Hi researchers, by programming an algorithm (FW) for TAP by respecting the standard model of Beckman (1956), I find in the results (equilibrium) some links with a greater flow than capacity and that is not valid in practice.
My question is:
Is this is normal (because the algorithm gives an approximate solution) or we must add the capacity constraint (Capacity Constrained Side) to have a more real and practical solution.
Thank you.
This is one of several effects of using a standard traffic assignment model - it is wonderful as an academic exercise, but it is also impractical because it is too simple. In order to come closer to a practical traffic assignment model, you may need to introduce further data into the model, distinguish how different travel modes affect each other, and perhaps even introduce a time domain - hence enter into modeling the time-varying effects of traffic. This is somewhat more difficult to analyze, but the literature on dynamic assignment is vast.
To actually answer your detailed question: in some travel cost functions - like the case of the BPR function from the 1960s [take a look at the Wiki page on "route assignment", where the BPR formula is described] - there indeed are what's called a "practical capacity" constant among the constants in the cost function for each link. This practical capacity is NOT a capacity per se, but rather a breaking point from which the cost will grow faster when the flow increases further.
Like in my previous answer, it is important to model travel behavior better than they did in the 60s, since otherwise the model will only yield an "academic" result, so to speak, but never a practically useful one.
As Michael rightly points out, there are dynamic assignment procedures that strictly respect capacity. But this surely is not something you program in a spare day or two. We are working on a Matlab toolbox for assignment (including dynamic) that we will release later this spring as open source but this will take a few weeks to release.
Maybe more practical (but also more expensive) is it to use commercial software like PTV's Visum. They have refinements to the standard static assignment that account for capacity constraints and a proxy of spillback effects (some call this quasi-dynamic assignment). This is a heuristic approach that in my (somewhat limited) experience works surprizingly fine. One additional advantage is that it comes with a refined model for intersection capacities and delay that can be configured much more realistically than standard cost functions (their ICA model). Another advantage is that is is embedded in a commercial GUI shell that allows for useful analyses like selected link, route bundles etc. I guess other software vendors have similar features that I am however less familiar with.
Lastly it is worth mentioning that Michiel Bliemer in Sydney is developing alternative quasi-dynamic assignment that is theoretically more solid than PTV's spillback heuristic; I guess DAT.mobility's OmniTrans software has implementations of that and maybe also Aimsun. You may want to contact Michiel for further information.
I am interested in DTA, Chris Tampère. I just want to know the overall steps you have followed in developing DTA model. Your reply will be appreciated.
Although 2 years ago; I suggest simply adding a hard capacity constraint.
Solution algos need amending of course. The equilibria then must be realistic in the sense that they do not exceed capacity! (Dynamic assignment is a very complicated next step which may be quite unnecessary for very many applications.)
Thank you Mike, DTA is indeed complicated. But we are trying to come up with awnsers to that problem. One of our solutions is the DTA toolbox Chris was talking about 2 years ago. It is up an running over here:
https://www.mech.kuleuven.be/en/cib/traffic/downloads
and provides some easy tutorials in matlab.
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