For route search and choice (Route search and Route choice), paths are assessed by their impedance or generalized costs respectively (PuT impedance functions). They include a perceived journey time PJT and a fare-based component (fare or share of fare points).
IMP = PJT • FacPJT + NumberFarePoints or Fare • FacFare
Perceived journey time (PJT)
The perceived journey time PJT, has the unit "Minutes" and consists of the following times:
PJT [min] =
In-vehicle time • FacIVT• weight attribute of the time profile item
+ PuT-Aux ride time• FacAXT
+ Access time • FacACT
+ Egress time • FacEGT
+ Transfer walk time • FacWT
+ Origin wait time • FacOWT (here, the origin wait time is computed according to a formula)
+Transfer wait time • FacTWT • weight attribute of the stop area
+ Number of transfers • FacNTR
+ Boarding penalty PuT (time profile attribute)
+ Boarding penalty PuT-Aux (transport system attribute)
+ Mean delay (time profile item attribute)
Here, journey times, costs, etc. are deterministic. The origin wait time and the transfer wait time result from the previously specified headway of the PuT line which the passenger boards at the origin stop or at the transfer stop. Within the limits of their headways, they depend in a random way on the transfer lines' relative position to each other, except in the case of coordination (Coordination).
The run time can be multiplied by a user-selected time profile item attribute in order to model the vol/cap ratio (for example the availability of seats) or other aspects of usability (for example the level of comfort) of a line.
Other individual time penalties and weighting factors for boarding events or transfers can be taken into consideration as follows (Using Visum: Headway-based assignment: Impedance tab).
- Wait time factors and penalties on the origin wait time from any attribute of stop areas and/or time profiles
- The wait time factor for the transfer wait time from any stop area attribute
- A boarding penalty of any time profile attribute (for PuT lines) or transport system attribute (for transport systems of the PuT-Aux type)
- A mean delay from any time profile item attribute
With the time penalties you can for example model, that some lines are favored by the passengers – because of their better quality of traveling, or because they are usually punctual. Via the wait time factors and penalties you can model that the passengers prefer waiting at some stops than others.
Via the origin wait time in combination with time profile-based weighting factors you can model that passengers do not randomly arrive at the stop but have a profound knowledge of the timetable in the case of long headways. In other words, you can restrict the origin wait time to the maximum value X via the weighting factor, for example: For all time profiles with headway T > X, enter X / T as the origin wait time weighting factor. In this case, the weighting factor 1 will be used for the time profiles with headway T < X.
Using PuT-Aux transport systems means no wait times, since the permanent availability of PuT-Aux TSys is assumed. Using boarding penalties for transport systems of the type PuT-Aux, you can still model a delay during transition.
Number of fare points
The Number of fare points is the total of all fare points that are traversed along the route. Fare points can be defined either for a time profile or by transport system for a link. For time profiles, four attributes are provided: Fare points per time profile item, fare points for boarding, for passing through, and for alighting at a stop.
Fare
As an alternative to fare points, the fare derived from the Visum fare model can also be used. There are no restrictions applicable in terms of number or properties of the fare systems or ticket types.
In contrast to the timetable-based variant, which includes the fare of the complete path as impedance component in the choice model, the impedance of the headway-based assignment includes the total of the fares by path leg. To reach precise correspondence to the real fare model, the property „Fare applies to = each path leg separately” is required for each of the used fare systems, i.e. each boarding passenger has to purchase a new ticket. In other cases, in particular for degressive fares over several path legs, the fare total included in the impedance can differ from the fare per total path.
The example below illustrates how fares are applied in the headway-based procedure.
The demand from A to B is 100 trips. The supply-side provides two alternative bus connections. The model consists of 5 fare zones, and for the tickets, a zone-based fare has been chosen as fare structure. The table lists the fares depending on the number of traversed fare zones.
|
Fare zones |
Fare [CU] |
|
1 |
3 |
|
2 |
5 |
|
>2 |
10 |
Example 1
Either line runs through from A to B, one in the North and one in the South. Either line runs regular services every 10 minutes. The North line traverses two fare zones, the fare in the impedance function is 5 CU. The South line traverses five fare zones, the fare is 10 CU. With an impedance definition of 1 • journey time + 2 • fare, the volumes of the south and north lines are the same.
|
|
North |
South |
|
Journey time (min) |
20 |
10 |
|
Fare zones (-) |
2 |
5 |
|
Ticket fare (CU) |
5 |
10 |
|
IMP = 1• Origin wait time+1• Journey time+ 2• Fare |
randomly in [0,10)+1• 20+2• 5 = randomly in [30,40) |
randomly in [0,10)+1• 10+2• 10 = randomly in [30,40) |
|
Volume |
50 |
50 |
|
Note: For the description of the volume distribution process in the headway-based assignment please refer to the particular section in this manual (Example for the headway-based assignment). Since both the headways and fixed impedance components of either route are identical, identical volumes are calculated. |
Example 2
Now, the North variant consists of two separate lines providing coordinated connections with a journey time of 10 minutes each. Neither transition times nor transfer penalties are regarded.
As the headway-based procedure's impedance calculation calculates the fares by path leg, a different impedance will be returned compared to the case mentioned above: For the first section, the fare is 5 CU (2 fare zones), for the second section, the fare is 3 CU (1 fare zone), thus the fare sums up to 8 CU in the impedance calculation. The volume distribution changes accordingly:
|
|
North |
South |
|
JT [min] |
20 |
10 |
|
Fare zones (-) |
2 |
5 |
|
Ticket fare (CU) |
5+3 = 8 |
10 |
|
IMP = 1*Origin wait time+1*Journey time+2*Fare |
randomly in [0,10)+1• 20+2• 8 = randomly in [36,46) |
randomly in [0,10)+1• 10+2• 10 = randomly in [30,40) |
|
Volume |
8 |
92 |
Remarks on the volume distribution: In the impedance range between 30 and 36, the South variant accounts for all shares. In the range between 36 and 40, the probability is 
. For the South variant, the resulting probability is 
.
Summing up the path leg fares in the impedance of example 2 corresponds to the situation, where a ticket has to be bought on each path leg. If a different fare system applied in reality (because the passenger has the right to use just a single ticket for the trip from origin to destination, for example), an inaccuracy turns out here. For compensation purposes, "transfer discounts" can be defined: Use the Transfer fares function which is provided with the Visum fare model for the definition of discounts that balance the fare amount charged too much in the case of fare system transfers. To correct the fare taking effect in the impedance formula, the following transfer fare had to be defined in this example: 5 CU - 8 CU = -3 CU.
|
Note: The only difference is how fares in the impedance function are taken into account. Finally, always the real fare is regarded, which is not the path leg fare total. This is particularly applicable to list outputs and skim calculations. In other words, for assignment analyses the actual fare is listed per passenger trip. |
Taking fares into account might significantly increase the computation time required for the assignment, it actually depends on the complexity of the fare model. Instead of using a fare model which mainly consists of proportional (e.g. distance-based) fares the usage of fare points is recommended.
