Shortening total trip time by short station dwell time and passing local trains

We are studying to shorten passengers' total trip time to improve train diagram by operation of rapid trains. We calculate and deal with combinations of stations to shorten the time where rapid train stop or the train pass to local train. There are many combinations in this problem, and we have to consider any limit Conditions. Therefore, we waste very long computation time to get the solution. To solve this problem, we adopted a following procedure using dynamic programming (DP), we could get a combination of the stations which has effectiveness. We have applied this method to metropolitan subway in Tokyo. We could get the evaluation value that we can expect to about 6[%] shorter trip time than the time of operation local train only. We may have better solution, however, it was shown the possibility to shorten the trip time by the rapid train. To shorten the time, this approach by improvement of train diagram has a merit not to need the equipment investment.