The impedance of a PrT route

All assignment procedures are based on a shortest path algorithm that determines low impedance routes. The impedance of a PrT route is volume-dependent and consists of the following impedances:

The route choices of travelers depend on objective and subjective factors. The route choice is particularly determined by the following skims:

  • The anticipated travel time for the route
  • Route length
  • Possible road tolls

In addition to this, a multitude of other factors can influence route choice. One can imagine, for example, that road users who know their way around will choose other routes than people who do not know the area and who mainly orient themselves according to the sign-posted traffic network. Impedance is therefore defined for each transport system and can be customized by the user. By default, it depends on the following variables:

  • Transport system-specific travel time, in loaded network tCur [s]
  • Link length [m]
  • Transport system-specific road tolls [money units]
  • User-defined AddValues
  • Link type factor [-]

You can also define the impedance in detail. You are then provided with all direct and indirect numerical attributes of the network objects links, turns, connectors, and main turns, for the definition of the impedance of a route (User Manual: Defining impedance functions for transport systems).

When composing the impedance summands, it can be differentiated between two basic components:

  • Summands that apply depending on the traffic volumes (for example value calculated tCur with a VD function)
  • Summands that are not dependent on the network object volume (for example, toll or link length)

The time tCur of a network object is calculated with capacity restraint functions (VD functions). Based on the assumption that the travel time (impedance) of network objects increases with increasing traffic volume, all assignment procedures are in turn based on the assumption that travel times of network objects are a monotone incremental function of traffic volume. Thus, in case of increased traffic in the network, the effect of deterrence to alternative routes can be modeled (Predefined VD functions).

Because the variables have different units (seconds, meters, money units), impedance cannot be specified in a universally applicable unit. For a combination of the variables travel time and road toll, it may be convenient to express impedance in terms of money units. In this case, travel times are converted into money units using a "value of time" factor.

Impedances of links

For every PrT-transport system of a link, a TSys-specific travel time (t0_TSys) for free flow is defined, which is calculated from:

  • link length
  • permitted speed (v0_PrT) of the link used
  • maximum speed of the transport system (v0_PrTSys)

A capacity-dependent impedance function continuously adjusts this basic travel time depending on the current traffic volume (Predefined VD functions).

Impedances of turns (Impedances at node)

Visum calculates turn impedances for every turn permitted at a node. A turn impedance includes an impedance time penalty t0, which increases in dependence on volume and capacity. Because the turns are positioned at the node, the impedances at turns are often described as impedances at the node (Impedances at nodes).

Impedances of connectors

Connector impedances are regarded as follows:

  • Absolute connectors are regarded as volume-dependent. This means that the TSys-specific connector time (t0_TSys) does not represent actual impedance which is volume-independent.
  • For connectors defined by percentage, they are considered volume-dependent if the option Connector shares: Apply to total origin/destination demand is selected. This means that with increasing volume, the actual connector time tCur_TSys will exceed the connector time t0_TSys of each connector (Predefined VD functions). With a high value for parameter b in the VD function and usage of the equilibrium assignment, a relatively exact distribution of traffic onto the connectors can be achieved.

Note: The impedance of turns and connectors in contrast to links only depends on the variable tCur and possibly on the AddValue. Because the impedance of a connector is not capacity-dependent, the following applies to the access and egress impedance: tCur = t0. The proportional distribution of traffic demand onto different connectors is, however, reached through a virtual capacity, so that tCur > t0 can also apply to connectors. For each assignment, the particular virtual capacity (100%) is then recalculated from the summed up volume total and the demand to be assigned in the current assignment, e.g. Vol(car-business) + Vol(car-private) + Demand(HGV) = 100% Connector capacity.
Impedances of main turns

Just like turn impedances, main turn impedances are calculated for each main turn permitted at a main node in Visum based on the volume and selectively a VD function, TModel, or ICA.
Preloaded volume

When impedances are determined, preloaded volumes can be considered. Preloaded volumes can be either user-defined additional values or volume values which result from the assignment of a different matrix.