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Method of Determining the Minimum Required Number of Sorting Tracks, Depending on the Length of the Group of Wagons

This article, based on the study of local and foreign experience, identifies the need to seek comprehensive solutions for the effective organization of the wagon-flows in JSC “Uzbekistan Railways”. Based on the processing of statistical data, it was determined that the length of a group of wagons in a one direction multi-group train is subject to the law “Erlang”. Based on the use of Fibonacci numbers to search for the best scheme for the formation of multi-group trains, the method of determining the minimum required number of sorting tracks depending on the length of the group of wagons has been improved. As a result of the application of this method by JSC “Uzbekistan Railways” at station “Chukursay”, the cycle time of the sorting hill was reduced by 12%, the time spent on sorting of transit trains was reduced by 5% and the processing capacity of the sorting hill was increased by 14%. Key-words: Multi-group Trains, Shunting Operations, Group Length of Wagons, Number of Sorting Tracks, Fibonacci Numbers, Erlang Law.


Introduction
In the process of sorting the flow of goods on the world's transport corridors, a leading role is played by increasing the speed, setting time and optimizing technological processes, as well as improving the technical and operational methods of management assessment. Much attention is paid to the development of methods for the measurement, evaluation and elimination of various inefficient loss factors affecting the trunk and local transport networks of developed countries, including the United States, Germany, Sweden, China, India, Russia, Kazakhstan and similar countries [1][2][3][4][5][6].
In this regard, special attention is paid to the development of methods for calculating and determining the values of parameters of inefficient time losses in the processing of wagons at sorting stations, as well as technology for controlling the flow of wagons.
Statistics of Uzbekistan Railways show that today rail freight is not organized efficiently enough. One of the main reasons for this was that it was found that the wagon loaded during the delivery of the cargo spent most of its time standing at the loading station or recycling stations, rather than moving on the section. The time spent by the loaded wagon to deliver the cargo to its destination was studied in 2 types: the time spent on the movement of wagons on the railway site and the time spent on other types of operations.
In JSC "Uzbekistan Railways" this indicator is 13% and 87%, respectively. The situation of this indicator in other countries was also analyzed. For example, in France, a loaded wagon spends 26% on on-railway site traffic and 74% on other types of operations, while in the United States this indicator is found to be 40% and 60%, respectively [7,8].

Materials and Methods
The analysis of the performance of the sorting station "Chukursay" under JSC "Uzbekistan Railways", including the analysis of the time of wagons at the station, showed that these indicators exceeded the norm for all analyzed periods. In turn, such inefficient waste of time in the operation of the sorting station leads to a decrease in the efficiency of operation technology for the organization and management of wagon flows not only at the station, but on the entire railway, and at the same time its competitiveness in the transport market. These, in turn, require the improvement of methods to reduce inefficient time losses in the operation of the sorting station in order to meet the technical and operational performance.

Search for Complex Solutions for the Effective Organization of the Flow of Wagons
The fact that the wagons loaded at JSC "Uzbekistan Railways" do not spend most of their time on the road leads not only to a decrease in the speed of delivery of goods but also to an increase in fines paid by the railway to the owner of the cargo. Delivery of goods to their destination on time is one of the main tasks of the railways to fulfil the contract of carriage, the non-fulfilment of which has a significant impact on the quality of transport services to users of railway services.
The research showed the need to find complex solutions for the effective organization of the wagon-flows in the conditions of disproportion in JSC "Uzbekistan Railways", taking into account the delivery time ( Figure 1).
A study was conducted to improve the non-optimality parameters of the multi-group train formation process at the technical stations of the search for complex solutions shown in Figure 1.

Determining the Length of a Group of Wagons in One Direction in a Multi-group Train
It is known that feasibility and technological calculations are carried out to optimize the processing of wagon flows in railway transport. In their implementation it is necessary to study the following most important parameters, which are inextricably linked: Number of wagons in the train; Number of interruptions in the train; The number of routes in the train.
Determining the number of carriages on a train requires an independent study. It is also possible to calculate from the formula proposed in [9] for the standard deviation of the number of wagons arriving at the station (freight object) per day: Here m c is the average number of wagons in the train.
From formula (1) to calculate the coefficient of variation of the number of wagons in the train can be given the following expression.
where N i -the wagon-flows (daily, monthly, etc.) directed to the i-cargo object (i-station).
The total calculations (more than 3.5 thousand trains) showed that In this L gr is the average length of a group of wagons in the formation of multi-group freight trains, m; λ is the density of the Erlang distribution law (magnitude inverse to the mathematical expectation); k is a parameter of the Erlang distribution law. Accurate identification of the basic parameter laws and numerical characteristics in the distribution of wagon flow allows us to assess the possibilities of development tracks of local sorting systems and speed up the process of sorting train trains.

