How (and where) to build a Railway
Mean Travel Time (MTT) and other ideas
🤓Me: “I’m going to rebuild Sri Lanka’s Railway Network. From scratch.”
😎You: “That’s nice. What lines would you build into it? And where would be the stations?”
How will I answer these questions?
Read on to find out.
Tabula Rasa and other assumptions
Let us begin with a clean slate (or as we say in Kompannavidiya, a “Tabula Rasa”).
Let us suppose that there are no existing railway lines in Sri Lanka. Since we are building a transport network from “scratch”, let us also assume that the country has no road network, or other means of transport. The only mode of transport is walking.
Also, for now, let us assume that we will only locate stations at district capitals (Colombo, Gampaha, Kurunegala, Kandy, Jaffna etc.).
Phase 1
The best way to start a big project is to start small. So, let us start with a single line connecting two of the above-mentioned capitals.
Suppose there are three alternative proposals.
- Colombo to Gampaha
- Colombo to Kalutara
- Gampaha to Kalutara (by passing Colombo)
How would you choose between these three proposals?
As with most things, we need to tradeoff cost and benefit.
How might we quantify benefit?
Personally, I like the concept of “Mean Travel Time” or MTT. Let me explain MTT with an example.
Mean Travel Time and Two Random Sri Lankans
Suppose two random Sri Lankans, A and B want to meet. Suppose A agrees to travel to wherever B is. On average, how long would it take A to travel to B?
This is what I mean by Mean Travel Time (MTT).
To see how we might estimate MTT, let us consider a fictional Sri Lanka with only three districts of the Western Province described in this diagram. The distances and populations approximate the real thing.
Let us consider the case where A is in Colombo and B is in Gampaha. The distance is 30km. Assuming A walks at 4km/h, the travel time is about 7.5 hours. Now since Colombo and Gampaha have populations of 2M people each, there are 2M x 2M = 4T pairs of people who might be A and B.
Consider all position AB pairs, we can compute the Mean Travel Time (MTT).
MTT =(
Weighted MTT for Colombo to Gampaha
+ Weighted MTT for Colombo to Kalutara
+ Weighted MTT for Gampaha to Kalutara
) / (
Weight for Colombo to Gampaha
+ Weight for Colombo to Kalutara
+ Weight for Gampaha to Kalutara
)
= 4 x 7.5 + 2 x 10 + 2 x 15 / (4 + 2 + 2)
= 80 / 8
= 10Hence, for our simple example, it is about 10 hours.
(Note, the “weight” mentioned above are the number of people pairs: 4T, 2T and 2T for the three pairs of districts, respectively.)
(We assumed that the travel time from anywhere in one district to anywhere in another, is the same. While obviously unreasonable for large regions, this becomes reasonable when we consider small regions like Grama Niladhari Divisions for our estimates.)
(Technically, we should also consider cases where A and B are the same place; like traveling from one place in Colombo to another. However, we can ignore this, as a zero travel time does not influence the final numbers.)
The Benefits of a Railway
Now suppose we decide to go with Option 1 (Colombo to Gampaha) for Phase 1. How would it change travel times?
Assuming our train travels at 60km/h, anyone in Colombo can now travel to Gampaha (and vice versa) in 0.5 hours; a significant improvement from the 7.5 hours spent walking.
Others also benefit. Anyone wishing to travel from Gampaha to Kalutara, can now take the train to Colombo (0.5hours) and then walk to Kalutara (10 hours) for a combined travel time of 10.5hours. This is an improvement on the previous 15 hours.
In aggregate, the new MTT after building the Colombo-Gampaha line is now 5.37 hours; an overall improvement of 4.63 hours.
Similarly, we can compute the improvement in MTT for the other options.
- Colombo to Kalutara — 4.04 hours
- Gampaha to Kalutara — 3.88 hours
Weighing Benefits and Costs
Finally, we need to trade off the improvement in MTT (the benefit) with the cost of building the track. Estimating costs is complex, but I am going to make (yet another) simplifying assumption: Let us assume that the cost is proportional to the length of track.
