The blocking back model (pseudo-dynamic assignment, pa) fills the gap between merely static procedures, which do not have any temporal reference and cannot determine congestion-related wait times, and dynamic procedures that require long computation times. The procedure is much faster than any dynamic assignment, requires less memory capacity and can furthermore deliver information on congestion phenomena. The procedure can be applied in conjunction with static assignment in order to estimate queue lengths and wait times in oversaturated networks. In contrast to dynamic-stochastic assignment, it is suitable for networks with > 50,000 links and only requires few additional data for temporal distribution of the demand.
The general idea is to re-assign route volumes that were calculated with any static assignment at an earlier stage. Output data of the procedure:
- new volumes on links, connectors, (main) turns and (main) nodes
- queue lengths on links and connectors
- wait times on links
The original volumes of links, connectors and (main) turns resulting from the assignment are stored with the following attributes:
- Volume demand PrT with base
- Volume demand DSeg
- Volume demand PrT
Original node volumes can be found in the following attribute:
- Volume demand PrT
Blocking back calculation
Along a route, the demand share is passed on from one link to the next until a restricting capacity has been reached. The following rules apply in this process.
1. The volume passing from one link to the next cannot exceed the capacity (PrT) of the link, the capacity of the To node, and the capacity of the turn. For links, the amount of traffic leaving the link counts (bottleneck at end of link).
2. The queue on a link can never exceed the stocking capacity of the link.
3. As soon as a queue forms on a link in some direction, no traffic can pass the link even if the respective route does not lead across the bottleneck that is causing the congestion.
The fourth rule which limits the inflow of a link, directly results from this.
4. The inflow of traffic on a link is limited to the amount resulting from capacity plus stocking capacity.
