[Blasterlord2]

It is NOT necessary to store the fare data on server.

I guess the "complexity" arises when commuters didn't tap when they are alighting from buses (no issue for trains since one is forced to tap at the exit gantry).
It will then be problematic when he boards another bus or enters a train station and the software in the fare terminal can't determine the distance traveled on the earlier bus trip.

BUT location of bus stops rarely change, so to achieve a fast (immediate) fare computation based on distance travelled, LTA can simply pre-compute the distance between all bus-stops with other bus-stops/train stations pairs. 
There should be less than 2000 bus stops and train stations in Singapore, so a 2D lookup array of 2K x 2K with each cell containing 2 bytes (sufficient to store either the fare or distance travelled) will be sufficient to store the entire fare data for Singapore and it only takes up 8 MB of memory (or 18MB if there are 3K bus stops and train stations).

This small size array is definitely not an issue for modern embedded computers so it can easily be loaded into the fare terminals/gantries.
The fare and balance can then be transacted and displayed instantaneously with ZERO (or minimal) delay.

I dun think LTA hasn't thought of what you have just suggested. Even if they haven't, their vendors would have suggested it to them.