This would be the expression if a≠b:
´ & ' " ( $)(% %
%
& *" ( $+(% "%# $
´ "%# $ "%# $ "%# $ "%# $
The difference is that in this last situation the number of passengers that come to i are all that were generated between period b when the train passes and the previous train b-1. Fb and Fa stands for the frequencies of the trains and passengers generation (so for 12 trains in an hour Fb=5 minutes, and for 6 generations Fa=10 minutes).
3.3.2. The total number of passengers to be carried must be equal to the total of passengers that come to the stations
So, the total passengers to be carried in trains between stations must be equal to the total number of passengers originated. The total number of passengers originated will be the sum of all the cells in the O/D matrix (if each period the number of passengers originated is the same, that was an assumption we made) times a. For a=b=12, we get this expression:
P-./ x-/ x./ / - .
P´-./ / - .
Were the first sum is the total number of passengers carried and the second is the total number of passengers generated. For a≠b, with nb being a variable number of trains making the trip in one hour and na being a variable number of periods in an hour were passengers are generated we will get: 21
P-.1 x-1 x.1
1 - .
2/
P´-./ / - .
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