Transport Solutions

We are a company that specialises in innovative solutions for the transport industry. After years of research, important insights on how to improve the industry have been established. In this example we will investigate the effect of more evenly spacing stations on a high-speed railway line. Please contact us for more in-depth calculations and making your vision become a reality.

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For example, there are two hypothetical high-speed lines, 1 and 2, each having a total of four stops along their route of length 300km. Line 1 has one station which is the starting point and has another station 20 km further down the line. The third station is 280 km away from the first and the final one is 300 km away from the first station. Line 2 has the same two starting stations, but the third station is 150km away from the first, leaving the final station 280 km from the first station. It is missing the last station.

We can assume that since both the lines have an equal number of stations, the journey time of the high-speed lines is roughly the same.

With line 1, both the last stations are close together, so they can be said to serve the same city, but on opposite ends of the city. If the population of this city is 1 million, then it can be said that each of the two stations at the city serves a population of 500,000 people, since this is the total population divided by the number of stations serving it.

Line 2 has a station on the outskirts of the end city with a million people, just like line 1 does. However, it is missing one station on the opposite end of the city. It therefore can be said that it only serves 500,000 people out of a possible 1 million effectively. However, it has another station that line 1 does not have which is linked to the major town instead. This station serves a major town (or small city) of 100,000 people. This is significantly less than the end stations of line 1, both of which reach 500,000 people. On the face of it, line 1 is better suited in catering for a commuter’s needs than line 2. However, other factors need to be considered.

Firstly, you will need to realise that on line 2, the trains are stopping at a small city/large town. Compare this to line 1 where two stations are at the starting city and two stations at the end city. On this line, passengers may use the train as a type of shuttle service inside the city, but they are more likely to use another form of transport such as an inner-city train, car, taxi or bike to reach their destination more quickly and cheaply. Whereas on line 2, the small city of 100,000 people, people cannot use a bike or taxi realistically to get to the next train station. They rely wholly on the train. Also, commuters at the starting city will depart at the town, while new passengers will board from the town to access the end city. The usefulness of the line having a stop at the town is effectively doubled.

Now we will see what effect the car, inner city train or aeroplane has in connecting passengers from the start of the journey on line 2 to the town which is 150 km away from the first station. An inner-city train is too slow with too many stops, and you will have to change trains to a national rail service when you exit the starting city. This national rail service may be quite slow as well since it is not high-speed. If it has an average operating speed of 150km/h, then to travel from the first station to the large town, which is at a distance of 150 km, would take 1 hour. With the high-speed train, it may have an average speed of 250 km/h. This means it can cover the same distance in 36 minutes. This is 24 minutes faster than the conventional train – almost half an hour. With the plane, the distance is too short to make it commercially viable, so this can be ruled out. The car is the main transportation component that can compete with the high-speed line in connecting this small city with the major cities. However, the car is slower than the high-speed train. It experiences many starts and stops, traffic delays and has a top speed far lower than the 300 km/h possessed by the train. We searched on google maps for a car journey of 100 km and it said it would take over one and a half hours. Therefore, for a journey of 150km, it would likely take over 2 hours.

Yet, there are problems with the high-speed train as well. There is a need in travelling to the station, waiting for a train and using this train to travel to the high-speed terminus. From here, the high-speed journey can begin. Once the passenger reaches the small city via the high-speed train, they will then have to travel to their destination which may be walking or catching a taxi or, if further out, catching another train. The car avoids all these problems, so the difference is not as large as the two hours by car vs the 36 minutes of high-speed train. The train incurs additional travel times in getting to the terminal etc. Nevertheless, it is reasonable to suggest at least half an hour is saved by using the high-speed rail rather than the car. It all depends on the population of communities which have easy access to the high-speed rail line. Since a city is densely populated, and since there are two stations on line 2 in the starting city (as there are on line 1), then it can be assumed that many people will make use of the train journey even if they possess a car. This is because for them, the train is much faster, and they could still be saving more than half an hour or so in travelling to the small city halfway along line 2. They will then have to travel somewhere in the town to their destination but since the town is small compared to a city, it may only take 5 or 10 minutes to reach their destination. Another problem with the car is that it will need to be parked somewhere, which could incur significant charges, thus making it impractical for some. Also, what about the people who do not possess a car? For these people, they may have to use a long-distance train which is not classified as high-speed, or they may use a coach service. As described earlier, a similar loss in time of half an hour can be assumed here as well.

Overall, we are simply trying to justify why the high-speed line is better than the car or long-distance train (which is not high-speed), but we have not really answered the question as to why the stations should be more evenly placed along a rail line. The reason why we compared it to other forms of transport was to try to estimate the time saved of having a high-speed line stopping at a small city rather than using an alternative form of transport. This figure can then be used for later calculations – as you will see soon.

The predicted time of half an hour is a lot of time saved but bear in mind that the small city itself is not a very popular destination for many passengers. It is one-fifth the size of the other station’s estimated population catchment area. How many people will depart at this station then? Again, many factors are at play but to simplify things we can say one tenth or 10% of passengers will depart from the train at this town as this seems like a reasonable figure. But, as explained earlier, passengers will board the train from the small city to the end city. So, in effect, you double the number of passengers using the station. A total of 20% of passengers will therefore make use of this stop. For these 20% of passengers, the time saved compared to traditional forms of transport is around half an hour. This can be averaged out across the whole 100% of the passengers by multiplying half an hour by 20% which is 6 minutes saved per passenger.

