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ANALYSIS OF THE MAIN INDICATORS OF FREIGHT AND TRAIN
TRANSPORTATION AT THE “KARSHI” STATION
Bozorov R.Sh.
1
а
, Boboev D.Sh.
1
d
,
1
Tashkent state transport university, Tashkent, Uzbekistan
Abstract:
This article provides a detailed analysis of the freight
and train transportation performance of the Karshi railway
station in recent years. Based on these analyses, it was noted
that there were delays in several directions at the station. In this
regard, it was determined that there is a need to improve the
station's work processes. To solve these problems, a multi-
criteria regression mathematical model of the station's
turnaround time was developed. According to it, it was
determined that the turnaround time depends on the length of
the loading and unloading front, the speed of loading and
unloading, and the volume of work at the stations.
Keywords:
Freight and passenger trains, load cycling, load front
length, regression model, least squares method.
During the study of the workflow of the “Qarshi” station, the work performed
at the station between 2022 and 2023 was carried out, that is, the analysis of the main
indicators of the station-that is, the amount of cargo flows loaded from the station, the
amount of wagons loaded, the amount of transit processed, the amount of wagons not
processed it will be possible to get acquainted with the analysis of these indicators in
the cross section of years from the table at the well (Table 1).
Table 1
Performance indicators of the “Karshi” station
Indicators
2022
report
2023
plan
2023
report
to the report
to the plan
%
(+,-)
%
(+,-)
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Loading, tons
275165
261189 268942
97,7
-6223
103,0
7753
Day
1007,9
956,7
985,1
-
-
-
-
Loading,
wagon
5046
4675
4584
90,8
-462
98,1
-91
Day
18,5
17,1
16,8
-
-
-
-
Static loading
54,5
55,9
58,7
107,6
4,1
105,0
2,8
Unloading,
wagon
16425
16520
16494
100
69
99,8
-26
Day
60,2
60,5
60,4
-
-
-
-
Wagon
dispatch
209094
213533 240236
114,9
31142 112,5
26703
Day
765,9
782,2
880,0
-
-
-
-
Working fleet
186910
242965 192823
96,9
5913
126,0
-
50142
Day
684,7
890,0
706,3
-
-
-
-
Empty wagon 20,0
20,0
20,0
100,0
-
100,0
-
Transit
non-
recyclable
1,0
1,0
1,0
100,0
-
100
-
Transit
recyclable
18,0
18,0
18,0
100,0
-
100
-
Recyclable
fleet
384050
380800 384198
100,0
148
100,9
3398
Day
1406,8
1394,9
1407,3
-
-
-
-
CNG wagons
1654
5172
2188
76
534
236,4
-2984
Day
6,1
18,9
8,0
-
-
-
-
Production.
1389,7
1382,0
1430,5
102,9
40,8
103,5
48,6
Contingent
198
189
188
94,9
-10
99,5
-1
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Figure 1. Load tonnage diagram
Table 2
Loading tons
January February March April May June July August September
In
9
months
2023
report
22977 26836 36790 24616 30999 28647 34588 30866 32624
268942
2022
report
30531 26700 36960 26008 30806 27350 34573 30028 32209
275165
+\- -7554 136
-170 -1392 193
//1297 15
838
415
-6223
%
75,2
100,5
99,5 94,6
100,6 104,7 100,0 102,8 101,2
97,7
An analysis of the activities of the “Karshi” workstation shows that the main
load increase is 97,7% less than the 2022 target of 6,223 tons, and 103,0% less than
the 2023 plan of 7,753 tons.
22977
26836
36790
24616
30999
28646
34588
30866
32624
30531
26700
36960
26008
30806
27350
34573
30028
32209
0
5000
10000
15000
20000
25000
30000
35000
40000
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Figure 2. Diagram of the number of unloaded wagons
Table 3
Number of unloaded wagons
January February March April May
June July
August
September
In 9 months
2023
report
1425
1341
1746
1748 2145
1901 2099
2073
2023
16494
2022
report
1409
1339
1656
1740 2145
1893 2098
2190
1955
16425
+\-
16
2
90
8
0
8
1
-117
68
69
%
101,1
100,1
105,4 100,4 100,0
100,3 100,0
94,6
103,5
100,0
Unloading of wagons at the “Karshi” station was 462 wagons more than last
year, or 90,8 percent, and 91 wagons less than the plan, which affects the increase in
statistical load. Statistical load was fulfilled by 107,6 percent compared to last year,
and by 105,0 percent compared to the plan (Figure 1-3).
