Running trains more frequently can reduce reliability:
Consider a train line that takes 200 minutes to travel. Assume trains break down once every hundred journeys, and take 4 hours to clear. When a train breaks down, no other trains can pass it.
Now consider the two extremes:
If there’s one train every 2 minutes the train line will essentially always have one broken train, and travelling the line will likely take about 7+ hours.
Meanwhile if there’s just 1 train going back and forth you’ll have 1 delayed train every month, which will delay people for 4 hours. You’re still better off in this scenario than the previous one.
The sweet spot in terms of average transit time is closer to a train every 2 minutes than a train every 400 minutes, but the sweet spot for predictability of the service will have fewer more reliable trains.
As anecdotal evidence, I notice that the Northern Line frequently had breakages and had a train every 2-6 minutes, and Israel Railways very rarely has breakages and has a train twice an hour on my line.
This all points to both investing a lot of effort into train reliability and running fewer, longer trains.
I don’t think it’s accurate to model breakdowns as a linear function of journeys or train-miles unless irregular effects like extreme weather are a negligible fraction of breakdowns.
Running trains more frequently can reduce reliability:
Consider a train line that takes 200 minutes to travel. Assume trains break down once every hundred journeys, and take 4 hours to clear. When a train breaks down, no other trains can pass it.
Now consider the two extremes:
If there’s one train every 2 minutes the train line will essentially always have one broken train, and travelling the line will likely take about 7+ hours.
Meanwhile if there’s just 1 train going back and forth you’ll have 1 delayed train every month, which will delay people for 4 hours. You’re still better off in this scenario than the previous one.
The sweet spot in terms of average transit time is closer to a train every 2 minutes than a train every 400 minutes, but the sweet spot for predictability of the service will have fewer more reliable trains.
As anecdotal evidence, I notice that the Northern Line frequently had breakages and had a train every 2-6 minutes, and Israel Railways very rarely has breakages and has a train twice an hour on my line.
This all points to both investing a lot of effort into train reliability and running fewer, longer trains.
I don’t think it’s accurate to model breakdowns as a linear function of journeys or train-miles unless irregular effects like extreme weather are a negligible fraction of breakdowns.