely arrival of these wagons. That increases
the turnover time of freight cars, causing damages to cars’
owners, and increases the costs of logistics for consignees
due to larger reserves required to meet demand [2].
In this connection, there is a need at present to construct
a system for transportation planning with a possibility to
predict the stages within a transportation process, which
would make it possible to track stages in the transportation
FORECASTING THE
ESTIMATED TIME OF
ARRIVAL FOR A CARGO
DISPATCH DELIVERED BY
A FREIGHT TRAIN ALONG
A RAILWAY SECTION
A. Prokhorchenko
Doctor of Technical Sciences, Associate Professor*
E-mail: andrii.prokhorchenko@gmail.com
A. Panchenko
V. N. Karazin Kharkiv National University
Svobody sq., 4, Kharkiv, Ukraine, 61022
L. Parkhomenko
PhD, Associate Professor*
G. Nesterenko
PhD, Associate Professor
Department of Management of Operational Work***
M. Muzykin
PhD, Senior Lecturer
Department of Life Activity Safety***
G. Prokhorchenko
Аssistant*
A. Kolisnyk
Аssistant, Postgraduate student
Department of Freight and Commercial Management**
*Department of Management of Operational Work**
**Ukrainian State University of Railway Transport
Feuerbach sq., 7, Kharkiv, Ukraine, 61050
***Dnipro National University of Railway Transport
named after academician V. Lazaryan
Lazariana str., 2, Dnipro, Ukraine, 49010
Запропоновано метод прогнозування очiкува-
ного часу прибуття (ЕТА) вантажної вiдправки
з урахуванням визначення тривалостi руху ван-
тажного поїзда дiльницею для залiзниць з систе-
мою руху поїздiв без дотримання розкладу вiд-
правлення. Характерною особливiстю залiзниць з
такою системою руху є складнiсть передбачення
стадiй перевiзного процесу, що вимагає розробки
дiєвих методiв прогнозування. На основi кореля-
цiйного аналiзу визначено залежнiсть загальних
макрохарактеристик поїздотоку та iндивiдуаль-
них параметрiв вантажного поїзда на його три-
валiсть руху на дiльницi. Запропоновано пред-
ставити залежнiсть прогнозної тривалостi руху
поїзда залiзничною дiльницею вiд наступних фак-
торiв: iнтенсивнiсть, щiльнiсть руху поїздопо-
току на дiльницi, частка пасажирських поїздiв в
межах загального поїздопотоку, довжина поїзда
та його маса брутто.
На основi порiвняльного аналiзу за показника-
ми точностi та адекватностi декiлькох методiв
регресiї для прогнозування ЕТА вантажної вiд-
правки вибрано регресiйну модель на основi штуч-
ної нейронної мережi – MLP. Для пошуку структу-
ри MLP застосовано метод перехресної перевiрки,
який передбачає оцiнювання достовiрностi мате-
матичної моделi за критерiєм точностi – MAE та
адекватностi – F-тестом. Знайдено структуру
MLP, яка складається з пятьох скритих шарiв.
Проведено прогнозування тривалостi руху поїз-
да в парному напрямку руху на дiльницi Основа-
Люботин. Для даного прогнозу значення MAE
склало 0,0845, що є достатньо високою точнiстю
для задач такого типу та пiдтверджує ефектив-
нiсть застосування MLP для рiшення задачi про-
гнозування ЕТА вантажної вiдправки.
Данi дослiдження дозволяють в перспективi
розробити автоматизовану систему прогнозуван-
ня ЕТА вантажної вiдправки для залiзничної сис-
теми зi змiшаним рухом та вiдправленням ван-
тажних поїздiв без дотримання нормативного
розкладу
Ключовi слова: залiзнична мережа, логiсти-
ка, очiкуваний час прибуття, машинне навчання,
штучна нейронна мережа
UDC 656.222
DOI: 10.15587/1729-4061.2019.170174
31
Control processes
process of cargo dispatch. One of the directions to improve
a system of planning is the implementation of a function of
periodic notification about the status of a cargo dispatch in
a train, which includes the estimated time of arrival at the
destination (ETA). Given that the duration of train traffic
is affected by different factors, information about which is
limited in existing automated systems of transportation
management, the possibility of applying any expert methods
for the prediction of transportation process is greatly com-
plicated. There emerges that task on implementing a method
for predicting a cargo dispatch ETA, which could be easily
automated and scaled for a problem of large dimensionality.
