Michal Paszkiewicz

Analysis of distances between bus stops

I have been sitting around wondering how great the distances are between bus stops. Most people probably do not worry about such things and that is a good thing - I can think about these things for you so you don't have to. Finding a lack of example statistics, I decided to do a bit of analysis of distances between bus stops in London. Below you will find the results.

Shortest

London has many bus routes with bus stops that are close together. This is quite normal for cities with dense populations, but few cities have buses that stop quite as often as in London. Below are presented the 5 bus routes with the shortest average distances between stops.

All of the above routes are in fact branches of particular bus routes that have greater bus stop distances on their other branches. If we disregard all routes with complex branches, we get the following 5 routes with shortest average distances between stops.

We find that when short bus route branches are disregarded, distances between bus stops in the top 5 are quite a bit longer on average. A distance of even 215m between bus stops is still quite a short distance - buses travelling longer distances will take a lot of time travelling if they have to stop every 215m. Such buses will also expend a lot of energy as more energy is used to accelerate a bus than to keep it going at a particular speed. However, there are many people who cannot travel 215m very easily and therefore being able to catch buses at such small interval empowers many people to travel by bus when they might not have been able to otherwise. Buses in London also do not usually stop at bus stops if noone is at the stop or if noone on the bus has signalled that they want to get off there. This aims to deal with the fact that frequent bus stops both slow buses down and use up energy.

Some buses in London also have "Hail and Ride" zones, where a bus can be stopped with a wave on the hand at any point on the route. Such a strategy is a triumph in accessibility and in my experience only occurs in suburbs where it isn't really abused. It certainly wouldn't be practical in urban areas where the bus could be stopped every few meters.

Longest

Of course, not all bus routes in London are short. Some bus routes in London have bus stops quite a distance apart - it wouldn't be fun to walk between them. Below are presented the 5 bus routes with the longest average distances between stops. Please note that the scale is much smaller on this plot so that the distribution fits in most browsers. The scale is highlighted red to make this more obvious.

Averages

Below is presented the distribution of average distances between bus stops on London bus routes.

It is immediately surprising how the majority of averages are quite consistent. Removing the branched bus routes brings the distribution of averages even closer together.

Medians

The median distances between stops on bus routes in London turn out to be lower than the median distances between the stops. This is due to the fact that most bus stops are in fact a short distance apart, but the mean of bus distributions is pulled up by a few exceptional stops that are much further away from their neighbouring bus stops than others are.

Once again, the close clustering of the medians is impressive. The consistency of both the averages and medians of the bus stop distance distributions is certainly more consistent than the spread of bus stop distances on the majority bus routes. In fact, the averages and medians are grouped closer together than the quartile spreads of the bus routes. Below is a graph of the distributions of the distances contained between upper and lower quartiles of the bus routes (I'm calling this "quartile spreads").

This can be a bit tough to interpret. The easiest way to think about it is by looking at details. If we look at the mean of the total quartile spread - 143m. This means that the average bus route has 50% of distances between bus stops differing by 143m at most. What a mouthful! The other 50% of bus stops will differ from each other by more than 143m. The quartile spreads of our averages and medians above are no more than 50m, meaning that they are far more consistent and strongly grouped than the vast majority of the bus route distances between stops. Indeed there are many bus routes that have very inconsistent placements of bus stops.

Low consistency

The top 5 bus routes with the least consistency in bus stop distances are displayed below. Unsurprisingly, these are some of the routes that on average have some of the greatest distances between stops.

High consistency

The top 5 bus routes with the most consistency in bus stop distances. They all seem to impressively fit at least 50% of journeys in a difference in distances of just a few metres. Similarly to the routes with the shortest average distances between stops, these are short branches of routes that otherwise are not quite so consistent. There are just one or two stops on these branches of the routes.

If we remove such branches, we get the following 5 most consistent routes.

Custom search

This page would be no fun if you couldn't interact with it, so I have placed a search function here below for you to find your own buses that you have used in London.

Search for your bus:

You can also seperate bus names by commas if you want to compare a few buses in the above search functionality. Adding an "i" or an "o" at the end of your bus route name will select only inbound or outbound routes of that name respectively.

Why do distances between bus stops differ so much on different routes? Partly it has to do with density - where there are fewer people, it makes less sense to stop often, as there would be fewer passengers to pick up. Some areas might not even have any people there - they may be industrial or rural, for example. Another reason is due to accessibility - in areas where there may be a lot of elderly or disabled people for example, it makes sense to have more bus stops so that they can have better access to buses. Sometimes bus stops cannot be a set distance apart, because of convenience - there may not be a good piece of pavement, or the road may not have space to allow a bus to stop at that point. What do bus stop distances mean for our journeys? As stated before - more bus stops can mean that a bus becomes less efficient - both in terms of energy and in how fast it can get from one area to another. There is always a trade-off between ease of access and bus efficiency - you can't have supreme ease of access without putting the buses at risk of delays due to people waiting for and hailing the bus at numerous stops on its route. Similarly, bus bunching is more likely to happen with more bus stops - if one bus has people waiting at multiple stops, it can be delayed by quite a lot while the bus behind it may not need to pick anyone up at those stops. This results in more cases where buses come in twos or threes. Authorities try to stop bus bunching by "regulating the service", meaning that buses will wait additional lengths of times at bus stops to ensure that they do not catch up to the buses in front. This can be quite frustrating for passengers, but is necessary to provide a more regular service. It is easy to get annoyed when buses seem irregular or arriving late, but it is much harder to ensure that they ARE regular and on time.

What is worth reiterating is that so many decisions in infrastructure have trade-offs - you must sacrifice one thing to achieve another. When we want two things that are both good, sometimes we have to accept that we cannot have both fully, but must have a part of each. For example, justice and mercy cannot both be fully achieved - if we are to be just, then those facing justice cannot have full mercy. Similarly, those to whom we are merciful cannot have full justice. Both justice and mercy are good and important things, but there has to be a balance between them. Such trade-offs are ever present in the world of buses. We cannot have both ease of access to bus stops and bus efficiency. We cannot have highly regular services and services that travel to their destinations in the shortest amount of time. We cannot have timetables that are both truthful and satisfying for customers. When making decisions with regards to bus route design and service, authorities need to find out what is most important to us and act accordingly. The balances decided upon by transport authorities will never make everyone satisfied - some people prefer one thing to another. However, any such dissatisfaction shold come with the knowledge that someone else's needs are being met as a result. People may still feel that they are being unfairly disregarded due to this - is someone else being prioritised over them? The only way we can ensure that we can be satisfied with such decisions is if we have open dialogues in our local communities so that we can understand each others' needs and come to an agreement as to what the middle ground is. If you are looking for a challenge, here it is - try to meet some people in your local area who live differently to you and try to understand them. Work together to find your common grounds. You will not be disappointed.

The data was acquired from TfL's open data API (on the 29th May 2019) which is a resource definitely worth checking out!

Edit: this post was initially published with erroneous data. It was initially calling this endpoint and using the "lineStrings" field, which does not equate to bus stop locations, but locations used to draw the map of the bus route. The data presented above is now correctly using the field "stopPointSequences". Big thanks to @zimpenfish on twitter for notifying me of the error. Distances between bus stops were calculated using the haversine function on two adjacent lon/lats. To see the original version of the post in order to see comparisons between erroneous and correct data, please click here.

published: Wed May 29 2019

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Michal Paszkiewicz reads books, solves equations and plays instruments whenever he isn't developing software for Transport For London. All views on this site are the author's views only and do not necessarily represent the views of TfL.