The Math Behind Traffic Jams

Last week, I was stuck in traffic, which is pretty much a natural phenomenon in Manila, and thought I'd put my math review to good use.

I wanted to find out if the unified color coding scheme actually has an impact on the overall reduction of the volume of cars in Manila. There are a couple of unknowns which put limitations to my asusmptions.

Unknowns:
The number of registered private vehicles in Manila
The distribution of plate numbers ending from 0-9

So, on with the calculation.

There are 10 possible plate number endings: 0,1,2,3,4,5,6,7,8,9.
Philippine plate numbers contain 3 numbers, and there are 1000 (10*10*10) possible ways to rearrange these numbers  (e.g. 341, 213, 111 etc.)

There are 26 letters in the alphabet that comprise the first 3 characters of the plate number. There are 17,576 ways to arrange these letters.

Combining the two, there's a total of 17,576,00 possible plate numbers that can be issued in the Philippines.

Assuming the LTO has only issued 10% of these plate numbers in Manila, that means we have 1,757,600 cars on the road, private and public inclusive.

If we take out 2 plate numbers every day, a total of 14,060,800 cars will be banned on the road for one day every week. Since we don't know how many plate numbers were issued for each number between 0-9, and how many are private vehicles, we'll assume that only 2% are on the streets (roughly, this means 2 out of 100 cars end in 1 or 2 and are private vehicles). That means we take out 281,216 daily, which translates to an overall reduction of 16%. And what about the other 84%? They're still honking their way along EDSA, Makati, C5, C3....