Optimal real-time junction scheduling for trains with connected driver advice systems

Highlights

• Optimal real-time scheduling of trains through junctions.

• Uses driver advice systems to produce arrival times and revised driving profiles.

• Preliminary trial in the UK reduced trains delayed at a junction from 6.1% to 1.6%.

Abstract

Many railways around the world are using driver advice systems to provide real-time advice to drivers on how to control their trains to stay on time with minimum energy use. Standalone driver advice systems use pre-prepared timetables. More recently, driver advice systems are being developed with data connections to central control systems, to allow real-time updating of schedules.

Dynamic rescheduling of trains in response to disruptions can be an intractable problem for large networks. Localised junction scheduling, combined with driver advice systems, can reduce time lost at individual junctions by ensuring that trains arrive at the junction with sufficient headways to ensure smooth traffic flows.

We have developed a system that combines real-time driving advice calculation with real-time junction scheduling to reduce delays at junctions, and have simulated the operation of this junction scheduling system at Neasden Junction in the UK, where about 10% of trains are slowed at the junction. When an express train was delayed by three minutes early in its journey, the result would have been three trains arriving at the junction within a 60 s interval. The junction scheduling system detected the potential conflicts 20 min before they occurred, and calculated new target times at the junction to resolve the conflicts. The connected driver advice systems responded by calculating new optimal speed profiles to meet the revised arrival times.

Introduction

Train driver advice systems are used on passenger and freight trains around the world to help drivers keep their trains on time with minimum energy use (Scheepmaker et al., 2017; Panou et al., 2013). A driver advice system typically uses a device in the cab to monitor the progress of a train journey relative to a predetermined schedule, then calculate and display advised driving modes and speeds.

On busy rail networks, keeping trains on time and recovering smoothly from small but inevitable disruptions is often more important than saving energy. There is increasing interest in developing connected driver advice systems, where driver advice systems in train cabs are connected via a communication system to central systems that monitor the trains on a network, detect disruptions, and issue updated schedules to trains in real time (Technical Strategy Leadership Group, 2012).

Dynamic rescheduling of trains in response to disruptions can be an intractable problem for large networks with many trains and many locations where trains might interact. Large problems such as this are often tackled by partitioning them into smaller sub-problems. Solving the smaller problems may not give an overall optimal solution, but the improvements may still be worthwhile. In this paper we consider a distributed approach to dynamic rescheduling where local scheduling is done for individual junctions.

The junction scheduling system monitors the trains approaching a junction and revises train schedules, in real time, to ensure smooth flow of traffic through the junction:

• the driver advice system on each train calculates the earliest possible arrival time and the desired arrival time at the junction

• a central junction scheduler uses these earliest and desired arrival times to check for conflicts between trains, and calculates a new target arrival time for each train to resolve any conflicts

• a revised timetable is sent to each train, and the driver advice system on each train calculates a new, energy-efficient driving strategy to meet the revised timetable.

It is important that the system operates in real time. In practice, trains can experience delay at any time, and delays can propagate to other trains. The rescheduling system must be able to respond quickly to ensure that only small adjustments to train speed profiles are required, which will help minimise the propagation of delays.

In December 2014, TTG Transportation Technology, First Group and Network Rail demonstrated the concept of junction scheduling at Heathrow Airport Junction, where traffic approaching London Paddington from Reading merges with express trains from Heathrow Airport. The prototype junction scheduling system used a data feed from track circuits to monitor the progress of trains travelling between Reading and the junction—a journey that typically takes about 17 min. Trains departing Heathrow arrive at the junction three minutes after departing Heathrow, so the system assumed that these trains would run to the published schedule. About two thirds of the trains from Reading were equipped with driver advice units. A revised junction arrival time was calculated in real time for each equipped train and uploaded to its driver advice unit. The impact of schedule updates was assessed by counting the number of trains with driver advice systems that were delayed on the approach to Airport Junction, without and with schedule updates. A train was considered to be delayed if the speed fell below 10 km/h in the 10 km prior to Airport Junction (there are no scheduled stops in this region). The overall results during the two-week test period are shown in Table 1. The results during peak periods are shown in Table 2. The ‘Jeffreys interval’ for each sample is the 95% credible interval—based on the data collected, there is a 95% probability that the percentage of delayed trains will lie in this interval.

The Airport Junction scheduling system was relatively straightforward, since it involved the merging of only two traffic streams. This paper describes real-time junction scheduling for more complicated junctions. We will illustrate how the system works using train flows through Neasden Junction in the UK. Fig. 1 shows the section of the rail network around Neasden Junction. Neasden Junction is shown as the large dot to the right of Wembley; other stations are shown as smaller dots. All trains operating in this area are equipped with driver advice systems. The junction scheduling system will consider trains approaching Neasden as far as 20 min away. This will include trains as they leave London Marylebone, and express trains as far west as Amersham or Chiltern Hills.

There are four traffic streams through Neasden Junction:

• ND: trains travelling in the ‘down’ direction (away from London) on the northern route

• NU: trains travelling in the ‘up’ direction (towards London) on the northern route

• SD: trains travelling away from London on the southern route

• SU: trains travelling towards London on the southern route.

These four streams are illustrated in Fig. 2. Conflicting movements are defined in Table 3.

This part of the UK rail network carries passenger trains operated by Chiltern Railways. The trains are equipped with the Energymiser driver advice system, a commercial system based on our previous train control work (Albrecht et al., 2016a, 2016b). We analysed the Energymiser logs of 8000 trains passing through Neasden Junction between 2016-01-01 and 2016-02-10. Fig. 3 shows speed profiles of trains passing through Neasden Junction. The red vertical line on each graph is Neasden Junction. The red speed profiles that slow near Neasden Junction are from trains that slowed unexpectedly prior to the junction.

Table 4 shows the average number of trains per day that slowed to less than 50 km/h in the 1.5 km prior to Neasden Junction. (This interval of track contains the signals that stop or slow trains approaching Neasden Junction.) Overall, there were on average 20 trains per day (10%) delayed at Neasden Junction.

The remainder of this paper reviews the literature relevant to dynamic junction scheduling, discusses how driver advice systems can be used to control arrival times at junctions, formulates and solves the junction scheduling problem, and demonstrates our method using examples from junctions in the UK.