either developed from simulation, in the case of future planned infrastructure, or established using actual stopwatch timings or recorded data for infrastructure that is in use.

The Norwegian Railway Directorate (2022) sets some official guidelines for rail modelers, with the aim to minimize lead times and ensure robust traffic management. Technical travel time is estimated through simulation tools, typically assuming 100% traction performance, adhesion, and track power supply. Then, in collaboration with the infrastructure managers, a set of allowances is included. First is the base allowance, which considers factors like driver behavior, adhesion conditions, vehicle performance, and passenger load, typically set at around 3%. A robustness allowance is also included, allowing for the recovery from delays along the route, which is typically set at a value ranging from 4% to 14% for passenger trains depending on the permitted speed.

Moreover, a synchronization allowance is applied to reduce delays between trains at converging sections, typically an additional 1 min. An allowance for unknown infrastructure is also applied, compensating for missing information in route models, typically set at around 2%. Last, an allowance is applied for longer lead times due to temporary infrastructure performance reductions, such as construction or maintenance activities.

Several sources cite the book Railway Timetabling & Operations (Hansen and Pachl 2014), which defines the scheduled running time as a combination of the following components: pure running time between scheduled stops, dwell time at scheduled stops, recovery time (or time allowance), and scheduled waiting time. Recovery time, the main focus of this small research task, is referenced in the book as a necessity to be added to pure running time. Its purpose is to allow trains to recover from minor delays. It is defined as the combination of regular recovery time and special recovery time.

• Regular recovery time is added to every train path as a percentage of the pure running time. The typical time allowance is 3%–7% on European railways and 6%–8% for passenger trains on North American railways. On some railways, the regular recovery time is evenly spread over the train path, and other railways prefer to concentrate the recovery time at the end of the run and at large intermediate terminals.
• Special recovery time is used to compensate for the influence of maintenance and construction works and sections with temporarily bad track conditions. Different from the regular recovery time, it is not added as a percentage of the running time but as a fixed allowance to the running time on the section concerned.

Separately, scheduled waiting time is added for scheduling reasons—for example, to synchronize schedules of different passenger lines at changing points, to synchronize schedules to a cyclic timetable, and to wait for scheduled passing or overtaking. Scheduled waiting times are mostly added to the dwell time of scheduled stops but sometimes also to the running time.

Notably, the book distinguishes the concept of train separation from recovery times or time allowances and clarifies that time allowance and running time are distinct from the concepts of train separation and minimum headways. While these elements are interconnected, for the purpose of this small research task, it is essential to analyze them independently.

The book also delves into the concept of timetable stability, which pertains to the lineʼs capacity to resolve delays and restore the regular state following disruptions. Effective train operations necessitate robust and consistent timetables, incorporating sufficient flexibility to prevent and minimize delays and their spread.

INTERVIEWS WITH U.S.-BASED RAIL TRANSIT AGENCIES

A number of U.S.-based rail transit agencies were contacted by email. Most were able to furnish some insights into their approaches to incorporating time allowances and operating margins into their rail scheduling practices. These agencies exhibit diversity in geographic location, size, and the types of rail services they provide.

L.A. Metro

The Los Angeles County Metropolitan Transportation Authority (L.A. Metro) incorporates a strategy of including a modest amount of recovery time, typically allocated at the arriving station at the end of the line. This buffer is designed to facilitate recovery from unexpected delays and ensure timely departures for subsequent trips. Although no fixed formula is used, L.A. Metro typically adds 1–2 min of recovery time at the end of line, with the specific duration varying according to the length of the line.

Long Island Rail Road

The Long Island Rail Road (LIRR) serves the New York and Long Island regions. It provided detailed insights into its operating margin policy. Fixed time margins, typically 1 min, are applied to each stop. Exceptions exist for stations with shorter platforms accommodating longer trains or experiencing regular loading or unloading delays, where additional dwell time may be added. Scheduling is done in minutes, not seconds.

Margins vary by factors such as stop, route, time of day, and season. For example, diesel services on the Montauk branch in the summer require increased dwell times at some stations because of higher weekend traffic.

Margins are estimated using observed reliability factors, with regular reviews of poor-running trains. If necessary, dwell or run times may be increased after thorough assessments. Signal and infrastructure constraints, along with loading/unloading, primarily influence the agencyʼs operating margin policy.

The policy has remained relatively constant over the years, reflecting the agencyʼs long-standing practices. Historical data on on-time performance and customer feedback play a crucial role in decision-making, striking a balance between reducing runtimes and ensuring a reliable schedule.

At its western terminals, LIRR uses gate time, advertising trains 1 min earlier to the public compared to employee timetables. This adjustment facilitates passenger movement from customer information boards to the station track.

METRA

METRA, the commuter rail system serving the Chicago metropolitan area, provided insights into its operational practices in response to inquiries regarding the use of operating margins. Historically, METRA has not employed operating margins, citing relatively low frequencies as a mitigating factor. The systemʼs service frequencies typically

do not necessitate concerns about trains catching up to each other, except in cases of significant delays.

