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Capacity Statement for Railways
Alex Landex, al@ctt.dtu.dk Centre for Traffic and Transport, Technical University of Denmark

1 Abstract
The subject “Railway capacity” is a combination of the capacity consumption and how the capacity is utilized. The capacity utilization of railways can be divided into 4 core elements: The number of trains; the average speed; the heterogeneity of the operation; and the stability. This article describes how the capacity consumption for railways can be worked out and analytical measurements of how the capacity is utilized. Furthermore, the article describes how it is possible to state and visualize railway capacity. Having unused railway capacity is not always equal to be able to operate more trains. This is due to network effects in the railway system and due to the fact that more trains results in lower punctuality. Keywords: Railway capacity, Capacity, UIC 406, Capacity consumption, Capacity utilization

2 Introduction
The railway sector has in recent years been divided into rail authorities, infrastructure managers and operators. Furthermore, more construction companies and consultants have started working with railways. The many new companies result in a need for consensus of how to express and communicate core elements such as railway capacity. As a consequence of no consensus on railway capacity the International Union of Railways (UIC) published a leaflet – the UIC 406 capacity leaflet – describing railway capacity in the year 2004. The UIC 406 capacity method defines railway capacity as “the total number of possible paths in a defined time window, considering the actual path mix or known developments respectively…” [25]. Since the publication of the UIC 406 capacity leaflet many organizations inside the railway sector have been working on how to expound the capacity leaflet to calculate the capacity consumption. This work has been published in a number of publications, e.g. [1], [2], [8], [9], [10], [11] and [23]. However, only little work has been done on how to state and present the railway capacity – e.g. [15] and [23]. Therefore, this article will present how to state and present railway capacity in a straightforward way according to the internationally accepted UIC 406 capacity method.

Annual Transport Conference at Aalborg University 2007

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First, the article gives a short introduction on how to calculate capacity consumption for railway lines in section 3. This is followed by a description of how to examine the utilization of railway capacity in section 4. Based on the calculation of capacity consumption and the examination of capacity utilization, it is described how railway capacity can be stated in section 5. This is followed by a discussion in section 6 and concluding remarks in section 7.

3 Calculating the capacity consumption
To measure railway capacity consumption it is necessary to know the timetable graphs for the railway line(s) examined. By using the timetables graphs for the given infrastructure the dynamics of rolling stock is implicitly included as the rolling stock is determining the size of the blocking stairs. The capacity consumption of the railway infrastructure is then measured by compressing the timetable graphs so that the buffer times are equal to zero, cf. figure 1. This compression considers the minimum headway times, which depends on the interlocking system and train characteristics [21].

Single track

Timetable graph compression

Double track (one direction)

Timetable graph compression

Figure 1: Compression of timetable graph according to the UIC406 capacity method. Partly based on [8]

As it is difficult or even impossible to compress the timetable graphs for an entire complex railway network, it is necessary to divide the network into smaller line sections which easily

Annual Transport Conference at Aalborg University 2007

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can be handled by the UIC 406 capacity method. Railway lines are divided into...
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