Assessing Temporary Speed Restrictions and Associated Unavailability Costs in Railway Infrastructure

This paper analyses the occurrence of temporary speed restrictions in railway infrastructure associated with railway track geometry degradation. A negative binomial regression model is put forward to estimate the expected number of temporary speed restrictions, controlling for the main quality indicators of railway track geometry degradation and for the maintenance and renewal actions/decisions. The prediction of temporary speed restrictions provides a quantitative way to support the assessment of unavailability costs to railway users. A case study on the Lisbon–Oporto Portuguese line is explored, comparing three statistical models: the Poisson, the ‘over-dispersed’ Poisson and the proposed negative binomial regression. Main findings suggest that the main quality indicators for railway track geometry degradation are statistically significant variables, apart from the maintenance and renewal actions. Finally, a discussion on the impacts of the unavailability costs associated with temporary speed restrictions is also provided in a regulated railway context.


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In transportation infrastructure systems, maintenance and renewal operations might cause some impacts in the 32 availability of the railway system, besides the associated costs related to these operations. One of these impacts is 33 the occurrence of temporary speed restrictions, which affect the normal operation of trains in the railway 34 infrastructure and cause unavailability costs. A main cause of the occurrence of temporary speed restrictions is the 35 degradation of railway track, namely the railway track geometry degradation. In order to study these impacts, 36 performance indicators of the railway infrastructure have to be measured and monitored [1], namely temporary 37 speed restrictions as an availability indicator. Besides, the analysis of such indicators has to take into account the 38 infrastructure influence on rail punctuality (delays), i.e. infrastructure fault datasets should be linked with 39 operational delay datasets to improve railway infrastructure management. Temporary Speed Restrictions are also 40 part of the performance indicators that regulators use to assess the infrastructure manager performance [3].

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Moreover, the imposition of temporary speed restrictions has been found to be an influencing factor on train 42 punctuality [4]. Operating speed has also been identified as a key variable in infrastructure design consistency [5].

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Many studies on delays in railway infrastructure have focused on quantifying the delays [6], given the occurrence of 44 a delay (e.g. a temporary speed restriction), exploring the impact of a given train delay in the network. These studies 45 do not discuss what caused the occurrence of a temporary speed restriction, and they just assume that it happens 46 and then they are interested in computing the different train delays imposed to a given network. From our 47 perspective, it seems that there is a missing link/connection/dependence between railway track geometry, the 48 maintenance and renewal actions, and the occurrence of temporary speed restrictions in the network. Moreover, in 49 any decision support system for planning maintenance and renewal actions in transportation infrastructures, the 50 assessment of unplanned impacts like the temporary speed restrictions are crucial for the definition of a 51 maintenance/renewal strategy that not only minimizes maintenance and renewal costs but also minimizes delays.

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The past research on railway delay modelling has walked a long path, mainly focused on the quantification of train 53 delays. Several studies aimed to model train delays, considering primary delays and knock-on effects or secondary 54 delays, i.e. the propagation of delays to other trains in the network. A delay estimation methodology is put forward 55 in [7], which defines an exponential relation between travel time delay and train mix for single and double track lines, validated with simulation results from a design of experiments and also with real-world delay values from a 57 sub-network existing in the Los Angeles area. Moreover, they provided an excellent review on previous research, 58 identifying two main approaches dominating the research in this topic: the analytical models and the simulation 59 models. Another approach also relied on simulation software (Rail Traffic Controller) results to fit an exponential 60 dependence with the number of trains per day to estimate average delay times for single and double track due to 61 in-service failures of different length (e.g. 1h, 3h and 5h) and associated costs [8]. They also conducted some analysis 62 on the variability of train delays for different traffic volumes. Further micro-simulation/simulation models that 63 support decisions regarding timetabling and railway operations were also explored in [9]. Another statistical 64 estimation approach to model railroad congestion delay from BNSF railway data for eight districts in the western US, 65 using multiple linear regression with an exponential functional form to explain the total train running time (i.e. the 66 free running time plus the congestion-related delay) using as independent/explaining variables: train-related and 67 track-related variables, primary and secondary-effect variables and capacity utilization effect variables [10]. 68 Moreover, delays incurred by the passengers have been analysed and an overall generalized waiting cost was put 69 forward, comprising: the cost of extra stopping in the stations, the cost of extended transfer times and the cost of 70 deviating from the ideal running time supplements [11]. This approach detailed all passenger flows in train 71 connections, namely: the transfer passengers, the through passengers, the departing passengers and the arriving 72 passengers; and assigning distinct costs to each type of delay. In the same research direction, i.e. focusing in delays 73 suffered by the passengers, passenger delay models were explored, instead of the typical train delay models, in 74 which passengers are adaptive agents that may choose a different route than their planned route (assuming in the 75 most optimistic scenario that they have a complete knowledge of present and future delays in the system) [12].

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These two contributions [11,12] represent the most important steps towards the quantification of railway delays 77 suffered by the passengers (or freight).

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Regarding the delays caused by the infrastructure manager, i.e. the infrastructure delays, there is a lack of published 79 references. To the best of our knowledge, the only reference discussing infrastructure delays is [13]. Delay risks associated with train schedules were modelled, detailing three types of delays: track related delays, train dependent 81 delays and terminal/schedule stop delays.

