Determine the volume of transportation and freight turnover on the railway. Passenger turnover, freight turnover, reduced tonne-kilometers. Methods for calculating cargo turnover

Indicators of railway operational performance are divided into quantitative and qualitative.

Quantitative performance indicators

Quantitative indicators characterize the volume of traffic, passengers and cargo, as well as the operation of rolling stock, these include:

1. Volume of transportation work:

a) for freight traffic - this is the number of tons of cargo transported

∑Р = Р 1 + Р 2 + … + Р n ;

b) for passenger traffic - the number of passengers sent

∑a = a 1 + a 2 + ... + a n.

2. Railway freight turnover determined in t km using the following formula

∑Рl = ∑Pl t,

where l t is the average range of one ton of cargo.

3. Passenger turnover- is determined by the number of passenger kilometers (pass km) and is found by the formula

∑al = ∑al p,

where l p is the average travel distance of one passenger.

4. Freight density (density)- this is the number of ton-kilometers per year per one kilometer of operational length of a given unit, determined by the formula

where L ex is the operational length of the corresponding unit.

6. Loading on a network, road, branch or station (U p), taken into account daily in physical cars.

7. Unloading(U in) - taken into account in physical cars for a network, road, department or station.

8. Norms for the transfer of wagons from road to road or from department to department:

a) for the acceptance of cars: U pr.gr. , U ave.por. , U av.general ;

b) delivery of wagons: U SD.gr. , U sd.por. , U sd.tot.

9. Job networks, roads and departments - taken into account in physical cars per day and determined by formulas

Qualitative performance indicators

Qualitative indicators characterize the use of rolling stock, these include:

1. Travel speed- this is the average speed of a train on a given section of the railway line without taking into account stops and time lost on acceleration and deceleration. Travel speed is determined by the formula

where t x is the travel time.

2. Technical speed- this is the average speed of the train along the sections of the section without taking into account the time of stops, but taking into account the time for acceleration and deceleration:

3. Area speed (commercial)- this is the average speed of the train along the section, taking into account the time of stops at intermediate stations and the loss of time for acceleration and deceleration:

4. Route speed- this is the average speed of a train on a given railway direction, taking into account the time of stops at all stations and the loss of time for acceleration and deceleration. Route speed is measured in km/day and is determined by the formula

5. Cargo delivery speed- this is the average speed of movement of cargo from the moment it is received by the railway until the moment it is issued to the recipient:

where l g is the cargo transportation distance; t g - the total time the cargo is in transport.

6. Speed ​​factors:

a) Section speed coefficient

b) Cargo delivery speed coefficient

7. Car turnover- this is the cycle time of operations from the beginning of one loading to the beginning of another, or from the beginning of one unloading to the beginning of another. This is a universal and one of the main indicators of the quality of railway work. The diagram and formula for determining the car turnover are as follows:

where l o is the full journey of the car - this is the distance that the car travels during the turnaround;

l in - carriage length or distance from one technical station to another;

t those is the time the car is idle at one technical station;

k m - local work coefficient:

t gr - idle time of a wagon under one cargo operation.

8. Working car park(R)

9. Average daily mileage of a car

where ∑ n·S o is the number of car-kilometers traveled by all cars in the working fleet per day.

- load on the car or axle after performing cargo operations, determined by the formula

- this is the average load on a loaded car or axle along the entire route of the car in a loaded state

- this is the average load per one car or axle of all cars of the working fleet during the period of their run, both loaded and empty

where α is the empty run coefficient.

13. Empty run ratio- this is the ratio of the number of car-kilometers of empty run to the number of car-kilometers of loaded run or empty trip to loaded trip

14. Car productivity- this is the number of tons per kilometer that falls per day per wagon of the working fleet, the formula for determining the productivity of wagons is as follows

15. Average daily mileage of a locomotive

where ∑MS is the number of locomotive-kilometers traveled by all locomotives serving train operations;

∑M is the number of locomotives engaged in train work.

16. Average train gross weight- is determined by dividing all gross ton-kilometers completed during a given day by locomotive-kilometers

17. Locomotive performance- this is the number of gross ton-kilometers per day per locomotive, determined by the formula

W l = Q S l,

where Q is the weight of the train.

