During volume balancing, the demand of an OD pair is redistributed considering each time interval of balancing, so that paths with lower impedances are allocated more demand and paths with higher impedances are allocated less demand. For volume balancing, all the paths found during route search are available, independent of the balancing time interval. The basis for calculating path costs is the experienced travel times, i.e. the travel times at the time the vehicle enters a network object are used.
There are two methods available for redistributing the demand:
- Averaging according to Method of Successive Average (MSA)
- Cost-proportional volume balancing
For MSA, the shortest path for each OD pair and each balancing time interval is calculated. The volume is thus redistributed in each time interval and each iteration for all less attractive paths towards the shortest path.
For cost-proportional volume balancing, first the average cost of all paths per OD pair is calculated. Redistribution is then carried out proportionally to the difference between the costs of a path and the average cost. For all paths that are more expensive than the average path cost, the demand is reduced. The more expensive the path, the more demand is removed. For all paths that are less expensive than the average path cost, demand is increased. The less expensive the path, the more demand is increased.
To influence the quantity of redistributed volume, select one of the following options:
- MSA (method of successive averages)
- Time interval-dependent
Select MSA if you want the volume to be distributed exclusively depending on the iteration counter n, i.e. within an Iteration, 1/n of the volume is redistributed. This implies that with progressive iterations, the quantity of the redistributed volume will become very small.
Select Time interval-dependent if you want the volume to be redistributed as with the MSA option, but only until the specified iteration is completed. In this case, within an iteration n, 1/n of the volume redistributed. After that, the step size is determined depending on the balancing time interval. A decisive factor for reducing the step size is a gridlock that occurs and cannot be dissolved during the running simulation. From the balancing time interval during which the gridlock occurs, the step size is kept constant. In previous time intervals, the step size is reduced. This time interval-dependent control of the step size is recommended in models with long assignment time periods, where several gridlocks might occur distributed over the assignment time period. In order to dissolve any gridlocks that occur later, enough volume must be redistributed.
If a simulation-based assignment is calculated using existing results, the Iteration offset for volume balancing parameter is taken into account. For the MSA option, the share of volume to be redistributed is as follows:
For progressive iterations, it is taken into account that within the first iteration, based on existing results, no path search is performed or volumes are redistributed. Only from the second iteration, is the volume redistributed according to the formula.
If an assignment is based on existing results and calculated using the Time interval-dependent option, the volume to be redistributed is calculated according to the above formula until the specified iteration is completed. Then the volume is redistributed in line with the procedure described above.
The step widths determined can be viewed as output attributes in the list of quality data of the simulation-based assignment.
