# Capacity

Russian: Пропускная способность

## The Capacity

Capacity is a measure of the ability to move a specific amount of traffic over a defined rail line with a given set of resources under a specific service plan.[1]

The capacity of line or transport object is measured by the largest number of units of rolling stock, that can be served by the transport object for a certain period of time with its technical equipment and technologies.[2]

## Types of capacity

There are: theoretical, planned, and resultative capacity.

• Theoretical - this is the maximum amount of vehicles that could run over the route during a specific time interval depending on the technical equipment.
• Planned capacity - determined by the number of vehicles required to carry out the traffic plan (needed volume).
• Resultative capacity of lines is determined on the basis of the capacity of individual devices, and lines in general - on the basis of resultative capacity of small parts of lines.

For example, the resultative capacity of separate sections of railway line calculating on the capacity of following elements:

• lines (the number of main tracks, the length of lines, the track profile, automation systems and communications, track development of stations, power supply limitations);
• stations (tracks for arriving and departing trains, switches);
• locomotives depot ("stalls" for periodic inspection and repair of electric and diesel locomotives, locomotive equipment devices and passing-by tracks);
• power devices (traction units, power transformers and traction substations network).

The minimum capacity of one of these elements may limit the capacity of the production unit as a whole and determine the value of resultative capacity.

Theoretical capacity can be generally defined by the formula:

$n=\frac{T_p}{T_m}$, (1)

where Tp - current time interval when capacity is determined, h;

Tm - time required for processing (transport, service) of one unit of traffic flow (1 m, 1 m3, a car, a ship, etc.) with a uniform and continuous use of the device or system within the estimated time.

For different devices, and transportation systems, this formula is clarified disclosing the value of technological time Tm.[3]

## Railway line capacity

Capacity of the railway line is the greatest number of trains or pair of trains with known mass, that can be runned in a unit time (day, hour), depending on the existing permanent facilities, type and capacity of rolling stock and the methods adopted by the organization traffic (type of schedulling).

The capacity is calculated for sections of railway lines with the same all over the technical equipment, cargo capacity and the size of passenger traffic. The primary end point of these sections are the precinct and sorting stations, the "zone" stations of suburban traffic, and sometimes the intermediate stations of out-coming or incoming flows.

The capacity of each element of the segment is determined of his daily or hourly productivity in the service of one pair of trains or trains.

The capacity of the line is determined by the limiting line:

$N=\frac{1440k}{T}$

where T - the period of the schedule to the delimiting the stretch, including; k - number of pairs of trains or trains this direction, the noise for a period of the chart.

This formula gives a value of N without technological losses and the total reliability of the technology. If this condition is not met, then the value of the numerator in the formula is reduced accordingly.

The capacity of sections of railway lines firstly is calculated for trains of only one category (in most of the cases - for cargo trains) so called parallel schedule. Then the calculations is made for non-parallel schedule - with impact of trains coming with other rates.

The the parallel schedule capacity depends on the time of travelling on the line, the reception and expedition times and intervals between trains in "the package", track capacity of stations.

In general, the capacity (in train pairs) of railway line is expressed by dependence:

$N=\frac{1440-t_{texn}}{T_{per}}\alpha_n$

where Tper - the period of the graph, min.; ttexn - the duration of maintenance interval (window), min.; αn - coefficient of reliability of technical devices.

For non-parallel schedule capacity for freight traffic expressed in number of freight trains of a given mass and velocity, that can be moved on a segment or a line when given number of passengers, express freight and expedited trains are on the route. Hours, that is due to the movement of these trains can not be used for ordinary freight trains, called the time of removal.

The capacity for predominantly freight movement, pairs of trains is expressed by dependence:

$N_gr=N-\epsilon_{ps} N_{ps} - \epsilon_{sb} N_{sb} - \epsilon_{usk} N_{usk}$

where N - capacity of the line for freight traffic with parallel schedule; Nps,Nsb,Nusk - respectively, the number of passenger trains, expedited freight trains and express trains; $\epsilon_{ps}, \epsilon_{sb}, \epsilon_{usk}$ - respectively, the coefficients of the removal of freight trains by passenger trains, expedited freight trains and express trains.

Line capacity is calculated from the full use of all facilities. However, it must have a reserve that is installed on the technical and economic reasons, expressed as the difference between the theoretical (or projected) capacity and demand, given (or planned) in the future.