Thus, it is a relevant task to construct a method for
predicting the expected time of arrival of a cargo shipment
included in a mixed train in order to reduce the risks posed
by train flows, meant to follow the plan of delivery but trans-
ported by a railroad system where the schedule of freight
trains departure is not obeyed.
2. Literature review and problem statement
Under conditions for the digitalization of transporta-
tion processes there is a possibility to handle large amounts
of data, which could be applied for constructing more effi-
cient systems to plan transportation with the possibility to
predict stages in a transportation process. One of the func-
tions that underlie modern successful planning systems
is the function for predicting the expected time of arrival
(ETA) [3]. This has led to the emergence of research aimed
at the development of methods to improve the accuracy of
forecasting the expected time of arrival (ETA) in many
transportation sectors.
Quite a lot of studies on the prediction of ETA are per-
formed in the automotive and aviation industries [4–6]. To
improve the information system that notifies passengers
about the expected time of arrival of buses to stops along
a route, artificial neural networks have been successfully
applied [4]. Paper [5] reports a system of ETA forecasting,
which is based on different regression models and recurrent
neural network (RN N), the results from which are select-
ed based on several indicators for accuracy. The results
obtained confirm that the proposed system of forecasting
generates more accurate predictions with a much smaller
standard deviation than existing systems in EUROCON-
TROL. Authors of [6], in order to predict a 4D trajectory
of aircraft routes at a terminal maneuvering area, have used
the new hybrid model that processes data based on cluster-
ing and Multi-Cells Neural Network (MCNN) to predict
ETA. Comparing the obtained results with the forecasts
constructed using a Multiple Linear Regression (MLR) has
proven the effectiveness of the proposed hybrid machine
learning model. Based on the above findings, we can con-
clude that the application of machine learning methods to
predict ETA is effective, however, the constr ucted prediction
models cannot be applied to railroad transportation.
Very little attention has been paid to solving the task
on predicting the execution time of cargo dispatches at the
railroad network of Ukraine and similar networks [7–9].
Paper [7] used an artificial neural network (ANN) of the
perceptron type in order to determine time points of arrival
of freight trains at technical stations. The authors recom-
mended to use such input parameters for the model as the
time and date (day of week, month) of train departure from
a nearby technical station, as well as the mass of the train
and the type of a locomotive. Given the conditions of freight
trains departures without complying with the schedule,
the information about the departure time and the type of a
locomotive can be obtained only under an operational mode.
This affects the accuracy of forecasting, and prevents the
application of the constructed model for tactical forecasting
tasks. To determine the track of arrival, a mathematical
model based on ANN has been applied [8]. A given mathe-
matical model solves the problem on classification in terms
of selecting a variant of freight train arrival under an oper-
ational mode and does not make it possible to predict the
duration of the train arrival under conditions of change in
the operational work of a railroad station. Resolving such a
task is addressed in work [9], which proposed using a neu-
ral-network model to solve the task on choosing the track of
train arrival at a shunting station, which makes it possible to
take into consideration the forecast of train arrivals and the
forecast of development of events at a receiving park. The
authors stress the effectiveness of application of the artificial
neural network for forecasting tasks, however, the study was
not directly focus on forecasting a cargo dispatch ETA. The
research that is maximally close to the set task on ETA fore-
casting is reported in [10]; ot addresses modelling of scenar-
ios for moving cargoes along the Ukraine’s railroad system
supply chains. The authors constructed the algorithm that
generates the scripts of delivery events in order to determine
the control time points according to technological norms
and practical experience. The disadvantage of this approach
to predicting the duration of dispatch is the lack of a possi-
bility to account for changes in the operating conditions at
railroad stations and to take into consideration the charac-
teristics of a transportation process on order to improve the
forecasting accuracy. There is no information regarding the
accuracy of the proposed method.
In the field of global railroad transport, of interest
is research [11], which points to the importance of ETA
forecasting in order to improve the efficiency of railroad
transportation in the United States, and reduce costs. The
functions of ETA notification make it possible to enhance
the level of customer service and to further implement the
automated planning of transportation. It has been proposed
to use the algorithms of machine learning, built using the
operational data on the railroad CSX Transportation, in
order to construct a system of ETA notification in real time.