However, METRA does implement strategies to maintain spacing between express and local trains. This spacing is contingent on the infrastructure of each line. For example, on lines equipped with three or more tracks, concerns about trains catching up are minimized because locals and expresses use separate tracks.

METRA implements schedule padding primarily at the end of trips, with additional time added because of construction projects. Published schedules note potential delays during midday hours, especially during construction periods, with extra time allocated at the last station of affected trains, typically around 10 min. The approach varies by line and the nature of the construction project, aiming to minimize delays during off-peak periods by coordinating meets at control points. Regular padding typically ranges from 2 to 4 min at the tripʼs conclusion, whereas mid-route padding depends on factors such as line characteristics and infrastructure.

New York City Transit

The New York City Transit (NYCT) rail scheduling practice historically has been to schedule to the half-minute at key timepoints. Schedules do not extend to the second or to each individual station, but NYCT provides estimated arrival times for customer information between timepoints (line segments, rather than every station), ensuring passengers are well-informed.

NYCT includes reasonable margins in the schedules for each line segment. It changes scheduled running times by time of day, where necessary, according to historic ridership and performance patterns. It also increases scheduled running times when work is planned on the right-of-way that requires trains to operate slowly past work zones. The New York subway is open 24 hours a day and therefore does not have regularly scheduled overnight shutdowns during which it can perform planned maintenance work without revenue trains in operation.

NYCTʼs base scheduled running times are based on actual running times between timepoints, and these running times are adjusted occasionally. It generally adjusts base schedules twice yearly. Generally, it schedules to the 50th percentile observed running time between timepoints, by time of day and day type (weekday, Saturday, or Sunday), within ±1.5 standard deviations to exclude outliers, and rounded to the nearest 30-s (second) increment. Some exceptions include segments where trains approach terminals, where they may schedule to more of a free-flow running time if there is congestion, because excess scheduled running time can itself be a cause of terminal congestion.

Running times are fairly stable, so they are updated only occasionally. For a timepoint-to-timepoint pairing, dwells at intra-timepoint stations and at the latter station in the pair are included in these running times for the whole segment.

No official margin policy exists, but when running times are revised, NYCT considers line-specific variables such as extended periods of construction/maintenance work, merges with other lines or other operational considerations, and feedback from operating staff.

NYCT adds margin time at certain locations in certain circumstances:

1. To account for construction/maintenance work along the right-of-way during off-peak times (middays, overnights, weekends). This margin (up to a few minutes) is generally added at a timepoint near the end of the line to account for upstream track work that delays trains.
2. At select locations and intervals as a margin to account for certain operational factors in the schedules. Because of the complex nature of NYCT operations, with most subway lines merging and diverging along their length with one or more other lines, it ensures that it does not have two trains scheduled to be in the same place at the same time. If it has such an instance, it is referred to as a bang, and it adjusts the timetable of one line or the other (occasionally both lines) to separate the lines by at least 1.5 min (preferably 2 min). It adjusts terminal departure times to avoid the bang, or it adds scheduled hold time as a margin so that one train waits while the other passes in front of it. Similarly, it may add a margin of time approaching terminals to allow for pocket clearance.

When asked whether there was an evolution in how their approach changed over the years, staff responded that they improved their access to data. In the past decade they have had access to an almost complete sample of running times from their train movement data, and they can track each lineʼs running time and discrepancies with scheduled running times more easily than they could before full electronic data.

SEPTA

A representative for the Southeastern Pennsylvania Transportation Authority (SEPTA), which operates the regional rail system serving the Greater Philadelphia region, provided information on dwell time and runtime variability, the common causes behind them, and recovery margins applied across the system. The SEPTA Regional Rail relies on Trainplan scheduling software to manage its operations. The software has a point-to-point runtime database consisting of stop-to-stop, pass-to-stop, stop-to-pass, and pass-to-pass operating times by track and equipment type. Timings are rounded up to the nearest 15-s increment.

Dwell times at stations are managed independently and can be adjusted manually or through schedule templates. Suburban stations typically experience shorter dwell times, ranging from 30 s during off-peak hours to 45 s to 60 s during peak periods. Larger suburban stations can have dwell times of 60 s to 90 s. Major stations, especially those in Center City, can see dwell times ranging from 60 s to 240 s because of longer boarding and alighting processes.

SEPTA Regional Rail is a through-service operation through downtown Philadelphia. Center City stations, being key central hubs, often experience significant counterflow traffic, with large numbers of passengers alighting and boarding. At certain stations, approximately 200 to 350 passengers disembark and 100 to 150 passengers board within a timeframe of 120 to 180 s. For example, Suburban Station is one of the core SEPTA Regional Rail stations in Philadelphia. Given the through-service, SEPTA uses Suburban Station as a location for crew changes that occur during passenger boarding and alighting. Suburban Station has a minimum dwell of 120 s, but during peak times can be 240 s or more for passenger movement and the crew change.

On lines such as the West Trenton line, some stations feature mini-high platforms solely on the inbound side; these have no outbound side platforms because of adjacent freight tracks. Passengers