White Paper

Allocating railway traffic with QUBO

What is the optimal train/track combination required to maximise the performance of a station, while guaranteeing the end user a high quality service?

The complexity of railway management

The management of train routing within a station is a complex problem, which requires the consideration of a multitude of constraints: the topology of the station, the management of the simultaneous arrival of several trains, the use of a specific optimisation logic, the rigidity of the railway network, as well as delays and malfunctions that are often difficult to predict. In particular, handling unexpected situations in an inadequate or untimely manner can generate repercussions thousands of miles away, causing disruptions and difficulties for end users.

Optimising Station Performance
with Quantum Computing

In reality, train/track planning is often carried out using a semi-manual approach, with the framing of the problem within a linear model aimed at ensuring simplification at the expense of efficiency. In this context, however, Quantum Computing can represent a valid solution for enhancing performance efficiency thanks to its calculation speed.

Reply has exploited its potential by creating a QUBO model, an acronym for Quadratic Unconstrained Binary Optimisation. It is a mathematical formalism designed to describe quadratic and binary variable combinatorial optimisation problems, and then solve them easily through the quantum capability.


Reply experimentation within an Italian railway station

Starting from the timetable of a medium-large Italian station, the Reply team modelled the facts using the QUBO algorithm, defining a series of constraints to help optimise the station’s traffic flow and improve the end user experience.
The results obtained thus far were highly effective: the management being trialled was able to optimise the use of the available tracks and increase the capacity of the railway lines, while also reducing the walking distance that passengers needed to cover to make a connection within the station, thus also improving the user experience.

Where Reply can
make a difference

Reply has launched a multi-disciplinary research group dedicated to quantum computing, focused on testing the potential of this technology and developing concrete solutions for companies and businesses. More specifically, the work conducted by the Reply team focuses on quantum optimisation algorithms, including the creation of concrete case studies and collaboration with international players. In the rail mobility sector, the practice developed by Reply has demonstrated the potential to manage the Train Platforming Problem (TPP) successfully through an automated and quantum-based approach.