18. Cost of transportation- this is the amount of operating costs per 10 reduced ton-kilometers

e = E exp/ ∑Рl,

where E exp is the sum of operating costs, including all annual wage costs, costs of materials, fuel, electricity, current cash costs for average repairs of rolling stock and depreciation.

Railway transport ranks second in terms of freight turnover (after sea transport) and second in passenger turnover (after road transport). Currently, its development is slowing down. In terms of the total length of the road network (about 1.2 million km), it is inferior not only to road transport, but also to air and pipeline transport. The main function of railway transport is the transportation of bulk industrial and agricultural goods (coal, steel, grain, etc.) over long distances. A distinctive feature is the regularity of movement, regardless of the weather and time of year.

The development of railway transport is determined by the following indicators:

• the total length of railways in a particular region;
• density (density) of the railway network (length of railways per 100 or 1000 km2);
• Freight turnover and passenger turnover.

In addition, important indicators are the degree of electrification of railways and other indicators characterizing its quality.

The differences in the level of development of railway transport by region are very large. For example, Western Europe is oversaturated with railways, and some in Asia do not have them at all.

In general, in the world, due to competition with road transport, the length of the railway network is decreasing, mainly in ( and ). Their new construction is carried out only in certain, mostly countries with transition economies (China, China, etc.).

In terms of the length of the railway network, the leading countries in the world are occupied by the largest (in terms of territory size) countries: the USA (176 thousand km), Russia (86), (85), China, Australia, Mexico. These countries account for more than half the total length of the world's railways.

European countries are the leaders in the density of railways (their density is 133 km per 1 thousand sq. km). The average density of the railway network in African countries is only 2.7 km per 1 thousand square meters. km.
In terms of the level of electrification of railways, European countries are also ahead of all (about 100% of railways are electrified, in Russia - 65%, in Russia - more than 50%, in Russia - 47%). Russia ranks first in the total length of electrified railways.

US railroad electrification is very low (1%).

In certain regions and countries of the world, railways have different gauges. The track is wider than in the countries of Eastern and Western Europe, North America, and Asia. The gauge of some other states (for example, the states of the Iberian Peninsula) does not correspond to the Western European gauge. In general, the Western European railway accounts for up to 3/4 of the length of the world's roads.

In terms of cargo turnover, the leading positions in the world are occupied by the USA, China and Russia, in terms of passenger turnover - Japan (395 billion passenger-km), China (354), India (320), Russia (170), Germany - 60 billion passenger-km;

In a number of developed countries (France, Japan, Germany, etc.) super-high-speed (with a speed of more than 300 km/h) railways have been created.

The railways of countries, foreign Europe, North America within their regions are connected into a single transport system, i.e. they form regional railway systems. For example, to carry out transit transportation between foreign countries and through the CIS territory, the Trans-Siberian “bridge” was laid, along which cargo passes to the ports of Nakhodka and Vostochny and further to.
When characterizing railway transport, it is necessary to note the qualitative changes in it at the present stage: the use of new types of engines, the creation of wheelless trains operating on an air cushion, magnetic and electromagnetic suspension.

The transport system plays an important role in the economic development of any country. In Russia, one of the main transport arteries is the railway, since it accounts for more than 40% of passenger turnover and 80% of the total freight turnover of the state.

The importance of railway transport in Russia is fundamental, because the country is characterized by long distances. The level of economic development of the state depends on the effective operation of this system. Every year, thanks to the well-coordinated work of the railway, the following is transported:

• about 98% manganese and iron ore,
• 92% ferrous metals,
• 88% mineral and chemical fertilizers,
• 87% coal and coke.

Since the first construction of the railway in Russia, which happened in 1830, this type of transport has required large investments, but despite this, the railway has a number of advantages:

1. operates around the clock in all weather conditions;
2. has a low cost of transportation (especially when transporting over long distances);
3. connects all regions and districts of Russia;
4. has the lowest environmental impact factor.

The role of railway transport

The role of railway transport in Russia is difficult to overestimate, because it is one of the largest in the world, thanks to which it provides 25% of the world's freight turnover and about 15% of the world's passenger turnover.

In Russia, railway transport is a branch of the economy, without which the uninterrupted operation of all economic sectors is not possible. In order to understand in more detail what role this transport system plays, it is necessary to consider its segments in more detail:

• Transporting passengers and cargo. Production of products can only take place when they are delivered to the consumer. For the manufacturing and mining industries, as well as for agricultural enterprises, railway transport (railway transport) is one of the most efficient and cheapest types of delivery.
• A developed transport system is the key to economic development.
• Acts as a link between different economic systems.
• As an independent industry, it offers its products with a number of features.

