For identical headways, the coordination's mechanisms of action is clearly defined. Since coordination groups can be defined for arbitrary time profiles in Visum, however, there is not always a natural definition of the aggregate headway.
The approach implemented so far, which corresponds with the procedure in the program VIPS, is based on the assumption that the passengers can differentiate between the individual time profiles in a coordinated bundle and also make their choice against attributes of the respective time profile.
The new approach, which is realized in the program via the option Assume coordinated time profiles to be undistinguishable, is based on the following algorithm. Ti are the headways of the coordinated time profiles.
- In a first step, the aggregate headway T for the bundle is set as follows.
T := 1 / (1 / T1 + ... + 1 / Tm)
- This is the harmonic mean of the given Ti. The number of services corresponding to this headway is equal to the sum of the number of services of the individual time profiles. Example: T1 = 6’, T2 = 7.5 (i.e. 10 + 8 services per hour) yields an aggregate of T = 10/3 which also corresponds to 18 services per hour.
- For each time profile, the proportion of the total number of services is given by i = T / Ti. This fraction is also used as the relative share of the demand within the time profile bundle, i. e. pi:= i. The aggregated impedance results from C := c1 • p1 + … + cm • pm where ci denotes the impedances of the time profiles.
- Using the standard algorithm, the virtual aggregate time profile m* with headway T and impedance C is compared with the other time profiles (Route search and Route choice).
Model approach
Here, the general assumption is that the time profiles in the coordinated time profile bundles are not distinguishable. The time profile attributes headway and impedance are irrelevant. Instead, the headway is calculated with the focus on the number of services.
As a consequence, each time profiles proportion of the total number of services can be used as demand share per time profile. Passengers that cannot differentiate between the different time profiles of a time profile bundle will automatically board the first service available. Therefore, the passenger volume of each contained time profile is proportional to the alternative's number of services.
Furthermore, the aggregate impedance is defined as the weighted mean of the single time profiles’ impedances, this time using the service frequency shares βi as weights. This makes sense because the resulting aggregate is the mean impedance of all services. For the passenger, this is the expected impedance when boarding the first available service of the TP bundle.
Example
The example illustrates the difference between the already existing approach and the new one:
For the undistinguishable approach, the aggregate headway T is equal to 6/7, i.e. only 46 seconds. The aggregate impedance is C = 22.77. This value is much larger than before since the high-impedance time profile 1 plays a more significant role now.
|
TP |
Impedance |
Headway |
Distinguishable (Standard) |
Undistinguishable |
|
1 |
24‘ |
1‘ |
0.0166 |
0.7692 |
|
2 |
20‘ |
5‘ |
0.3366 |
0.1538 |
|
3 |
16‘ |
10‘ |
0.6466 |
0.0769 |
