Research

trafIt solutions has a strong background in our own research and development in the fields of operations research, automatic optimization and visualization.

Increasing Punctuality by Optimizing the Allocation of Timetable Supplements
Project in collaboration with SBB-I

Railway delays disrupt operations, impacting network efficiency. Timetable supplements, providing time reserves, are vital for delay recovery but can also reduce attractiveness and capacity. This paper presents a heuristic algorithm to optimize supplement placement, improving punctuality without compromising connections. The framework offers a flexible platform for testing and refining supplement strategies across various railway networks, promising enhanced operational efficiency and passenger satisfaction. Simulations showed that iterative reallocation of timetable supplements can lead to substantial improvements in punctuality.

Approach

Optimizing the placement and quantity of timetable supplements has been a focal point of numerous studies and scientific inquiries.Our research focusssed on:

• Improve a given timetable directly instead of testing strategies. The timetable can be created in traditional fashion or by automatic generation.
• Analyze the effects of optimization for a complete operational day as the delay situation changes considerably.
• Combine optimization of stopping and running time supplements.

Central to our methodology is the utilization of the simulation tool OnTime. Employed by SBB and other railway operators, OnTime plays a pivotal role in predicting the operational quality of timetables and assessing the impacts of infrastructure or timetable adjustments (Franke, Seybold, Büker, Graffagnino, & Labermeier, 2013). What sets OnTime apart from other simulation tools is its reliance on delay distributions and an analytic calculation of their propagation rather than a Monte Carlo approach, which enables it to forecast the operational quality of a timetable for an entire timetable period and comprehensive network in a single simulation run. This unique feature makes an efficient iterative refinement of timetables possible.
A recent study conducted at the University of Applied Sciences and Arts of Northwestern Switzerland devised a toolkit for OnTime to explore various supplement distribution strategies (Salvia & Lozancic, 2023). SBB contributed real-world test scenarios using recent timetables to evaluate these strategies. The study implemented straightforward deterministic supplement reallocation tactics and assessed their impact on operational quality through OnTime simulations. Encouragingly, the results indicated a notable enhancement in SBB's punctuality metric: the percentage of train arrivals within a 3-minute window.
Building on this result, we developed a comprehensive framework to devise, assess, and refine different supplement placement strategies. Using OnTime as the digital operational model, we implemented and tested modifications to supplement placements within existing timetable concepts. This approach allows for systematic exploration and optimization of supplement strategies to enhance overall operational quality.
In every iteration the timetable is slightly adjusted by moving supplements then evaluated after an OnTime simulation run, upon which new adjustments are made. The framework was built in a fashion that allows to simply adapt the optimization approach by providing it with a method for choosing a desired amount of supplement for each running and stopping time, which we called strategy, and an evaluation function to decide whether the last timetable adjustment should be retained or discarded.

The framework calculates the new placement of the supplements by solving the following quadratic optimization problem:

where A is the set of all train activities, i.e. every trip between two stations and stop in a station, Tj is the set of all activities between two fixed stations (thus, ⋃𝑇𝑗=𝐴)𝑗, wi the desired amount of supplements according to the chosen strategy and ri is the current amount of supplements. Thus, this optimization problem finds the amount of supplements for each activity that minimizes the quadratic difference to the desired amount of supplements (Eq. 1) such that the amount of supplements between two fixed stations remains unchanged (Eq. 2) and the change to the previous supplement time is at most the chosen maximum change of m. Finally, max(ri-m, 0) guarantees that the supplements are non-negative (Eq. 3).

 Case Study

SBB provided a test case with the conceptual timetable of 2022. The timetable includes all daily passenger trains as well as the reserved freight train paths on the Swiss normal gauge network, approximately 11,000 trains in total for a day of operation plus their turnarounds and connections. Passenger trains are planned with run time supplements of at least 7%, freight trains have more than 10%. The infrastructure model is made up by all headways for sections and stations. Primary delays are modelled as delay distributions deduced from operational data (Labermeier, 2013) for running, stopping, and departing of trains. The calibration of the OnTime model was conducted to reflect the actual punctuality of the 2022 timetable period not only for the network in general but also at individual stations. Matching recorded operational punctuality data was aimed for and a deviation of at most 3% was accepted. The calibrated OnTime model is the basis for various projects at SBB to evaluate future timetables and infrastructure on the resulting operational quality.
The calibrated model functions as a digital operational model to test the changes of supplement positioning on the operational quality. We used the 3 minutes punctuality measure at about 50 dedicated measuring points. Each iteration of the algorithm, executed on a standard laptop, lasted approximately 6 minutes, of which roughly 1 minute was used by the optimization framework to evaluate the previous iteration and calculate the supplements for the next iteration. The remaining time was used by OnTime to simulate the timetable. The best results were obtained using the random strategy when we allowed changing supplement values by up to 2 seconds in each iteration. After 200 iterations, the overall punctuality of the timetable increased by more than one percentage point from the initial value that was already very high at about 92%. The next Figure illustrates the improvement in punctuality over successive iterations.

The following picture illustrates the difference between the 3-min punctuality of the reference timetable and the timetable with optimized supplements. Green stations show an improvement in punctuality, the intensity of colors indicates the magnitude of difference.

Schematization of Infrastructure Topology

 Basic information on railway topology is often given with geographic coordinates. To use the track topology a different visualization is desirable:

• compact
• schematized
• positioned and aligned

 To better visualize track topology trafIT developed an automatic schematization:

• Schematic view with 45° (or 60°) angles, shortening of sections
• Automatic generation in ~1min instead of manual drawing

The schematization is integrated in railOscope for any additional processing.