## The capacity of the auto-mobile road

The capacity of the road is defined as the sum of the capacities of the lanes. The capacity of one lane of the road is calculated with subject to:

$T_{m}=\frac{l_m l_p l_a}{v}$

where lm - the vehicle stopping distance is equal to $\frac {v^2}{2a}$ (a – acceleration of the motion); lp - The path traversed by a driver's reaction time is equal to vt; la - The length of the car.

## The capacity of river routes

The capacity of river routes determined by the formula (1), but much depends on the capacity of gateways and the time of their employment by the courts:

$T_{m}=\frac{t_{sh}}{2m}$

where

tsh - the time required for locking through vessels moving in opposite directions; 2 - coefficient for locking through of vessels in both directions; m - the maximum amount of vessels in the lock chamber at the same time.

## Maritime and air trainsport capacity

Marine natural ways to have no restrictions on capacity. The capacity of maritime transport is determined by the ability to pass through the channels and equipment of the port. Air transport capacity depends on the capacity of airports to receive and depart of airplanes.

## The pipeline and conveyor transport capacity

For continuous modes of transport (pipeline and conveyor) capacity is determined by the formula (1) with a time of delivery of the cargo a certain type:

$T_{m}=\frac{1}{q v}$

where q - volume or weight of the load at 1 m path length (pipeline or conveyor); v - speed of movement of goods in the appropriate units, m / sec, m / min.

The capacity of processing items, equipment, and repair of rolling stock on all modes of transport (stations, ports, airfields, depots, backwaters, garages, etc.) is calculated by the formulas of the same type but having different parameters specific to the appropriate mode of transport.

The development of the growing freight traffic can be achieved through organizational, technical and re-constructive measures. The development of traffic raises question to increase the capacity of railway lines, that is defined as the difference between planned and theoretical capacity.

## Carrying capacity

Carrying capacity is usually defined in general as to the railway line, and for other means of communication.

There are theoretical and planned carrying capacity. Carrying capacity of the line obtained as a result of the possible use of its capacity for cargo transportation with the appropriate satisfying passenger needs in traffic.[4]

Carrying capacity - the maximum value of cargo (in tons net per annum), that can be moved within a year on the line and is determined for each segment separately.

Carrying capacity of the railway line depends on the capacity, the rules of mass freight trains, structures of train flow by categories of trains and freight traffic, to leave and expresses the power line used for freight traffic, while ensuring a given number of permits and other passenger trains emergency treatment.

Carrying capacity is determined by the number of locomotives, wagons and other means of variables (fuel, electricity) and the security staff (locomotive brigades on duty at the station, etc.).

It depends on the proportion of theoretical capacity of the line for freight traffic, the average weight of a train in the area, comparisons of net and gross train, as well as the number of teams and express trains, and is given by:

$G=\frac{365(N_{gr} Q_{gr}^{br} \phi_{gr} + N_{usk} Q_{usk}^{br} \phi_{usk} + N_{sb} Q_{sb}^{br} \phi_{sb})}{10^6 k_n}$\

where $Q_{gr}^{br} , Q_{usk}^{br} , Q_{sb}^{br}$ - the average gross weight of freight trains, respectively, ordinary, express, expedition trains, t; ϕgrusksb - The ratio of net weight of the train to the gross mass of the relevant group of freight trains; kn - Coefficient of irregularity of monthly traffic.

## References

1. Krueger, H., 1999. Parametric modelling in rail capacity planing. In: Proceedings of the 1999 Winter Simulation Conference, pp. 1194–2000
2. Основы взаимодействия железных дорог с другими видами транспорта. Повороженко В.В. и др. –М.: Транспорт, 1972. – 304 с.
3. Большая энциклопедия транспорта: в 8 т. Т. 4. Железнодорожный транспорт/ Главный редактор Н.С. Конарев. – М.: Большая Российская Энциклопедия, 2003. – 1039 с.
4. Железные дороги. Общий курс: Учебник для вузов/М.М. Уздин, Ю.И. Ефименко, В.И. Ковалев, С.И. Логинов, Б.Ф. Шаульский. Под ред. М.М. Уздина. – 5-е изд., перераб. и доп. – СПб.: Информационный центр «Выбор», 2002. – 368 с.