The research proved the possibility to improve the accuracy
of ETA forecasting when using a vector support regression
model and the model of deep neural networks. The greatest
accuracy was demonstrated by the ensemble method of ma-
chine learning, Random Forest. However, the disadvantage
of this approach is the large amount of memory to store
the derived models. In addition, there is a tendency of the
algorithm to retrain under conditions of handling data with
much noise, which is quite typical for a railroad transporta-
tion system where a departure schedule is not obeyed.
Paper [12] addresses the development of methods for
forecasting trains traffic in time and space under an on-line
operation mode. The constructed methods are proposed for
a future consultative system of railroad transport dispatch.
The author stresses the importance of using methods for
predictive reasoning and machine learning. In article [13],
similar tasks on predicting the arrival time of a train were
solved in a different field – improvements to the operation
of traffic signals near the highway-rail grade crossings
Eastern-European Journal of Enterprise Technologies ISSN 1729-3774 3/3 ( 99 ) 2019
32
(HRGC). The results confirm the importance of applica-
tion of prediction methods in the construction of industrial
dispatching systems. Research [14] addresses the impact of
crossings in the Melbourne metropolitan area, Australia, on
the overload in a network of automobile flows. At the macro
level of analysis of dependences, the relationship between the
frequency of trains, the percent change in traffic time and
the magnitude of a flow of cars has been established. The
derived equation can predict changes in the time of cars flow
traffic considering the number of railroad crossings and the
frequency of trains.
This confirms the effectiveness of applying data charac-
terizing a transportation process at the macro level. Thus, one
of the directions to improve a method of ETA prediction for a
railroad system where trains do not comply with a departure
schedule is to take into consideration the macrocharacteris-
tics of train f lows traffic at a railroad station and to establish
a dependence of the time required for a freight train to travel
along a railroad section on operational conditions.
Scientific achievements are actively implemented into in-
dustries; thus, the project F-MAN that implied the constr uc-
tion of a wagon fleets management system for the railroad
network in the European Union has successfully employed
an ETA prediction module [15]. ETA calculation depends
on notifications about the location of a wagon sent by its
onboard devices and is based on the constructed cumulative
probability distribution functions for the time that a wagon
would require to reach its destination. The module for calcu-
lating ETA is based on innovative concepts and algorithms
that are able to improve and adjust effectiveness during op-
eration of the system (self-learning algorithms).
The association RailNetEurope (RNE), which brings to-
gether European operators of railroad infrastructure, active-
ly introduces experimental projects aimed at implementing
the functions of ETA prediction for trains in international
traffic [16]. The examples of implementing the systems of
ETA forecasting in the railroad network of the European
Union confirmed the relevance of research in that article.
However, the EU’s railroads have a less degree of uncer-
tainty in comparison with railroad systems similar to AT
“Ukrzaliznytsya” where there is a system of freight trains
traffic that does not comply with a schedule of departures.
This requires the development of new forecasting methods,
which would take into consideration the specificity of a
transportation process, as well as limited information.
The task on improving the function of ETA prediction
has received much attention in all transportation sectors.
To improve the accuracy of ETA forecast, a variety of meth-
ods are used, which make it possible to account for factors
inherent to the examined processes. However, there are
almost no studies addressing the construction of methods
for the prediction of the expected time of arrival of a cargo
dispatch for the railroads with a system of trains traf fic with-
out complying with the timetable of departures, where the
specificity of transportation organization dictates a consid-
erable uncertainty of the transportation process. Lately, the
methods of machine learning have been commonly used to
forecast ETA. To improve the accuracy of forecasting under
conditions of significant uncertainty, one should take into
consideration information about the macrocharacteristics of
train flows traffic at a railroad station. All this necessitates
research in the respective field, which is the basis for the
automation of a cargo dispatch ETA forecasting aimed to
reduce the risks in a transportation process.
3. The aim and objectives of the study
The aim of this study is to construct a method for the
prediction of the expected time of arrival of a cargo dispatch
that would take into consideration determining the time
that it would take for a freight train to travel a station. That
could improve the quality of predicting a transportation
process and, as a result, the planning efficiency for railroads
with a system of freight trains traffic where the timetable of
departures is not obeyed.
To achieve the set aim, the following tasks have been
solved:
– to analyze the macrocharacteristics of train flows
traffic along a railroad section and to establish dependences
of time that it takes for a freight train to travel a section on
operating conditions;
– to perform a comparative analysis of regression meth-
ods to predict the time that it would take for a freight train
to travel a railroad section;
– to formalize a mathematical model to predict the time
that it would take for a cargo dispatch in a mixed train to
travel a section;
– to check the accuracy and adequacy of the constructed
mathematical model for forecasting the time that it would
take for a freight train to travel a section.