Namely, as a result of the implementation of measures aimed at increasing the efficiency of transportation, it was possible to improve the basic qualities of railway transport performance indicators. So in recent years in the country:

• the local speed of freight trains has increased,
• turnover of freight cars decreased,
• the average weight of freight trains has increased,
• The average daily productivity of locomotives and freight cars increased.

All districts and regions of Russia are connected together by railways, thereby meeting the transportation needs of not only the population, but also industry and agriculture. All modes of transport complement each other and form a single transport system.

Transportation of products has its own units of measurement:

• tonne-kilometers (freight turnover)
• tons (number of cargo)
• passenger kilometers (passenger turnover)
• passengers (number of passengers)

Key performance indicators of railways

• Freight density on railways. This indicator calculates the amount of cargo transported over a certain period of time. Sometimes the reduced load intensity can be calculated through the reduced cargo turnover. Freight density on railways is characterized by an average amount.
• Passenger turnover of railway transport is the volume of transport work for transporting passengers, calculated in passenger kilometers per year.
• Freight turnover of railway transport is the volume of transport work for the transportation of goods, calculated in ton-kilometers per year.

Strategy for the development of railway transport until 2030

In 2008, the government of the country developed a strategy for the development of railway transport until 2030. It provides for the expansion of the railway network, bringing technical and technological railway transport to the world level, and increasing the competitiveness of the country's railway transport. Over the next 14 years, it is planned to build important strategic, socially significant and cargo-generating lines, the total length of which will be more than 15,800 km.

The state strategy provides for:

• introduce more than 20,000 km of new railway lines,
• organize transport support for 18 promising mineral deposits and industrial zones,
• create lines that will ensure the movement of passenger trains at speeds of up to 350 km/h, with a length of 1528 km,
• update the rolling stock (purchase of 23,000 locomotives, 900,000 freight cars and 30,000 passenger cars),
• increase the density of the railway network by 23.8%, while completely eliminating transportation and capacity restrictions.

To achieve the set goals, more than 13 trillion have been allocated for the development of railway transport. rub., in addition, there are plans to actively use the mechanism of public-private partnership. 40% of investments will be allocated for the construction of new railway lines, 31% for the development of existing facilities, and 29% for the renewal of rolling stock.

If the above is implemented, it will be possible to ensure socio-economic growth, increase the mobility of the population, optimize the flow of goods, strengthen economic sovereignty, national security, and the defense capability of the country, reduce total transport costs, and increase the competitiveness of the national economy.

The volume of VT work is calculated in ton-kilometers and passenger-kilometers. A unit of output is the work expended on moving one ton of cargo or 1 passenger over a distance of 1 km. The volume of VT work is calculated separately for each type of transportation.

The work of moving cargo is determined by the cargo ton-kilometers or cargo turnover performed. Freight turnover is defined as the product of the number of tons of cargo moved (shipped) and the distance of their transportation.

When moving passengers, two indicators of transport performance are determined: passenger turnover and passenger tonne-kilometers. Passenger turnover is measured in passenger kilometers and is equal to the product of the number of passengers transported and the transportation distance.

Passenger ton-kilometers must be calculated to be able to determine the overall operation of transport (comparing passenger turnover with freight and postal turnover). To convert passenger turnover into passenger tonne-kilometres, a coefficient equal to the weight of the passenger with the free baggage allowance is applied.

Reduced cargo turnover (ton-kilometers) is the total work of the airline in providing air transportation services. This is the volume of production produced by an airline when transporting 1 ton of commercial load over a distance of 1 km.

The total volume of transport work is determined by the reduced transport products, which is equal to the sum of ton-kilometers by type of transport.

2. Performance indicators include:

Speed ​​(travel).

The economic significance of increasing speed is to reduce transportation time; the value of speed plays an important role in planning the airline's activities.

The following types of speeds are used in GA:

1) cruising;

2) scheduled;

3) commercial speed.

Cruising speed is the speed of uniform horizontal flight of the aircraft when the engines are operating in cruising mode and at the design flight altitude and weight of the aircraft (indicated in the flight characteristics of the aircraft).