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Nevertheless, there has been little research on the impact of maintenance and renewal decisions in railway delays 83 and unavailability costs. For simplicity, let us put forward a classification for different delays, following the idea of 84 quantifying delays depending on the agent responsible for causing it, in order to frame this research work in a larger 85 research framework. The term 'agent' is used considering the vertical separation between the Infrastructure 86 Manager (IM) and the Train Operating Companies (TOC), which means that we may have as agents: the IM, the 87 different TOC and also the passengers or freights (i.e. the final users). Having said that, delays can be classified into 88 three groups: 89 i) infrastructure delays, i.e. the delays whose responsibility is assigned to the infrastructure manager; 90 ii) train operating companies delays, i.e. the delays whose responsibility is assigned to the train operating 91 companies; 92 iii) the passengers or freight delays, i.e. the delays whose responsibility is assigned to the passengers or the 93 final users.

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This classification is particularly useful as it emphasizes the need of more research on the link between degradation 95 processes, maintenance and renewal actions of the IM's responsibility and the above-mentioned infrastructure 96 delays. Note that other railway agents that could also be integrated in this conceptual framework for a vertically 97 separated sector would be the regulator or the regulatory entity and the maintenance contractors.

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To a certain extent, there is a parallel between this proposed delay classification and the one put forward before in 99 [13], especially in the first two groups, i.e. the infrastructure delays (or track-related delays) and the train operating 100 companies' delays (train dependent delays), respectively. However, the terminal/schedule stop delays from [13] are 101 not necessarily equal to the passenger delays as a passenger can catch a delayed train without incurring into any 102 delay impact in his/her trip.
Let us now focus on the infrastructure delays as they are the most relevant for IM decision-making process regarding the infrastructure delays due to temporary speed restrictions (i.e. the unplanned infrastructure delays).

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Some of these delays are not even totally perceived by the passengers, by the operators and even by the regulator.

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These delays were above defined as planned infrastructure delays because they are associated with medium-/long-109 term downgrades of speed performance due to reductions of the maximum permissible speed. As these changes 110 immediately affect the train schedule production, they are not perceived by the other railway agents and in fact, 111 they may hide a poor performance of the IM in terms of asset management regarding maintenance and renewal 112 actions. However, the aim of this paper is to discuss solely the unplanned infrastructure delays due to temporary 113 speed restrictions and these planned infrastructure delays are left for further research, though some first steps have 114 been taken in [14] within a bi-objective optimization model for maintenance and renewal decisions.

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The outline of this paper is as follows: this first section introduces the need to assess the occurrence of temporary 116 speed restrictions in railway infrastructure and reviewed the past research on railway delays, focusing on the delays 117 related with maintenance and renewal actions (or the 'infrastructure delays'). Afterwards, a review is provided on 118 the statistical methodology followed within the Generalized Linear Model (namely the negative binomial regression, 119 the Poisson and the 'over-dispersed' Poisson regressions), in which the different regression models are estimated 120 for our case study and compared using the Akaike Information Criterion (AIC). A context discussion on the impacts 121 of the assessment of temporary speed restrictions and associated costs in the railway regulatory framework is put 122 forward. Finally, the last section highlights the main conclusions and suggests further research in this topic.

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This section explores and discusses the statistical methodology followed in this paper to predict the occurrence of 125 temporary speed restrictions in railway infrastructure within the Generalized Linear Model framework, namely using 126 the negative binomial regression model, the Poisson and the 'over-dispersed' Poisson regression models.
To assess the temporary speed restrictions related with rail track geometry, a database from the Portuguese IM 128 (REFER), called 'e-LVs', was analysed. This application/database compiles a series of information regarding 129 temporary speed restrictions, namely: the identification details as the line, the direction and the location; the delay 130 details as the theoretical/computed delay, the restriction speed, the maximum permissible speed, the initial and 131 final times, the motive; and other information not relevant for the following discussion.

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Of course, many temporary speed restrictions have other motives than the ones related with the rail track subsystem 133 or related with the railway track geometry. Take for instance the example of the temporary speed restrictions due 134 to maintenance actions associated with the catenary subsystem. Those speed restrictions were not included in the 135 following assessment because only the speed restrictions related with rail track geometry condition, maintenance 136 or renewal actions were included in this analysis. In fact, IM is responsible for 20% up to 30% of the total delays in 137 the railway system, and the track system and their faults are responsible for around 3% of the total delays in the 138 railway system [1,2].

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The Immediate Action Limits (IAL), the Intervention Limits (IL) and the Alert Limits (AL) are set by the European 166 Standard EN 13848-5 [16] for all rail track geometry defects. For further information on these rail track geometry 167 defects and their indicators, the reader is referred to [17][18][19][20], while for further details on the railway track system, 168 irregularities and variability of some physical parameters, the reader is referred to [21,22].

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The Poisson distribution is usually parameterized through the parameter λ and has the following probability

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The main difference between the over-dispersed Poisson regression model and the Negative Binomial regression 192 model is that the variance of the former is a linear function of the mean, while the variance of the latter is a quadratic 193 function of the mean [23]. The negative binomial regression model has been used in several studies related to 194 infrastructure modelling [24], from estimating transition probabilities in highway infrastructure degradation [25] to 195 hurricane-related outages in the electric power systems [26], or even in railway safety [27] and road safety [28].

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Moreover, the variables controlling all other rail track geometry defects, i.e. IAL, IL and AL, also proved to be 357 statistically significant predictors. Finally, the maintenance (Tp) and renewal (Rw) decisions were also statistically 358 significant predictors, and exhibited Incidence Rate Ratios equal to 1.150 and 6.009, respectively. Some discussion 359 on the need to include unavailability costs associated with temporary speed restrictions was also provided.

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Regarding further research, the final objective of the present model is the integration of the expected number of 361 temporary speed restrictions and associated delays in an objective function in order to optimize the Alert Limits that 362 trigger preventive maintenance actions, as part of a planned maintenance strategy.