Then, the best tradeoff would be that with the Maximum Reduction in MTT per unit Track Length:
In our toy example, we would start with Colombo to Gampaha as Phase 1.
(To be clear, this assumption is weak at best. For example, building a track from Anuradhapura to Kilinochchi, where the land is flat with few natural obstacles, is an order of magnitude cheaper than building a track from Nuwara Eliya to Ratnapura via the Peak Wilderness Natural Reserve).
More Phases
We can use the exact same logic for Phase 2, and so on.
Here is a summary of a hypothetical railway network that has been simulated using the ideas described above.
Phase 0: Base Mean Travel Time (MTT)
The network-free MTT at “Phase 0” is about 29 hours.
Note, when we repeat the simulation using Divisional Secretariat Divisions (DSDs) and Grama Niladhari Divisions (GNDs), the corresponding MTT is about 30 hours and 32 hours respectively, indicating that this 29 hour estimate is not completely off. Also, the networks generated using DSDs and GNDs are like what we get for districts, be they more spatially precise.
Phase 1: Colombo to Gampaha
Unsurprisingly (as was the case with our toy example) the first line on our hypothetical network is Colombo to Gampaha, which are closely situated in the country’s most densely populated area.
Phases 2 to 5: Like the Current Network
After Phase 5, we have a subset of the actual railway network, with the coastal line to Matara, and the main line to Kurunegala (Polgahawela Junction).
Note, the steady increase in MTT per Track Length. This is due to network effects, where new lines benefit from the existing network.
Phases 6 to 11: Not Like the Current Network
We have noticed six new lines that are not on the current network.
- Phase 6 — Kurunegala to Puttalam
- Phase 7 — Kalutara to Ratnapura
- Phase 8 — Kurunegala to Kandy
- Phase 9 — Kandy to Badulla
- Phase 10 — Puttalam to Anuradhapura
- Phase 11 — Badulla to Ampara
Ratnapura and Ampara are densely populated areas not served by the current network. Ratnapura was formerly part of the network, but the connection was from Colombo via Avissawella; not from Kalutara.
Puttalam, Kandy, Badulla and Anuradhapura, while currently on the network, are connected to the network in new ways.
Badulla has a faster connection to Colombo, by bypassing much of the central hills. The route to Kandy mirrors the Central Expressway, while driving via Puttalam is sometimes the faster route to Anuradhapura.
MTT per Track Length continues to increase, exploiting more network effects.
Phases 12 to 20: The end of network effects, and the beginning of diminishing returns
MTT per Track Length continues to increase until Phase 20. There are some lines found in the existing network (Kandy-Nuwara Eliya, Gampaha-Kegalle, Matara-Hambantota, Anuradhapura-Jaffna, Kandy-Matale, Polonnaruwa-Trincomalee), and some new lines (Batticaloa-Ampara, Badulla-Monaragala, Matale-Polonnaruwa).
At Phase 20, the MTT per Track Length peaks at about eighties per km of track. After which, it steadily starts to decline. What this means is that while additional track results in a reduction in MTT, the rate of decline slows down. Every subsequent unit of track is less beneficial than the previous one.
Phases 21 to 40
MTT per Track Length is down to 44s/km.
Phases 41 to 60
MTT per Track Length is down to 26s/km.
Concluding Thoughts
As I usually do, I like writing about topics which I have no business writing about. Transport, Railways, and Public Infrastructure are all topics that I have no formal training in. My interest is purely as a hobbyist.
Also, please heed the assumptions and note that many can be taken-apart and dismissed.
I’d love to hear about what you think of MTT, how you would design a railway network for Sri Lanka, and any other relevant comments, questions, or feedback!
The Complete Video
The code used for the simulations and high quality images can be found at:
