A node model for macroscopic dynamic traffic loading & assignment with spillback. In a dynamic loading or assignment, if traffic arriving at a node exceeds one or more exit link's capacity, flows must be constrained among the approach links, with a "node model." This is especially necessary for spillback to be represented and propagated. This is an original and simple solution that overcomes problems in previous node models with causality and consistency. Applies to general intersections, not just merges; satisfies Tampère's seven requirements. Requires no turn-specific "priority factors." (For cases of just one outlet link, it matches the capacity-proportional merge model. Maintains first-in first-out consistency.)
Paper presented at the 2011 TRB Annual Meeting
Published in Transportation Research Record 2263, Network Modeling 2011
Link to paper, full text requires TRR access privileges
Errata:
1) pg 120, under "Macroscopic Model Comparisons," the first Q should be theta.
2) The objective function L is actually convex-up, i.e. having a global maximum.
Preprint [View] [PDF]
Abstract and Poster [View] [PDF]
Analyzed in Smits, Bliemer, Pel, and Arem, "A family of macroscopic node models," in Transportation Research Part B, v. 74, April 2015, Elsevier
NEW revised 4/2/2019 - Notes on this "capacity-consumption equivalence" node model
A basis of an accelerated solution algorithm, solves single-constraint cases in finite time (including worst-cases for the basic iterative algorithm)
COMING SOON: an improved and concisely specified accelerated algorithm
Comparisons to Smits et al.'s very-similar "equal delay" model.
Remarks on Tampère's "maximizing flow" criterion.