4. Features in the prediction of the expected time of
arrival under conditions when trains depart without
observing the schedule
Implementation of the function of ETA prediction (esti-
mated time of arrival) at a railroad network requires taking
into consideration the specificity of organization of the
operating model of a railroad system. A given function must
be implemented for each cargo dispatch ‒ for a single car, a
group of wagons, or a route, which corresponds to the num-
ber of cars within the complete train. Given that a network
has a large number of dispatches, the task is to implement a
method of forecasting, which could be easily automated and
scaled for a problem of large dimensionality. The function
of ETA prediction should provide a forecast from a station
where a train is formed to the station of destination, which
requires taking into consideration the topology of a railroad
network and the technology of transportation. A technologi-
cal process of the freight train traffic implies scheduled stops
of the train at technical service stations (sorting or sectional
stations) in order to change locomotives or locomotive crews
and for technical and commercial inspections of cars to en-
sure traffic safety. For cargo dispatches that require the cal-
culation of ETA, the direction and the category of a train by
which they would be delivered are known in advance. This
information is defined by a train formation plan that is com-
piled and approved for each freight year [17]. That makes it
possible to define the route of a cargo dispatch in advance
and specify those sections and stations for which it would
be required to predict the duration of travel. Though the
graph of a railroad system is highly branched and has loops,
a route of the examined wagons can be mapped linearly, by
listing consistently all the technical stations at which the
train is to stop. Fig. 1 shows a schematic of the selected route
for a cargo dispatch from a forming station to the station of
destination, which for this cargo is a transfer to maritime
transportation.
33
Control processes
Fig. 1. Schematic of linear decomposition of a route in order
to predict the expected time of arrival of a train at
the destination station
The total route duration can be divided into two com-
ponents – the time that trains spend at technical service
stations and their traffic along railroad sections between
them. Operating conditions and factors that affect the time
that cars spend at stations and the time when they run differ
and require separate study. It is proposed to investigate the
factors and construct a mathematical model to predict the
time that it would take for a freight train to travel a railroad
section in order to calculate the expected time of arrival at a
technical station along the route.
5. Original data and study into conditions of trains
travelling along railroad sections
5. 1. Studying the macrocharacteristics of train f lows
traffic at a railroad section
As practice shows, the time that it takes for a train to
travel a railroad section does not coincide with the planned
duration, regulated by the timetable of trains. According
to research [18, 19], the railroad systems, specifically AT
“Ukrzaliznytsya”, where the principle of traffic is based on
dispatching freight trains “when ready” without observing
the schedule of regulatory timetable of trains, are charac-
terized by considerable uncertainty. Thus, there is a devia-
tion of the actual time of traffic from the planned one that
reaches 20‒40 %. This can be explained by the inability to
determine the local velocity of a train in line with a stan-
dard schedule, based on the traction calculation of traffic
duration, which considers the motion of a single train along
the section without accounting for the interdependence
of trains in a flow [20]. However, even adding
the reserves of time does not make it possible to
compensate for the arising deviations from the
planned traffic. This, to a greater extent, is due
to the problems of mutual influence of trains
when their flows increase at railroad sections.
The network of AT “Ukrzaliznytsya” most com-
monly employs a system of interval traffic of
trains along a section, called “auto-lock”, which
refers to systems based on the principle of delim-
itation of intervals between trains “fixed block
signaling”. Under such conditions, increasing the
number of trains at a section increases the time
that it takes for a train to travel a section due
to the unsynchronized load on block sections.
As a result, trains move to the yellow and red
traffic light signals, which requires a decrease
in speed. According to existing regulations, the
train running to the yellow signal must move
at lower speed than to green [18]. In addition,
the time that it takes for freight trains to travel
a railroad section depends on numerous factors.
These include setting a temporary traffic speed limit in
order to provide for “windows” needed for repair and mod-
ernization of the infrastructure. As swell as the length and
weight of trains, which affect the execution of operations
of crossing and overtaking. The most important factor is
the unaccounted-for processes of interdependence of trains
when their number in a f low increase.