Route speed – average speed during a non-stop flight between two airports.

Commercial speed is the speed of the aircraft, taking into account the time the aircraft is parked at intermediate airports.

Delivery speed - takes into account the time spent by the passenger on the road from the place of stay to the airport upon departure, and the time of delivery of the passenger from the airport to the destination upon arrival of the aircraft (“door to door”).

Annual flight hours.

The annual flight hours of a listed aircraft is an important indicator of the volume of work and aircraft utilization.

Flight hours are usually divided into production hours, which are performed during commercial flights, and non-production hours, which include training and auxiliary service hours.

Training flight time - includes flight time spent on training flight personnel.

Auxiliary – service time: flights related to testing in the air of an aircraft, engines and instruments after maintenance; ferrying the aircraft for repair, from repair, to a new location; fog dispersal flights, etc.

The so-called unproductive flight hours. These are flights the execution of which is not necessary for the operation of the enterprise (returns from a flight due to the unreliability of the weather forecast, detection of a malfunction, etc.).

Aircraft hourly productivity.

Hourly productivity is an indicator by which the intensity and efficiency of the use of transport aircraft by type is assessed. This indicator determines the volume of production carried out by the aircraft within an hour. With its help, the use of aircraft during flight on a specific overhead line, as well as throughout the enterprise as a whole, is assessed.

The economic importance of aircraft productivity is as follows: the higher the aircraft productivity, the lower the cost of its flight hour and the cost of 1 tkm, which leads to a reduction in costs and an increase in the profit of the enterprise.

Aircraft performance is a function of three quantities: the maximum payload, the degree of its utilization and the flight speed.

The commercial load of an aircraft includes passengers, mail, and cargo. The maximum possible load value is set based on the full occupancy of passenger seats, luggage and cargo spaces, and the maximum is determined depending on the non-stop flight range, as well as on the amount of fuel refueling. The use of commercial load is determined by the percentage of use, which is calculated for the flight, as a whole, for the overhead line, and the enterprise.

The maximum commercial load is an individual characteristic of each type of aircraft; it is determined by the take-off weight of the aircraft, its passenger capacity, the volume of cargo space, strength and alignment restrictions. The value of the maximum commercial load is indicated in the technical specifications and should not be exceeded under operating conditions.

3. Indicators of quality and efficiency of the transport process:

Average transportation distance.

The average transportation distance is calculated separately by type of transportation (passengers, mail, cargo), as well as by overhead line, for the airline as a whole, and for the civil aviation industry. This is necessary for the correct assignment of landing at intermediate airports; to determine the aircraft required by the airline to operate flights (short-, medium-, long-haul).

The average transportation distance is determined by dividing the indicator characterizing the volume of work performed (passenger turnover, cargo turnover, postal cargo turnover) by a quantitative indicator (number of passengers, cargo, luggage transported).

Flight safety (FS).

Air transport today is the safest for passengers. BP is the main indicator of the quality of air transport.

Flight safety is a set of measures to ensure the safe conduct of flights, a comprehensive characteristic of civil aircraft and aviation services, and (or) work that determines the ability to carry out flights without threatening the life and health of people.

Aviation accident is an event that occurred during the use of an aircraft for the purpose of performing a flight, associated with a disruption in the normal functioning of this ship, its crew, other aviation personnel, or associated with the impact of external conditions and leading to loss of life, significant damage, destruction or loss of the aircraft.

Investigation is a process that includes the collection and analysis of information, the preparation of conclusions, including the establishment of causes and the development of safety recommendations, carried out with the aim of preventing aviation accidents.

Recently, the so-called aviation safety of the civil aviation industry, because attempts to use air transport for non-peaceful purposes do not stop, and those who use aviation as an object for terrorism are becoming more cunning in their actions.

Aviation safety is the normal and safe operation of aviation, ensured by the prevention and prevention of accidents in its activities.

Unlawful interference in aviation activities is an unlawful action or inaction that encroaches on the normal and safe activities of aviation, resulting in accidents to people, material damage, seizure or hijacking of aircraft, or creating the threat of such consequences.

The progress of aviation directly has a positive impact on the rise of the state’s economy. And any attack on civil aviation facilities harms its national interests, in addition, acts of illegal interference are directly related to the enormous economic damage to civil aviation enterprises (airports, airlines), their partners in the aviation business, as well as clients - consumers of air transport services.