Now, we can consider the time lost in not having two stations at the end city of 1 million people. Each station would cover an area of around 500,000 people but without one of the stations, a population of 500,000 people do not have access to the high-speed rail line and for simplicity, they are effectively cut off and will look to join the high-speed line by using some other means of transport. Since there are four stations on line 1 and each station covers an area with 500,000 people, each station can be assumed to be identical, but the starting stations do not see many people departing. It is only the end stations that see the people exit the high-speed line. Since there are two stations, this equates to 50% of passengers exiting from each station. That is a massive number, and we do not have to do more calculations – it is clear that having an extra station at the city of 1 million is hugely beneficial and is more important in saving time than having the station near the town of 100,000 people.

However, what would happen if the transport links in the city were very good and connected to all parts of the city? If this was the case, one could imagine that on line 2, which has one station absent at the end city, passengers could reach the area where the absent station was situated by exiting the high-speed line and walking to the inner-city train’s platform. From here, they would wait for the inner-city train to arrive which would then ferry them across to their destination. It would take the same amount of time as the high-speed train would do in reaching the area where the absent station is. (Remember, the high-speed train cannot travel so fast once it stops – it is essentially behaving like an inner-city train.) The only inconvenience caused by changing to the inner-city form of transport from the high-speed rail line is the nuisance in changing platforms and the time taken in walking to the platform and waiting for the inner-city train to arrive which may take a couple of minutes. As mentioned earlier, on line 1, there are four equal stations which can be assumed for simplicity, having an equal amount of activity but only the last two stations see people exiting the service. So, one half or 50% of passengers would have preferred to have departed from the fourth station on line 1 which is now absent on line 2. They may lose 1 minute in travelling to the inner-city platform and 4 minutes waiting for the new train to arrive. Therefore, they lose 5 minutes of their time in transferring to an inner-city form of transport to reach their destination which is 2.5 minutes per average total passenger. This is far lower than the time saved by having a train serving the small city which was saving 6 minutes per passenger on average.

Also, bear in mind that there are many other factors to consider. Some will work in favour of line 2 while others will work in favour of line 1. One such example working in favour of having stations more equally placed such as in line 2 is that in line 1, any one of the two stations connecting the dense city can be replaced. We treated them as the same, but they are unlikely to be so. One may be associated with greater activity than the other. Therefore, just replace the one with the least footfall and keep the one with the greatest activity. This will save more time for potential passengers. For example, if one station has 25% of passengers departing while the other station has 75% of passengers departing from the station, then keep the 75% one and get rid of the 25% one. In doing so, the station now being placed at the large town only has to become more economically viable than the 25% station, rather than competing with the station that saw 75% or in the original model, 50% activity. This in turn will make the proposed scheme of evenly spaced stations more of a realistic proposition.

Another factor that favours line 2 is the fact that when people are forced to use inner-city forms of transport to make up for the loss of a high-speed station, they will realise that the inner-city form of transportation is more precise in delivering the commuter to their destination. You could have multiple platforms near the high-speed terminal – each one taking the commuter to a different part of the city. Compare this to line 1 where there are two high-speed rail stations in the city. This is obviously advantageous but either station is unlikely to always be the final destination for a passenger. They will normally have to board another form of transport to get to their precise area within the city. This reduces the time saved by having two high-speed rail stations in the same city. So, the time lost by not having two stations at the end city would be less than 2.5 minutes per average passenger, since both scenarios require you to change trains.

            Conclusion

Many people within the railway world know that it is bad practice to have too many stops on a high-speed line as it relegates it to a slow inner-city train. Yet, this practice still continues on a partial level as densely populated areas are commonly linked with more than one stop. What we have shown here is that it is clearly profitable to ditch this idea if the size of an alternate population centre is one tenth or more of the population of the other stop’s catchment area.

The amount of time saved for some passengers by deploying a station at a smaller city rather than sharing it with a proper city is huge. However, this is a simplified discussion, and it is certainly important to go into greater detail about the complex dynamics involved in this problem. It is not just the time saved, but the hassle of changing stations for passengers as well as the economic impact in deciding the position of stations that needs to be considered.

For reducing the number of stations at a dense area, you would need to consider whether there is already a good transport system in place to compensate for the loss of the station, or if an upgrade is needed, it would be at a reasonable cost. If the cost was to increase, then this idea would become increasingly unattractive. Also, what needs to be considered is the size of all the population centres at which the train stops. If the difference between the new stop’s population centre is very low compared to the other stop's population centres, then it would also become harder to push this idea through.

Nevertheless, because of the enormous amount of time saved for the population of people residing in that country by evenly spacing out the stations, you do not need to replace the missing station with a world class inner-city form of transportation. Any reasonable form of transportation would be sufficient in saving time for the population of people residing along the line. Just do some calculations for yourselves regarding the position of stations on the high-speed train line. Even some general calculations will show enormous amounts of time saved for the people residing along the line, thus making the line with more evenly spaced stations a more attractive form of transport planning.