Given the difficulties related to predicting the time that
it takes for freight trains to travel a section, in this study we
propose exploring the macrocharacteristics of the process
of train flows’ interdependence at a railroad section. For
solving the task on analyzing patterns in the organization of
trains traffic, an important role belongs to the fundamental
diagram of a traffic flow [21]. According to this approach, a
train flow can be considered a continuous medium, and its
macrocharacteristics can be described by the relation of a
flow’s speed and density and the intensity of train traffic,
which is called the fundamental expression of the transport
flow or a train flow
() (),
ij ij ij ij
λ ρ =ρ ⋅ν ρ (1)
where
()
ij ij
λρ is the intensity of traffic, trains/hour; ij
ρ is
the flow density, trains/km;
()
ij
νρ
is the local speed of
trains traffic, km/h. All three quantities in expression (1)
are bound via a complicated relationship, and, therefore,
research aimed at establishing these dependences could
predict the time that it takes for a train to travel a section
considering the individual parameters for a train and the
macro-parameters for the traffic of a general train flow.
To search for an effective method for predicting the ex-
pected time of arrival of a freight train, in the current work
we propose conducting an experimental study along the
section Osnova-Lyubotyn (Ukraine). It is one of the most
loaded railroad sections at Kharkiv railroad node of the
regional branch “Southern Railroad” at AT “Ukrzaliznyt-
sya”. This section is a point along the routes of train flows
with exported and transit cargoes, which are transported
to/from the railroad stations at Odesa region. The scheme
of section Osnova-Lyubotyn is shown in Fig. 2. The section
Osnova-Lyubotyn has an operational length of 32.2 km, two
tracks, powered by direct current.
ti
j
ti
j
.ti
j
.
ETA for a destination station
station i=1
station j=2
station nstation 3
Odd direction
Fig. 2. Graph of the railroad junction at Kharkov node of the regional
branch “Southern Railroad” at AT “Ukrzaliznytsya”, which combines
railroad sections along the direction Osnova-Lyubotyn
Eastern-European Journal of Enterprise Technologies ISSN 1729-3774 3/3 ( 99 ) 2019
34
The experimental study is based on actual data on op-
eration along the section Osnova-Lyubotyn at the railroad
network AT “Ukrzaliznytsya” over a period of maximum
volume of transportation in July–September, 2017. Fig. 3
shows the dependence of daily intensity, density, on time
that it takes for a freight train to travel along the section
Osnova-Lyubotyn in an even direction.
Under conditions of the mixed model of a railroad section
operation, the speed of a freight train, and, as a result, the
duration of traffic, are affected by the proportion of pas-
senger trains within an overall train flow. Fig. 4 shows the
dynamics of change in the share of passenger traffic within
an overall train flow over 24 hours, as well as average over
24 hours, for three months (July–September, 2017) along
the section Osnova-Lyubotyn.
Fig. 4. Dependence of the number of passenger trains on
the overall train flow at the section Osnova-Lyubotyn:
a – dynamics of change in the share of passenger traffic
within the overall train flow over 24 hours; b – dependence
of frequency on the percent share of passenger traffic on
average over 24 hours
Our analysis of the dynamics of change in the share of
passenger traffic within the overall train flow within 24 hours
testifies to the irregularity in the traffic of passenger trains.
Fig. 4, a shows a significant increase in the share of passenger
trains in the morning hours. This can be explained by the
location of the section Osnova-Lyubotyn near a big passenger
station, Kharkiv-Passenger. It should be noted that in the
railroad systems of mixed traffic a priority is
given to passenger trains that run in line with
the regulatory timetable. The fact that passen-
ger trains obey the schedule when freight trains
depart without observing the schedule leads to
the increased delays of the latter at a section.
Given that the greatest frequency of passenger
trains is on average 20 % within the overall
train flow over 24 hours, one can make an as-
sumption about the impact of a given factor on
the traffic duration of a freight train.
5. 2. Analysis of operational parameters
affecting the time that it takes for a freight
train to travel along a railroad section
In addition to the general macrochar-
acteristics of a train flow, the duration of a
train traffic is affected by its individual set-
tings. One of the most essential parameters
for a train, which depend on the constraints
for infrastructure and define its operating
conditions for passing along a section, is a
conditional train length (the number of cars
in a train) and its weight gross. To theoret-
ically substantiate the accepted factors that
affect the total time that it takes for a train
to travel a section, in this work we proposed to investigate
correlation connections among these factors for an effec-
tive parameter. For the sample size (N=425), we calcu-
lated correlation coefficients by Pearson. The determined
correlations are significant at the level p<0.05. Fig. 5
shows the calculated correlation matrix by Pearson [22].
