Problem
How to calculate revenue by transit MODE from a Public Transport assignment.
Solution
To calculate the revenue by transit mode is possible by simply multiplying the skim matrix of (actual) fares by mode times the demand matrix of the corresponding User Class.
Indeed, the FAREA for the specific mode, is the weighted average based on the TripsIJ proportion. Therefore to obtain the revenue by mode, we need to multiply the FAREA value * TripsIJ between the specific OD. This can be done with a Matrix program by multiplying the output SKIMIJ = FAREA matrices times the input OD matrix.
A simplified example is provided for the CUBETown network below, for O=2 and D=21, with an excel file showing the calculations.
communities.bentley.com/.../PT_5F00_revenue_5F00_byMode.zip
The example works as follows.
There are 25 zones in total, but path-building is executed between zones 2 and 21 only. With OD trips matrix between O=2 – D=21 = 100 passengers.
2 transit modes:
- MODE NUMBER=1 LONGNAME="Rail Transit" NAME="Rail"
- MODE NUMBER=2 LONGNAME="Bus Transit" NAME="Bus"
5 lines (4 bus, 1 rail):
- LINE NAME="Flash", MODE=2
- LINE NAME="Blue", MODE=2
- LINE NAME="Flashb", MODE=2
- LINE NAME="Red", MODE=2
- LINE NAME="Rail", MODE=1
2 FARESYSTEMs:
- MODE 1 (rail) has a FLAT system with fare 1.20 $ (fixed)
- MODE 2 (bus) has a DISTANCE based fare with 0.8 (if first transit leg of a trip) + 0.3*distance
In the example, we have the following routes, evalutated between 2 and 21:
N: 2 Mode WaitA TimeA Actual B/XPen Percvd Dist Total Lines(weight)
-> 804 100 - 8.82 8.82 - 8.82 0.37 0.37
-> 758 2 3.50 4.12 16.44 0.00 17.84 2.08 2.45 Red(1.000)
-> 21 100 - 13.33 29.77 - 31.17 0.56 3.01
Mode TimeA Dist IWaitA XWaitA
2 4.12 2.08 3.50 0.00
100 22.15 0.93
Fare= 1.42
Probability= 0.2534
N: 2 Mode WaitA TimeA Actual B/XPen Percvd Dist Total Lines(weight)
-> 1342 100 - 9.58 9.58 - 9.58 0.40 0.40
-> 1344 1 2.00 3.47 15.05 0.00 15.85 1.62 2.02 Rail(1.000)
-> 21 100 - 15.01 30.06 - 30.86 0.63 2.65
Mode TimeA Dist IWaitA XWaitA
1 3.47 1.62 2.00 0.00
100 24.59 1.03
Fare= 1.20
Probability= 0.4393
N: 2 Mode WaitA TimeA Actual B/XPen Percvd Dist Total Lines(weight)
-> 1342 100 - 9.58 9.58 - 9.58 0.40 0.40
-> 1346 1 2.00 3.78 15.36 0.00 16.16 1.76 2.16 Rail(1.000)
-> 748 200 - 0.82 16.18 - 16.98 0.03 2.19
-> 757 2 2.50 0.22 18.90 0.00 20.70 0.14 2.33 Flash(1.000)
-> 21 100 - 11.49 30.39 - 32.19 0.48 2.81
Mode TimeA Dist IWaitA XWaitA
1 3.78 1.76 2.00 0.00
2 0.22 0.14 0.00 2.50
100 21.07 0.88
200 0.82 0.03
Fare= 1.24
Probability= 0.3073
Accordingly to the computed probabilities of using the different routes we have (OD demand = 100):
- 25.34 passengers using the Red line. The fare is computed as 0.8 + 0.3 * 2.08 = 1.42
- 43.93 passengers using the Rail line. The fare is 1.20
- 30.73 passengers using Rail + Flash. The fare is computed as 1.2 + 0.3 * 0.14 = 1.24
The revenue by mode is the following:
- The revenue for Mode 1 (rail) is: 43.93 * 1.20 + 30.73 * 1.20 = 89.59
- The revenue for Mode 2 (bus) is: 25.34 * 1.424 + 30.73 * (0.3 * 0.14) = 37.37