Sunday, February 25, 2007
Now I know why going downtown takes so long -vwv

Before the days of the NEL, there used to be a bus that travels from my place to City Hall. Nowadays, I take a bus to Serangoon MRT and take the train to City Hall. Sometimes, it's really fast. But on other times, I can't help but feel it's taking really long. I never gave it much thought until recently when I suddenly realized I was looking at the average traveling time and that's the problem.

The important thing is not so much the mean traveling time but the standard deviation, which is the measure how precise the mean traveling time is. With a small standard deviation, you'll almost always take about the same time to travel downtown. With a large standard deviation, you'll usually be very late or very early. The thing about the standard deviation is, it always adds up.

In the old days when I can take a bus downtown, the mean time is
40 min bus ride
+ 5 min waiting
= 45 min.
The standard deviation for the bus wait is perhaps about 2 min.

Now when I go downtown, the mean time is
5 min bus ride to Serangoon MRT
+ 10 min bus waiting
+ 10 min train ride to Dhoby Ghaut
+ 4 min train waiting
+ 3 min walk to North-South line
+ 3 min train ride to City Hall
+ 2 min train wait
= 37 min.
An approximate 8 min improvement. Nice.
But what about the standard deviation? It is
2.5 min bus waiting
+ 1.5 min train waiting
+ 1 min train waiting
= 5 min.

Assuming that more than 80% of the time, we arrive within plus minus 1.5 standard deviations of the mean time. The implication is this:

For more than 80% of the time,
the old route will take between 42 to 48 min.
The new route will take between 29.5 to 44.5 min.

So if I want to arrive on time for the worst-case scenario, I can leave the house a pathetic 3 minutes later than before but there's a very high chance I'll arrive too early and waste my time waiting for people.

Or if I'm really optimistic and assume minimal waiting for all the buses and trains, I can leave the house an impressive 12.5 minutes later than before but there's also a high chance I might end up very late and waste other people's time.

But since I'm more of the former, no wonder I don't feel like I'm getting much benefit from being forced to take the NEL. Not to mention I can no longer sleep on the bus throughout the trip.

-- permalink --
Yiheng made 1:04 PM

3 Comments:

I agree. That's why I prefer a direct, long bus journey than taking trains.
By  bOb™, at 6:04 PM  

Our current transport model inclined towards the hub-and-spoke model, so you can expect there to be more transits. Having a monopoly on transport in Singapore doesn't help either.

What might be interesting to do is to setup (us) a competing SME-ish transport company. Ask users to register with us their location and typically travelling time and costs...and we will undercut SBS/SMRT with our competitive services. Think Priceline + Tiger airlines combined. Basically just destroying the hub-spoke network and addressing the market inefficiences by optimizing travelling routes for our group of customers.

-Lower cost.
-Get to where you need to go quicker and less waiting.
Not a bad idea huh?
By  Soqcrates, at 6:57 PM  

Good idea. Since it's a small scale business, we can just whack SBS/SMRT on routes where they are the weakest, i.e. require multiple transits.
By  Anonymous, at 7:27 PM  

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