A data analysis reveals (Fig. 5) that all variables demon-
strate positive correlation and are statistically significant.
According to the assessment of the tightness of connections
based on the “Chaddock table”, relationships can be char-
acterized as moderate and weak. This can be explained by
the nonlinearity of dependences and the weakly-structured
statistical data that can be evaluated rather poorly by the
Pearson correlation. In addition, there are no any other
readily available data that could make it possible to describe
the process related to a freight train running along a section.
Under such conditions, it is appropriate to construct a math-
ematical model for predicting the expected time of arrival of
a freight train based on available information.
According to the above, in the current work it is pro-
posed to represent the dependence of a predicted time that it
takes for a train to travel along a section ij
t on the following
factors: the intensity of traffic, the density a traffic train
flow along a section, the share of passenger trains within
the overall train flow, the conditional length of a train (the
number of cars in a train) and its gross weight. According
to the specified factors, the implicit mathematical model for
predicting the time that it takes for a train to travel along
a railroad section can be described by a dependence of the
following form
a b
c d
Fig. 3. Interdependence between the intensity, density, and duration of
train flow traffic along the section Osnova-Lyubotyn in an even direction:
a – dependence of daily average duration of train traffic in the density
of trains at a section; b – dependence of daily local speed on intensity;
c – dependence of intensity on density; d – 3D dependence of intensity,
density, and traffic duration
share of passenger trains in overall
train flow
frequency
hours within 24 hours
share of passenger
train
s
share of
freight trains
ab
35
Control processes
( )
,,, , ,
ij ij j ij ij ij
t f mQ= λρφ
(2)
where ij
t is the time that it takes for a train to travel along a
railroad section, limited by technical sections, respectively,
i and j, h; ij
λ is the intensity of trains traffic along a sec-
tion, h−1; іj
ρ is the density of train flow at a section, trains/
km;
ij
φ
is the proportion of passenger trains within the
overall train flow, %;
ij
m
is the conditional train length
(the number of cars in a train), cond. wag.;
ij
Q
is the gross
weight of a train, tons.
6. Search for a method to predict the time that it takes for
a freight train to travel along a railroad section
At the first stage of the search for a method to predict the
time that it takes for a freight train to travel along a railroad
section, in this work we compared several methods of regres-
sion analysis to search for dependence (2). To assess quality
of the built models, we used a mean absolute error (MAE),
the value for coefficient of determination R2 and a Fisher
criterion [22]. Comparative analysis of regression methods
to predict the time that it takes for a freight train to travel
along a railroad section is given in Table 1.
Table 1
Comparative analysis of regression methods to predict the
time that it takes for a freight train to travel along a railroad
section
Method
Mean abso-
lute error,
MAE
Value for
coefficient of
determina-
tion R2
F-test
Linear regression model 0.09559373 0.4648786 78.18613485
Regression model based
on a neural network 0.09185588 0.596569902 131.4408072
Ridge regression model 0.09942611 0.443689963 75.91870887
Bayesian ridge
regression model 0.09582799 0.464744424 75.91870887
Based on the specified indicators (Table 1), the worst
among the selected methods has proven to be a multiple
linear regression model [22], which confirms the above con-
clusions regarding dependence (1), which describes complex
non-linear processes of section operation. The most appro-
priate method was a regression model based on the artificial
neural network, a multi-layer perceptron, MLP. Given that
the comparative analysis employed the neural network with
standard default settings, in order to improve the accuracy
of predictions it is appropriate to adjust the architecture of
an artificial neural network so
that it matches the examined
problem, which we solve.
7. Design of the architecture
of an artificial neural network
to predict the time of freight
train traffic
An artificial neural network
(ANN) refers to the methods of
machine learning (ML) [23]; it
has parallel computing struc-
tures, consisting of nonlinear
elements in terms of compu-
ting ‒ neurons [24]. This makes
it possible to establish non-lin-
ear dependences over a rath-
er short time, which is ensured
by its scalability. High adapt-
ability and the uniformity of
analysis and design of AN N are
relevant under conditions of in-
dustrial application within the
existing AT “Ukrzaliznytsya”
network “Unified Automated
Control System of Cargo Transportation”. However, such
shortcomings of ANN as a lack of transparency, compli-
cated choice of architecture, and strict requirements to
a training sample, require research into the feasibility
of ANN application for a task on predicting the time
that it takes for a freight train to travel along a section.
