Graph theory is an important tool while studying several practical problems.
Recently, I read a paper which tries to analyze the problems tormenting Indian
Railways, by mapping the railway network to network flow problem of graphs. A
simple simulation and study of the network highlighted inherent problems with
the prevailing system of Indian Railways.
The authors considered only express trains for the study. The graph had the main
stations as vertices, and an edge exists between two stations if there exists
a trunk route (high capacity route used by express trains) between those two
stations. It was assumed that all trunk routes have the same capacity (that is,
same number of parallel tracks), the trains travel with uniform speed, and there
is no delay (that is, everything runs perfectly according to the time-table).
The results showed that perfection is impossible, given the current time-table
followed and distribution of railway traffic over the country. Even when running
perfectly, trains come within critical distance of each other. Hence, some has
to be delayed. This also increases the risk of accidents in the event of signalling
equipment failure. The increase of railway traffic has also been very skewed, with a
relatively high increase in the number of trains in the Indo-Gangetic Plain ( which
is not a surprise since the Railway Ministers were from UP, Bihar or West Bengal since
1996). However infrastructure improvement has been minimal. As a result, around 20%
of the trains of the region get delayed by more than an hour, and the number of accidents
have also been maximum in the Indo-Gangetic Plain.
The study has stressed the need for improvement of infrastructure (increasing tracks,
restructuring of time-table, etc.). Merely increasing number of trains in every
Railway Budget is only going to worsen the situation.
Link for the paper: http://www.sciencedirect.com/science/article/pii/S0378437112000027?v=s5