# Capacity analysis

Capacity analysis is a method that allows the examination and determination of parameters relating to different types of capacity and capabilities for general transmission and movement in a specific time unit [1]. Capacity analysis is used for the needs:

## Capacity Analysis in Transport

Transport capacity is the maximum transport capacity of a means of transport in a given period of time, in specific conditions defined by current technical and organisational factors. Technical factors determine the payload or load capacity of the means of transport, the speed of the vehicle or the type of vehicle transported [2]. Organisational factors depend on the speed of loading and unloading, the route of the means of transport and the degree of utilization of the payload [3].

## Capacity meters

The main measure characterising passenger transport of each type is capacity, defined as the product of the number of passengers (train, bus) and the distance travelled by them. The unit of transport work is the passenger-kilometre [4]. However, the complexity of passenger traffic makes this meter a synthetic one, not reflecting the actual complexity of the movement of vehicles. Therefore, in the case of a number of factors must be taken into account when calculating the transport work for a train as an example, such as [5]:

• the distance travelled,
• wagon class
• type of passenger traffic.

## Assumptions for capacity analysis

The concept of capacity in passenger traffic (e.g. rail) can be defined as the number of passengers that is movable in a given period of time, taking into account the convenience of travel [6]. Determination of seating capacity passenger coaches may concern the whole railway network, or only the line or section to be analysed [7].

## Calculation of capacity

The following formula may be used to calculate the seating capacity [8]:

Zol = Np • nw • nm • Wp • $$\frac{ls}{lp}$$[passengers/day]

whereby:

• Np – number of trains running on a given line,
• nw- number of wagons in one train,
• nm – number of seats in one car,
• Wp - coefficient of utilisation of wagon capacity
• ls - Average distance of a train running on a given line,
• lp - Average travel distance of one passenger.

For example:

• Number of trains running on the line: Np= 36 trains/day
• Average number of wagons of 1st class in one train: nw= 1,19 wagons
• Average number of wagons of 2 classes in one train: nw= 4,64 wagons
• Number of seats in a Class 1 car:
• nm= 9 compartments • 5 seats = 54 seats
• Number of seats in a Class 2 car:
• nm= 10 compartments • 8 seats= 80 seats
• Average train running distance on a given line: ls = 2764/18 = 153,56 km

The wagon capacity utilisation factor is the quotient of the number of passengers in the wagon and the number of seats in the wagon [9]. When determining the maximum capacity of rolling stock, it is assumed that all the seats in the train are occupied, and therefore the coefficient value is Wp=1 However, when determining the level of capacity utilisation of rolling stock, it is necessary to determine the coefficient on the basis of the current train turnout and to calculate its average value [10]. Let the exemplary average distance of one passenger is lp=63 km. On the basis of the above data, the maximum capacity of 1st and 2nd class cars and the total capacity for both classes of cars can be calculated.

• Zol1= 36• 4, 64 • 80 • 1 • 153,56/63 = 32606 passengers 1 class/day.
• Zol2 = 36• 1,19 • 54 • 1•153,56/63 = 5644 passengers 2 class/day.
• Zol = Zol1+ Zol2 =32606 + 5644 = 38250 passengers /day.

## Capacity analysis in determining congestion and bandwidth

Capacity analysis is also used to traffic measurements, determine congestion and bandwidth. In a stochastic concept of highway bandwidth analysis, the capacity of an object on a highway is treated as a random variable, not a constant value. In this way, the stochastic approach provides new measures of traffic flow performance based on traffic reliability aspects [11]. A method for estimating bandwidth distribution functions based on empirical data based on statistical methods for the analysis of lifetime data is introduced. This method has been developed for the analysis of motorway throughput. However, it has been shown that the stochastic approach is also applicable to intersections [12].

## Capacity Analysis in IT

Each computer is equipped with memory, i.e. electronic systems for storing data and programs. Memory is an ordered (numbered from 0) set of elementary memory cells of a specified length. RAM (Random Access Memory) is a memory with free access (access to any RAM cell is possible at any time). RAM is an internal, operating memory, data can be read and written from it. It contains the data necessary to perform calculations and the results of these calculations. This memory is ephemeral, i.e. when the computer is shut down by any means, the information contained in the RAM is lost [13]. Data from internal memory can be protected against loss by storing them in external memory, e.g. on a hard drive. Particular types of RAM differ from each other[14]:

• capacity, read/write speed, power consumption and voltage needed to power them.

Bandwidth is the ability to transfer data in a time unit. Actual frequency is the actual data rate of the computer. To calculate the bandwidth, you need to know the effective frequency and multiply it by the width of the data bus (or vice versa). Example for DDR-400 memory [15]. Capacity = 400MHz * 64b = 400MHz * 8B = 3 200MHz * B = 3 200MB/s

## Capacity Analysis in Management

Capacity in management is understood as efficiency, effectiveness and potential [16]. It is a result of undertaken actions, described by the relation of the achieved effects to the incurred outlays. It means the best effects of production, distribution, sales or promotion, achieved at the lowest costs, such as economy, enterprise, process, finance, management, investment or motivation [17]. Capacity determines the functioning of an organisation and determines its development. It is an important tool for measuring management effectiveness. It covers the phenomena inside and outside the organization. It shows the speed of reaction to challenges that flow from the market, as well as the expectations of its participants. Capacity is also a measure of effectiveness and efficiency, understood as a measure of the extent to which the set goals are achieved [18]. Capacity is measured using partial indicators characterising the effectiveness of particular production factors, e.g. labour productivity or capital productivity, and synthetic indicators of the effectiveness of the entire enterprise, e.g. return on capital, assets, sales. Capacity can be identified ex post and ex ante [19]. When calculating ex ante capacity the expected effects are estimated with the use of specific resources and time, while ex post Capacity is determined by the results of specific actions [20].

Author: Natalia Chowaniak

## Footnotes

1. M. O’Neill, G. Warren, 2016, p.1
2. M. O’Neill, G. Warren, 2016, p.2-4
3. M. O’Neill, G. Warren, 2016, p.2-4
4. R. Chambers 2018, p.13-16
5. R. Chambers 2018, p. 13-16
6. M. O’Neill, C. Schmidt, G. Warren 2016, pp. 18-21
7. M. O’Neill, G. Warren, 2016, p.5-6
8. M. Vangelisti, 2006, pp.44-50
9. KJ. Cremers, Martijn, A. Petajisto, 2009, pp. 3329-3365
10. KJ. Cremers, Martijn, A. Petajisto, 2009, pp. 3329-3365
11. M. Vangelisti, 2006, p. 50
12. M. Vangelisti, 2006, p. 50
13. M. O’Neill, C. Schmidt, G. Warren 2016, pp.18-21
14. M. O’Neill, C. Schmidt, G. Warren 2016, pp.18-21
15. M. O’Neill, C. Schmidt, G. Warren 2016, pp.18-21
16. M. O’Neill, G, Warren, 2016,p.4
17. M. O’Neill, G, Warren, 2016b,p.4
18. M. O’Neill, G, Warren, 2016,p.5
19. KJ M Cremers, A. Petajisto, 2009, p.6
20. KJ M Cremers, A. Petajisto, 2009, p.6

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