Regularity of flights.

The regularity of flights and the accuracy of schedule implementation are the most important indicators of the quality of airline services. It is easier to ensure accuracy on modern aircraft with improved technical characteristics, which are not subject to restrictions on weather conditions, noise or harmful engine emissions.

To reduce the cost of air transportation, a large number of flight hours are required for each scheduled aircraft, which inevitably leads to the scheduling of some flights with inconvenient departure and landing times and an increase in the likelihood of flight delays for various reasons. Because In order to effectively use the aircraft, its movement plan is drawn up with minimal reserves of time, the airline must reserve a free aircraft to ensure accurate execution of the schedule. It is more important to accurately observe the time of arrival of the aircraft at the destination for further flights without delays than the departure time (you can catch up on the flight delay time by choosing a flight level at which the wind is blowing in a favorable direction).

For delays in the arrival of a regularly scheduled flight, passengers of prestigious airlines are paid compensation, the amount of which depends on the distance of the flight and the delay time (distance up to 3.5 thousand km, delay time less than 2 hours - 75 euros/person; distance up to 3.5 thousand km, delay time more than 2 hours – 150 euros/person; distance more than 3.5 thousand km, delay time less than 4 hours – 150 euros/person; distance more than 3.5 thousand km, time delays of more than 4 hours – 300 euros/person).

The NPB of the Republic of Kazakhstan establishes the limits of liability of air carriers for flight delays and the amount of compensation for air passengers.

4. Technical indicators include:

Carrying capacity.

Market carrying capacity (capacity) is a quantitative indicator that shows the maximum possible volume of services that can be provided to customers at a certain point in time and at a certain price.

The legal basis for international air transport is commercial rights or “freedom of the air”.

The carrying capacity of international air transportation is regulated at the state level through negotiations and the conclusion of bilateral agreements on air services. Over the past 50 years, states have developed various forms of capacity regulation, which are reflected in bilateral agreements.

ICAO has developed methods for regulating capacity, which are classified into 3 main categories:

1) Preliminary determination method.

2) Bermuda Agreement method.

3) Free determination method.

Available seat-kilometers is the sum of the products of multiplying the number of passenger seats available for sale at each stage of a flight by the length of the stage.

Passenger load factor is passenger kilometers expressed as a percentage of available seat kilometers.

Available ton-kilometers is the sum of the products of multiplying the number of tons of available payload at each stage of the flight by the length of the stage.

Commercial load factor is the total number of ton-kilometers completed, expressed as a percentage of available ton-kilometers.

Bandwidth.

Capacity is the ability to serve a certain number of passengers (aircraft) per unit of time in compliance with established service requirements. The main element determining airport capacity is runway capacity. The capacity of other elements of the airport (taxiway, apron, airport terminal, station area, access roads) is brought into line with the capacity of the runway.

The runway capacity is measured in “aircraft per hour” (aircraft per hour). This is the maximum number of takeoff and landing operations (consecutive takeoffs, sequential landings, or alternate takeoffs and landings combined) that can be performed at an aerodrome per unit of time under given conditions in compliance with flight safety rules.

AVK capacity is the average capacity determined by the number of passengers served during rush hour.

Federal Agency for Railway Transport

Federal State Educational Institution

Higher professional education

"Petersburg State Transport University"

Department of Transport Economics

TRANSPORTATION PLAN AND OPERATION OF RAILWAY ROLLING STOCK IN FREIGHT TRAFFIC

Guidelines

To complete the course project

For students of specialties

"Organization of transportation and management

In transport (railway)",

"Economics and enterprise management

(railway transport)"

SAINT PETERSBURG

PGUPS

Purpose The course project is to consolidate the knowledge on the topic “Planning of transportation by rail”, obtained in the lecture course, as well as the acquisition and development of practical skills in performing technical and economic calculations related to planning the operational work of the railway.

Course project assignment

The course project consists of interrelated sections that require:

– draw up a plan for loading and unloading, receiving and handing over wagons;

– build a diagram of car flows of loaded cars, calculate the density of traffic and the mileage of loaded cars along the road;

– determine the balance of empty cars and draw up a diagram of car flows of empty cars;

Based on the initial data (see appendices 1–3) and data obtained by calculation, it is necessary to determine:

– volume of ton-kilometer work (net), locomotive and train runs, gross ton-kilometers;

– the required fleet of locomotives and quality indicators of their use;

– working fleet of cars and quality indicators of their use.