1425
1341
1746
1748
2145
1894
2098
2073
1955
1409
1339
1656
1740
2145
1893
2099
2190
2023
0
500
1000
1500
2000
2500
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Figure 3. Workforce chart
According to the data, the number of CIS cars is 76,0% more and 236,4% less
than planned. The quality indicators of the downtime of wagons per 1 cargo operation
are 100,0% compared to the previous year, 100,0% compared to the plan, transit
downtime with processing is 100,0% compared to the report, 100,0% compared to the
plan. The downtime of transit without processing was 100% compared to the previous
year and 100% compared to the plan; Labor productivity was reported by 102,9%, the
plan was fulfilled by 103,5%. In order to more effectively organize the productivity of
station work processes, it is advisable to use various mathematical modeling methods
in the organization of station work processes. Mathematical modeling processes are
certainly used in every field of production, especially in the field of railway transport,
for this purpose, let us consider the issue of finding an empirical function for wagon
turnover using regression modeling and the method of least squares for the “Karshi”
station. That is, let the empirical function for determining wagon turnover be the
function of the dependence of the station's cargo flow, the number of wagons to be
shipped, the length of the section and the speed of the wagons:
)
,
,
,
(
V
L
N
Q
(1)
For this purpose, let’s write the objective function of regression modeling and
the least squares method (Figure 4),
n
i
i
n
i
i
i
e
V
d
L
c
N
b
Q
a
1
2
1
2
min
min
(2)
0
)
,
,
,
(
0
)
,
,
,
(
0
)
,
,
,
(
0
)
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(
0
)
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(
V
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e
V
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d
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L
N
Q
c
V
L
N
Q
b
V
L
N
Q
a
e
d
c
b
a
(3)
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n
i
n
i
n
i
n
i
n
i
e
V
d
L
c
N
b
Q
a
e
V
e
V
d
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c
N
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Q
a
d
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e
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c
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c
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e
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e
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c
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b
Q
a
a
1
5
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5
5
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1
4
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(4)
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(
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,
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(
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873
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,
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10
(
2
(5)
The above expressions were determined in C++ using the least squares method
and Cramer's equations as follows:
#include <iostream>
#include <vector>
#include <iomanip>
using namespace std;
vector<double>
gaussElimination(vector<vector<double>>&
A,
vector<double>& B) {
int n = A.size();
for (int i = 0; i < n; i++) {
int maxRow = i;
for (int k = i + 1; k < n; k++) {
if (abs(A[k][i]) > abs(A[maxRow][i])) {
maxRow = k;
}
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for (int k = i; k < n; k++) {
swap(A[maxRow][k], A[i][k]);
}
swap(B[maxRow], B[i]);
if (abs(A[i][i]) < 1e-12) {
throw runtime_error(“There is a zero pivot element, the system has no
solution or has multiple solutions.”);
}
for (int k = i + 1; k < n; k++) {
double c = A[k][i] / A[i][i];
for (int j = i; j < n; j++) {
A[k][j] -= c * A[i][j];
}
B[k] -= c * B[i];
}
vector<double> x(n);
for (int i = n - 1; i >= 0; i--) {
x[i] = B[i];
for (int j = i + 1; j < n; j++) {
x[i] -= A[i][j] * x[j];
}
x[i] /= A[i][i];
}
return x;
}
int main() {
// 5 coefficients of a system of unknown equations
vector<vector<double>> A = {
{ 765.9, 873, 2, 50, 1},
{ 894.5, 818, 2.5, 52, 1},
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{ 1226.3, 1074, 3.5, 55, 1},
{ 820.5, 992, -2, 4,5, 60,1},
{ 1033.3, 959, 1, 5, 64,1}
};
vector<double> B = { 10, 12, 14, 17, 19 };
try {
vector<double> result = gaussElimination(A, B);
cout << “Solution to the system of equations:” << endl;
cout << “a”<< “ = “ << setprecision(6) << result[0] << endl;
cout << “b”<< “ =” << setprecision(6) << result[1] << endl;
cout << “c”<< “ =” << setprecision(6) << result[2] << endl;
cout << “d”<< “=” << setprecision(6) << result[3] << endl;
cout << “e”<< “ = “ << setprecision(6) << result[4] << endl;
} catch (const runtime_error& e) {
cout << “Error:” << e.what() << endl;
}
return 0;
}
Figure 4. The result of determining the wagon turnover in a C++ program
using a regression model and ECCU
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Based on the results obtained during the modeling process, the following
universal function was generated:
169522
,
0
17247
,
0
32905
,
2
00530801
,
0
00154426
,
0
V
L
N
Q
(6)
As a result, the following graphs were generated (Figures 5-8)
Figure
5.
Graph
of
wagon
turnover
versus
cargo
volume
9,59090353
10,36303353
11,13516353
11,90729353
12,67942353
13,45155353
0
2
4
6
8
10
12
14
16
500
1000
1500
2000
2500
3000
Ɵ
Q
Ɵ=Ɵ(Q)
11,9798657
11,4490647
10,9182637
10,3874627
9,8566617
9,3258607
0
2
4
6
8
10
12
14
500
600
700
800
900
1000
N
Ɵ
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Figure
6.
Graph
of
wagon
turnover
versus
wagon
volume
Figure 7. Graph of the dependence of the wagon turnover on the length of the
branch line
Figure 8. Graph of the dependence of the wagon turnover on the section speed
The calculation results showed that there is a need to improve the work
processes of the “Karshi” station. Taking this into account, a multi-factor empirical
function of the wagon turnover time at the station was developed using regression
modeling and the least squares method, which are considered mathematical modeling
methods for improving the station’s work processes. Based on this function, it is
possible to determine the wagon turnover time proportionally to the length of the
tracks, the length of the loading and unloading front, the station's cargo and wagon
turnover, and the speed of the train.
9,999978
11,164503
12,329028
13,493553
14,658078
15,822603
0
2
4
6
8
10
12
14
16
18
2
2,5
3
3,5
4
4,5
L
Ɵ
Ɵ=Ɵ(L)
4,825878
5,688228
6,550578
7,412928
8,275278
9,137628
0
1
2
3
4
5
6
7
8
9
10
20
25
30
35
40
45
V
Ɵ
Ɵ=Ɵ(V)
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