A Method of Determining the Minimum required Number of Sorting Tracks depending on the Length of the Group of Wagons
The scattered location of railway stations and freight facilities leads to the formation of a group of wagons in the prescribed manner, that is, in the group under formation, the location of wagon stations or freight facilities is required to match the sequence. These, in turn, require the determination of the minimum number of shunting flights and the selection of the sequence of their execution in the formation of a group of wagons in the prescribed manner. The problem of inefficient use of sorting routes during train distribution and assembly causes several problems in the distribution of multi-group trains.
In the process of creating multi-group trains on the combinatorial method of sorting local wagons, the number of groups in the train and the number of available tracks play an important role.
In the field of railway transport, the main problem was to determine the relationship between the number of groups formed in different years and the number of existing tracks. To find a solution to this problem, it is advisable to focus on a higher mathematics course. The theory of numbers was This can be seen in Figure 3 below. As can be seen from Figure 3, the greater the number of groups in the train, the greater the number of tracks required. This in turn leads to an increase in shunting flights [12].
However, in practice, the issue of efficient use of existing roads comes first. Considering the required number of sorting tracks or the level of occupancy of existing tracks, it is important to select a group of wagons in a multi-group train using the Fibonacci numbers.   Figure 4 shows the technology of the group selection of wagons using the shunting locomotive "TEM-2" according to the combinatorial sorting method using multi-group trains using  2  1  7  7  3  7  5  5  5  6  6  1  1  8  7  2  2  5  11  9  4  13  3  3  10  12  13 2 11 11 11 9 10 13 6 12 3 5 13 5 М 3 1 5 5 The state before the distribution of the train In the 1st sorting work 1 2, 4,6,8,9,11,13 3,7,10 5,12 In the 2nd sorting work 5,12+6,13 1+2 9 3,7, 10+4,8,11 In the 3rd sorting work Using Fibonacci numbers, we determine the amount of time spent on the given train sorting technology according to the combinatorial sorting method using Table 1. The frequency of formation of the length of the group of wagons received at the station depends on the required number of sorting tracks, the degree of filling of existing tracks or the number of empty tracks. Determining the required or empty number of sorting tracks is done in the following order. Once the group of wagons previously admitted to the station has been placed at their addresses on the qualifying park tracks, the filled portion of the useful length of the assembly track is determined. The length of the filled part of the sorting tracks is determined by the sum of the lengths of the group of wagons thrown from the sorting hill: where L (i)filli-is the length of the filled part of the sorting track that specializes in the direction, m. When the condition (12) is met, the process of removing the assembled train is simulated: some groups of wagons on the assembly track, that is, "moving" to the boundary pile at the exit of the assembly track in question, are left uninterrupted. After that, the following indicators are determined: The value of the busy length of the track after removing the train: The value of the empty length of the path after removing the train It was observed that the time spent on the distribution and assembly of multi-group trains using this method studied above is not the same as the current sorting method, and the number of shunting flights performed based on these methods is also different. At the same time, the combinatorial sorting method took 52.9 minutes, and the process consisted of 4 cycles, 2 groupage flight. From these indicators, it was found that the smaller the number of cycles and the number of flights performed to create a multi-group train, the smaller the time spent on this technology.

Results and Discussion
The structure of multi-group trains is one of the most difficult elements in the process of processing wagons at stations, which significantly affects the delivery times of cargo. Hence, one of the urgent issues is to improve the structural processes of multi-group structures in order to reduce the downtime of wagons at stations in conditions of changing freight flows. An improved method for optimizing the distribution and assembly of multi-group trains has been introduced in universities, laboratories of research institutes, design institutes and technical stations in the railway transport industry. At the station "Chukursay" under the management of JSC "Uzbekistan Railways" introduced a method (proposed method) developed based on the law that the number of groups in a multi-group train depends on the required number of tracks. After the introduction of this method, it can be said that the station "Chukursay" has achieved several economic benefits in the field of transportation. We calculate the indicators that affect the economic efficiency of the station "Chukursay". A total of arrived trains N arr.total =35 per day arrives to station "Chukursay" for processing. Of these, N multi-group train 1 =10 (it accounts for 28% of the total number of trains arrived to the station) are multi-group trains, N single-group train 2 =25 (72%) are single-group trains. According to the current sorting method, the average time minutes (assumed to be 100%) is allocated to the station to sort the trains that arrived for processing. According to the proposed method, the average time minutes (88%

UZS
As a result of the application of the improved method at the station "Chukursay" of JSC "Uzbekistan Railways", the cycle time of the sorting hill was reduced by 12%, the time spent on sorting of transit trains was reduced by 5% and the processing capacity of the sorting hill was increased by 14%. This can be seen in Figures 6-8. The number of sorting tracks and the required length, depending on the length of the group of wagons to be distributed; The number of sorting operations in the formation of a group of wagons in the prescribed manner; The optimal number of shunting flights when forming a group of wagons in the prescribed manner;