The current work employs the basic type of a neural net-
work for the construction of a prognostic model – a multi-lay-
er perceptron (MLP) that uses the method of learning with a
trainer [25]. The principal diagram of the model for predicting
the time that it takes for a freight train to travel along a sec-
tion based on MLP is shown in Fig. 6.
Fig. 6. Principal diagram of the model for predicting the time
that it takes for a freight train to travel along
a section based on MLP
var5 – share of percentage trains, %
var1 – conditional train length, wagons
var2 – train gross weight, tons
var3 – train flow intensity, hours−1
var4 – density, trains/km
var6 – train run duration, hours
Fig. 5. Correlation matrix by Pearson to analyze the influence of a train’s individual
parameters and the macrocharacteristics of a train flow on the time that it takes for a train
to travel along the section Osnova-Lyubotyn
Train run time
Input x
Traffic intensity
Traffic density
Share of passenger
traffic
Train length
Train gross weight
Output y
Hidden Layers
Weights Neurons
Eastern-European Journal of Enterprise Technologies ISSN 1729-3774 3/3 ( 99 ) 2019
36
To define the structure of MLP, we have applied a
cross-validation method. A given method implies the reli-
ability estimation of a mathematical model based on the cri-
terion of accuracy ‒ MAE, and adequacy – F-test. The sam-
ple of data N=425 was divided into a training set, 60 % of the
total number, and a testing set. The testing set was randomly
selected from the overall data set. MLP was adjusted using
an error backpropagation algorithm. The method of learning
with a trainer for a mathematical model of forecasting based
on MLP is implemented cyclically through learning based
on a training set, which is structure of the following form
<input 1
Xκ,…, n
Xκ – output 1
Yκ>,
where
κ
is the number of the sample within a training
sample.
After learning, there is a check of the model based on a
testing set that has a similar structure.
7. 1. Results of predicting the time that it takes for a
freight train to travel along a railroad section
We defined the structure and carried out checking pro-
cesses for accuracy and adequacy of the predictive neural
network automatically in the Python environment. The re-
sults of cross-validation based on operational data along the
section Osnova-Lyubotyn in an even direction are shown in
Fig. 7. While implementing the method of cross-validation
the algorithm used 4,417 iterations. To test the adequacy
of the neural network, the estimated values for Fisher sta-
tistics (F-test) were compared with the permissible ones
(F-perm=2.42). The trend equation for MAE is negative; it
has the following parameters y=–1.18е–05х+0.326, a trend
equation for calculating the values for Fisher statistics takes
the form y=3.9е–0.5х+3.38.
a
b
Fig. 7. Results from cross-validation: a – dependence of
mean absolute error on the number of checking iterations;
b – dependence of Fisher criteria on the number of checking
iterations
Based on the method of cross-validation, we have defined
the structure of MLP with six hidden layers of the network
that have the following numbers of neurons: the first layer ‒
5 neurons, the second ‒ 10, the third ‒ 5, the fourth ‒ 5, the
fifth ‒ 20, the sixth – 20. The neural network employed a sig-
moid transfer function; the error backpropagation method was
used as a configuration algorithm [24]. Based on the testing
set, in the current work we predicted the time that it takes
for a train to travel in an even direction along the section Os-
nova-Lyubotyn. For a given forecast, the value for MAE was
0.0845. Mean deviation does not exceed the error of 4.43 min-
utes, which is a rather high accuracy for problems of this type.
a
b
Fig. 8. Results of predicting the time that it takes for
a freight train to travel along the section Osnova-Lyubotyn in
an even direction based on MLP: a – dependences between
the intensity and duration of traffic in the modelled and test
values; b – dependences between the density and traffic
duration in the modelled and test values
To confirm robustness of the obtained results, the pro-
posed method of forecasting has been verified based on opera-
tional data at the section Osnova-Lyubotyn in a reverse (odd)
direction. Based on analysis of practical operation of the exam-
ined section, one can argue that the traffic of trains along the
section in the opposite direction does not fundamentally differ
from even direction in terms of operational characteristics.
That makes it possible, under conditions of limited amount of
data, to “roughly” check the trained neural network. However,
to improve the accuracy of ETA forecasting in the reverse
direction, the further research implies constructing a separate
neural network based on the proposed method. The results
obtained have confirmed reliability of the built neural network
and a possibility to apply it for predictions of this type.
