A public transport related thought experiment

[hU0N]

I came across this thought experiment that I quite liked, thought I'd share it since it's transit related. Here goes:

Imagine you live on a railway line like the Rosewood Line, but you work in Brisbane CBD. Your only public transport option is the train line which has regular trains. Imagine that, due to rollingstock shortages, every second train is a shuttle to Ipswich that connects well with a Brisbane train. And every other train is a Caboolture train, offering a one seat, all stops trip to the CBD. Imagine that there is very little journey time difference between the two.

Now, imagine that you cannot predict in advance whether any particular train will be a shuttle or a one seat ride. Each morning QR flip a coin to decide if the even trains will be shuttles and the odd trains one seat rides, or vice versa. All you know is that if a shuttle pulls into the station, then the next train is guaranteed to be a Caboolture train.

So, when you arrive at the station each morning to catch the 7:15 train, are you hoping that today it will be a shuttle? Or are you hoping for a Caboolture train? And if the train which arrived at 7:15 was not your preferred type, would you consider waiting for the next train, your preferred type (assuming you had enough time)? Finally, if you would consider waiting, how long would you wait for (eg. if trains came every 15 mins,  would you wait for the next one? What if they only came half hourly? Hourly?)

Hope you have a bit of fun thinking about it like I did.

[Gazza]

Always the first train available, to give buffer against any delay.

[dancingmongoose]

I'd be hoping for a through train, as it's more convenient due to not having to transfer. But I'd still get on the first train that arrived.