“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
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Volume-82, Issue-2, May -2025
70
MAIN ISSUES TO BE RESOLVED IN ORGANIZING
THE MOVEMENT OF PASSENGER TRAINS
Bozorov R.Sh.
1
а
, Boboev D.Sh.
1
d
,
1
Tashkent state transport university, Tashkent, Uzbekistan
Abstract:
This article briefly describes the mathematical model of
passenger flow planning in railway transport. Also, the factors
affecting the speed of trains are known, which can be divided into
the classification of factors affecting fuel consumption and
throughput. The speed of trains is directly related to the delivery
time of goods. However, during transportation, the time spent by
goods on trains is only one third of the delivery time. The
remaining delivery time, including the time spent by goods at
stations to perform technical and technological operations, is not
directly related to the speed of travel. The speed of trains is
studied in terms of maximum permissible, traffic, technical,
section, route speeds. Speed, like all elements of the transport
process technology, is divided into two types. One is regulatory
and technological documents regulating the speed, and the second
is their implementation. Currently, more attention is paid to the
development of regulatory technological documents than to their
implementation.
Keywords:
Freight and passenger trains, empty containers, wind gusts,
wind speed, aerodynamic pressure, sand drift, obstacles.
The following tasks are solved when organizing passenger train traffic:
- determination of the volume of passenger traffic taking into account the
dynamics of promising development;
- selection of train weight, locomotive type, composition (scheme), speed of
movement by train category;
- calculation of the optimal option of the train formation plan;
- determination of the volume of movement according to the category of
passenger trains;
- choosing a scheme for stopping passenger trains based on the train running
schedule;
- scheduling of train traffic with connecting passenger trains and freight trains;
- determination of the turnover of passenger trains that provide high indicators
when using the train operating schedule and rolling stock;
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
5.449
https://scientific-jl.com/ped
Volume-82, Issue-2, May -2025
71
- setting technical standards for passenger work and calculating
indicators [1-10].
The volume of passenger flow is determined on the basis of reporting data from
previous years, including Express data on the flow of passengers at large stations and
reports on the number of passengers of the train. The disadvantage of such a calculation
is that failures in passenger transportation are not taken into account. To determine the
volume of passenger flow, it is advisable to conduct economic research in areas
belonging to railway lines. On the basis of the analysis of passenger traffic, scheduled
passenger flow schedules are developed, which indicate the number of passengers from
each movement. Passenger flow diagrams are compiled from these tables. Since the
volume of passenger flow in both directions, as a rule, is assumed to be the same, it is
practically enough to draw up a diagram for one line [10-15].
Correlation analysis is used in volitional analysis of Transport volume. In this
case, it is considered in 3 stages:
- drawing up a correlation equation in the general mathematical formula, which
represents the nature of the relationship between the characters studied and the size of
the passengers sent;
- solving the accepted model by finding the parameters of the correlation equation;
- assessment and analysis of the results obtained.
It allows you to draw the following conclusions based on their mathematical
modeling by analyzing and interpreting the graph of changes in the indicators under
consideration over time.
1. Changes in the volume of train flows are directly related to time, i.e.
Y = a
0
+
a
1
∙t
(1)
Where: a
0
, a
1
-required dependency parameters;
t - is time, i.e. the ordinal number of the year.
2. The change in passenger flow volume is expressed as an inverse relationship
over time:
Y = a
0
+ a t
⁄
(2)
3. Passenger flow volume is stable.
The second step, that is, the solution to the accepted correlation model, consists
in finding the parameters of the correlation equations. The values of these parameters
are determined using the least squares method, which means that in a rectangular
coordinate system, the theoretical line must pass at the closest distance to the initial
Real points. Otherwise, for all lines, the difference between the ordinal degrees and the
sum of their squares would exist minimally [16-24].
The parameters of the degree are found by solving the following systems of
equations:
𝑎
0
𝑛 + 𝑎
1
Σt
= Σ
Y
(3)
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
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Volume-82, Issue-2, May -2025
72
𝑎
0
Σt
+
𝑎
1
Σt
2
=
ΣYt,
𝑎
0
Σt + 𝑎
1
(4)
Where: y - is the actual levels of the indicator being analyzed;
N - is the number of levels.
Solving this system allows us to determine the parameters of the equation that is,
the direct connection:
a
0
= ΣY/n, a
1
= ΣYt/Yt
2
,
(5)
for the inverse relation:
𝑎
0
𝑛 + 𝑎
1
Σ
(
1 𝑡
⁄ ) =
ΣY
(6)
𝑎
0
Σ
∙
(
1 𝑡
⁄
)
+𝑎
1
Σ
∙
(
1 𝑡
2
⁄
)
=
ΣY
∙
(
1 𝑡
⁄
).
(7)
Solving the system gives the parameters of the inverse correlation equation.
𝑎
0
= ΣY 𝑛
⁄
,
𝑎
1
=
Σ
∙
(
𝑌 𝑡/
⁄
Σ
∙
(Y/
𝑡
2
)
(8)
Working templates are compiled for calculating parameters, on the basis of which
the parameters of the necessary equations are determined. Parameters of each equation
(indicator) 1-2 listed in tables,
a
0
=
22411,3
/
5
=
4482,26 person.
a
1
=
6883,1
/
10
=
688,31 person.
Table 1
Expected changes in passenger traffic on long-distance routes
Years
Y
t
t
2
t
Y
Ẏ
2020
3340,6
-2
4
-6681,2
3793,95
2021
3060,7
-1
1
-3060,7
5170,57
2022
4446,5
0
0
0
4482,26
2023
6502,0
1
1
6502,0
3793,26
2024
5061,5
2
4
10123
3105,64
Σ=22411,3
Σ
t
2
=
10
Σ
tY=
6883,1
Σ
Ẏ=
22411,3
The formula for calculating the expected volume of passenger traffic on long-
distance routes is:
Ẏ(t)
=
4482,26
−
688,31
∙
t
Expected volumes of passenger transportation on long-distance routes in 2025:
𝑌̇
𝑇
=
4482,26
−
688,31∙5
=
1040,71 person
=
1041 person
Table 2
Prospective changes in passenger flow in suburban transport
Years
Y
t
t
2
t
Y
Ẏ
2024
17357,8
2
4
34715
16815,28
2023
15419,7
1
1
15419.7
14960,83
2022
11235,5
0
0
0
13106,38
2021
11447,0
-1
1
- 11447
11251,93
2020
10071,9
-2
4
- 20143,9
9397,48
Σ=65531,9
Σ
t
2
=10
Σ
tY=
-18544,5
Σ
Ẏ=
65531,9
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
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https://scientific-jl.com/ped
Volume-82, Issue-2, May -2025
73
𝑎
0
=
65531,9
/
5
=
13106,38 person.
a
1
=
18544,5
/
10
=
-1854,45 person.
The formula for calculating the expected volume of passenger transportation on
suburban routes:
Ẏ
T
=
13106,38
−
1854,45
∙
t.
Expected passenger traffic volume on suburban routes for 2025:
𝑌
𝑇
=
13106,38
–
1854,45
∙
5
=
3834,73
∙
kishi.
=
3834 person
Analysis of these tables shows that the correlations are directly related and
determine the growth of passenger traffic in the future. This can be explained by the
following factors:
- increasing tariffs for ticket documents;
- launching high-speed electric trains and creating additional preferential ticket
services, etc.
Based on the received passenger flows and a near-term analysis, passenger
transportation planning for the coming period is carried out. This takes into account
mass organized transportation events (exhibitions, sports competitions, relocation,
conscription, etc.).
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Volume-82, Issue-2, May -2025
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