Take the assignment for options from Appendices 1, 2 - according to the student’s number in the teacher’s journal, and for correspondence students - according to the last digit of the code; from Appendix 3 - by the first letter of the last name.

FREIGHT TRANSPORTATION PLANNING

1.1 Freight transportation planning methodology

The main indicators of freight transportation are:

– the number of tons of cargo transported (volume of transportation);

– cargo turnover;

– number of shipments;

– traffic density;

– average transportation distance;

– unevenness of transportation.

In this course project, certain simplifications have been introduced to reduce the volume of calculations. Thus, operational performance indicators (number of shipments, unevenness of transportation, etc.) are not calculated; The given conditional railway includes only two sections (A–B and B–C), and individual parameters of the operational operation of the railway are given as the initial values ​​of freight traffic (see Appendix 1–3). But these simplifications do not affect the methodology for developing a freight transportation plan.

Freight transportation planning is of great practical importance, as it is the starting basis for the development of other sections of the production and economic activity plan of railways (labor and wages; fixed and working capital; operating expenses and costs, etc.). It must be emphasized that freight transportation provides over 2/3 of all income from all rail transportation.

Number of tons of cargo transported (traffic volume) is usually measured at the time of departure. On the road, the volume of traffic is determined as the sum of departures (loading) from all stations of the road and receipt of goods from neighboring roads, that is:

The volume of transportation by road is divided into the arrival of cargo within a given unit and delivery to other units, that is:

.

Then the total volume of traffic on the road is distributed by type of communication (Fig. 1.1).

IN local traffic transportation is carried out within the same road, and directly - transportation on sections of two or more roads.

IN direct message highlight:

Direct message

Import Export

Local service

Rice. 1.1 Distribution of traffic volume by type of communication

– in v o z, i.e. arrival of cargo from stations on other roads to this road;

– in you in about z, i.e. sending cargo from stations on this road to other roads in the network;

– t r a n z i t, i.e. transportation of goods arriving from other roads and traveling through this road to other roads in the network.

Thus, the volume of traffic on the road is equal to:

.

Reception of cargo can be considered as the sum of import and transit:

,

and delivery of cargo - as the sum of export and transit:

.

The departure of cargo, in turn, is equal to the sum of exported cargo and cargo transported locally:

,

and arrival – the sum of imported goods and goods transported locally:

.

Freight turnover – this is the work of moving cargo, defined as the product of the mass of the cargo and the transportation distance. Freight turnover is measured in ton-kilometers. Distinguish net cargo turnover- this is the work of transport, taking into account only the movement of cargo, and gross turnover, taking into account the movement of cargo along with the tare weight of the rolling stock.

Net cargo turnover can be tariff and operational.

Tariff freight turnover is calculated based on the so-called tariff distances in transportation documents (waybill and road manifest).

Operational cargo turnover is determined by the actual mileage of the cargo from the driver’s route.

The ratio of net freight turnover to gross freight turnover can be characterized by the efficiency factor of railway transport:

.

Number of submissions – a specific indicator of transport. A shipment is a consignment of goods documented by one transportation document (road manifest). One shipment can be a whole train, moving from one sender to one recipient (route); there may be one or more wagons (wagon) or a container (container), or there may be one box in a wagon (small). In a course project, the number of submissions is not calculated.

The transportation plan determines traffic density – the number of tons of cargo transported through 1 km of the transport network per unit of time. The density of traffic is established overall and in the following directions: cargo (even) and empty (odd).

The traffic density value is equal to the arithmetic average of the density value at the entrance and exit of the site in each direction.

The average density, or load intensity, of freight traffic as a whole along the road is determined as the quotient of net freight turnover divided by the corresponding operational length:

Average transportation distance – this is the distance over which each ton of cargo is transported on average; it is defined as the ratio of net cargo turnover to the volume of transportation

Unevenness coefficients are not calculated in the course project.

1.2 Calculation of transportation plan indicators

The initial data for calculating the transportation plan indicators for a conditional road are the size of freight flows, which are given in Appendix 1. The diagram of a conditional railway is presented in Fig. 1.2.