8. Discussion of results of applying the constructed
mathematical model for predicting
the expected time of arrival
The obtained results from predicting ETA for a cargo
dispatch delivered by a freight train along a railroad section
error trend minimal value
МАЕ
4
3
2
1
0
Fcrit
F-test trend maximum Fperm
12
10
8
6
4
2
0
error trend minimal value
МАЕ
4
3
2
1
0
Fcrit
F-test
trend maximum Fperm
12
10
8
6
4
2
0
density
test predicted
traffic time
0.425 0.45 0.475
0.5 0.525
0.55 0.575
2
1.5
1
0.5
0
intensity
test predicted
t
r
affic time
0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
density
test predicted
traffic time
0.425 0.45 0.475
0.5 0.525 0.55 0.575
2
1.5
1
0.5
0
intensity
test predicted
t
r
affic time
0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
37
Control processes
based on a multilayer neural network confirm the effective-
ness of a given method. The disadvantage of classic methods
of prediction, which were tested when solving the stated
problem within the framework of the current research, is the
need to adjust the model for each section. When applying
the resulting neural network to predict ETA, a given draw-
back is eliminated. A neural-network structure can be easily
trained and scaled for other railroad sections. The advantage
of the proposed method is the possibility to use it under
conditions of limited information about a transportation
process, as well as accounting for changes in the operational
conditions at a section. The combination of macrocharacter-
istics for train flows at a section and the individual parame-
ters for a train has made it possible to improve the accuracy
of forecasting the time that it takes for a freight train to
travel along a railroad section compared when compared to
the approach suggested in study [10].
The quality of forecasts derived from the trained MLP,
verified for accuracy and adequacy, can be improved with
the accumulation of the history of cargo dispatches delivered
by mixed freight trains.
The constructed method of forecasting is the first stage in
research aimed at designing a system of ETA forecasting for
a cargo dispatch along the entire route. The research could
prove useful when constructing an automated system for ETA
forecasting for a railroad system with mixed traffic where the
timetable of departures of freight trains is not obeyed. The
proposed method of forecasting needs additional checking at
other sections of a railroad network. In order to solve the set
task comprehensively, the further research would tackle the
construction of a mathematical model to predict the time that
a cargo dispatch spends at technical sections.
9. Conclusions
1. We have examined operational conditions for a freight
train that travels along a railroad section. It has been pro-
posed, to improve the accuracy of forecasting the time that
it takes for a train to travel along a section, to take into
consideration, in addition to general macrocharacteristics
of a train flow, the individual parameters for a freight train.
To theoretically substantiate the accepted factors that affect
the total duration of train run along a section, we performed
correlation analysis. The calculated Pearson coefficients
have positive correlation and are statistically significant.
The relationships among the following factors have been
established: the intensity of traffic, the density of train flow
traffic along a section, the share of passenger trains within
the overall train flow, the conditional length of a train and
its gross weight, which all affect the time that it takes for a
train to travel along a section.
2. To define a method for predicting the time that it
takes for a freight train to travel along a railroad section,
we compared several methods of regression analysis: a linear
regression model, the regression model based on a neural
network; ridge regression model; Bayesian ridge regression
model. Based on such criteria of comparison as a mean abso-
lute error (MAE), the value for coefficient of determination
R2, and F-criterion by Fisher, the most appropriate method
chosen is the regression model based on an artificial neural
network the type of a multi-layer perceptron, MLP, trained
by a trainer.
3. To improve the accuracy of prediction, the current
work has formalized a mathematical model based on the
artificial neural network architecture design. To define the
structure of MLP we applied a cross-validation method,
which implies the assessment of reliability of a mathematical
model based on the criterion of accuracy ‒ MAE, and ade-
quacy – F-test. The structure of the neural network has been
established, which consists of five hidden layers. Our exper-
imental study aimed at training a given neural network was
based on historical data on trains traffic along the railroad
section Osnova-Lyubotyn.
4. To verify the constructed mathematical model, we
forecasted the time that it takes for a train to travel in an
even direction along the section Osnova-Lyubotyn based
on the testing set. For a given forecast, the value for MAE
was 0.0845. Mean deviation does not exceed the error of
4.43 minutes, which is a rather high accuracy for problems
of this type. The adequacy of the obtained prediction results
has been tested by the Fisher criterion. The results derived
have confirmed the reliability of the constructed neural net-
work and a possibility to apply the constructed method for
ETA prediction for a cargo dispatch delivered by a freight
train along a railroad section.
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