Classification model to classify large number of classifiers?
It looks like a very difficult problem, since there are many possible classes and very little information in the features to distinguish them. For the record, the reverse problem of estimating the travel time based on the route would probably be more feasible. 

So you can't expect great performance on a problem like this, the goal will be to design the problem in a way which makes things as simple as possible for the classifier to do a decent enough job. Here are some suggestions:


Start with training a model specific to a pair BSTN,ASTN. 
Discard the least likely routes, i.e. routes which are rarely used for the pair BSTN,ASTN (for instance routes with frequency lower than 10).
Inspect the data to see if the features allow a distinction between the (main) classes. For instance you can plot the distribution of BSEC, TFtime, Ttime for different routes: if the distributions are close there's little chance the classifier will succeed. You can also train a decision tree and inspect it manually so see what happens.