Modelling Queues in Static Traffic Assignment
Michael Bundschuh, Peter Vortisch, PTV AG, DE; Tom van Vuren, Mott MacDonald, UK
The paper presents a method to include spill back in the context of a static assignment and thus to achieve a more realistic modelling of congested networks but to avoid the computation time penalty induced by fully dynamic assignment methods
The paper presents a method to include congestion phenomena in the context of a static as-signment and thus to achieve a more realistic modelling of congested networks but to avoid the computation time penalty induced by fully dynamic assignment methods, especially those incorporating flow simulation. The proposed method is not an assignment procedure in the pure sense since it does not compute routes and volumes. Instead, the result of a static assign-ment is modified.
The idea of the proposed method is simple: travel demand is redistributed along routes com-puted by any static assignment procedure beforehand. In a first phase the volume of each route are passed from one link to the next along the route until capacity of a link is reached. This propagation of volumes obeys the following rules:
1. The traffic volume on each link is limited by the capacity of the link. The model as-sumes the bottleneck at the end of the link, i.e. the capacity restricts the outflowing volume.
2. The queue length on each link is limited by the queuing capacity of the link.
3. Traffic can not flow across a congested link (i.e. a link with a queue), even if the traf-fic follows a route that does not include the bottleneck causing the congestion.
4. The inflow of a link is limited by the sum of capacity and queuing capacity.
For the computation of queue lengths, an assignment time period must be assumed. In order to avoid dependency on the processing order of links and routes, the volumes are propagated incrementally in small portions.
The second phase of the method computes the delay times caused by congested links. During this phase no further traffic is fed to the network. Only the traffic stored in the queues is propa-gated along the routes according to the same rules as before. This again is done in small time slices. The second phase ends when all queues are dissolved and no more traffic is in the net-work.
If this pseudo-dynamic assignment is computed after a normal static assignment method, in-formation about queue-lengths and delay times are generated, but they do not yet influence route choice of the drivers. Feedback to route choice can easily be implemented in assignment methods that assign the total volume in increments. Here the pseudo-dynamic assignment can be computed after each incremental step to compute modified travel times for the next incre-ment.
The computational effort of one incremental step in both phases is comparable to the update step of the link volumes as it is part of every assignment procedure. The computing time of the pseudo-dynamic assignment is dominated by the chosen number of incremental steps in the two phases. For the first phase a sufficiently large value should be used in order to ensure a sufficient independence from the link processing order. For the second phase a coarser step-ping is possible. If used in practical situations with realistic traffic volumes and realistic net-work sizes the additional computing time of the proposed simple method is already close to the maximum that would be accepted by users. The pseudo-dynamic assignment is implemented in the transport planning software package VISUM and is already in use in some projects. The final paper will report results from application and a comparison to SATURN results.
Association for European Transport