Don't merely practice your art, but force yourself into its secrets... - Ludwig van Beethoven
John Gibb
Senior Transportation Engineer
DKS Associates, Sacramento
Company website www.dksassociates.com
ResearchGate profile: https://www.researchgate.net/profile/John_Gibb2
I welcome feedback, inquiry, reports of dead links, and to hear who is using this information and how, along with confirming and/or counter-examples, at:
jag (at) dksassociates (dot) com
or jagua703 (at) gmail (dot) com
(Omit the spaces and use the actual punctuation marks - to mask from spambots.) I am not in Facebook.
Barzilai-Borwein methods for travel demand model feedback
Step sizes for feedback iterations determined during runtime from the linear trend of successive iterates
Coming soon: Extensions to account for noise in the iterates
Feedback assignments stopping criteria
Measured relationship between an assignment's relative gap and the error of skims measured from that assignment
A runtime minimization strategy - stopping criteria for feedback (not final) traffic assignments that is sufficient, but no finer than necessary, so skim errors are small compared to how much they are changing between iterations
Node models of capacity-constrained traffic
Macroscopic dynamic traffic assignment requires both a link model (cell- or link-transmission model) and a node model.
When arrivals to a node toward one or more exit links exceed the links' intake capacities, the node model arbitrates the flow allowed from each approach link.
The first node model satisfying Tampère's seven requirements built on a clear (albeit simple) premise of a behavior of traffic.
Accelerated iteration procedure, solves common cases exactly in finite iterations.
Other conference papers
Efficient equilibration of activity-based models, by running the activity-based model upon only a sample of the households during each demand-loading loop, and accumulating the sample loadings (with appropriate scaling).
2007 TRB Applications Conference paper [View] [PDF]
John Bowman's ETC paper http://jbowman.net/papers/2006.Bowman_Bradley_Gibb.Sac_estimation_and_validation.pdf
A quasi-warmstart assignment procedure is also discussed, that speeds assignments, useful with assignment software that enables "preloading" but lacking a true and efficient warm-start procedure. By this procedure, trips from older iterations of the demand model stay on the same network paths to which they were originally assigned, while new-iteration trips are assigned in a conditional equilibrium, the old trips being present as "preloading". True relative gaps are computed post-hoc, and are not as tight as the software reports (which apply only to the "new" trips being assigned). True gaps improve in later (demand-model) iterations to levels comparable to those in regular assignment of successively-averaged trips with comparable runtime. Although this method is convergent under mild conditions, I do not recommend this procedure anymore, because (1) the newer paper "Adaptive stopping criteria for traffic assignments within convergent feedback demand models" gives a better way, with progressively finer gaps, (2) true warm-start assigners are now available in many modeling software packages, (3) while this quasi-warmstart procedure is probably the best way to do link-flow successive averaging (having successive correction, rather than averaging of independent assignments), the propagation of link-flow errors of early assignments to the final flows limits the true rate of convergence, as it does with independent assignments. If you need to converge the assignment finer after so-many feedback iterations, your only recourse is more full feedback iterations; a finer assignment alone does not eliminate residual assignment error from earlier iterations, and (4) post-hoc reassignment does not duplicate the link flows.
Matching models applicable to disaggregate capacity-constrained park-and-ride lot choice (with other potential applications in worker-job, household-house, student-school, etc.)
Working paper [View] [PDF] includes the Crawford-Knoer matching model. Individual trips choose P&R lot of best utility (including potentially a random term); those arriving after the lot fills up must either choose another parking location, or depart earlier. Crawford-Knoer solves the user-equilibrium of this constrained competitive choice. It is like the Gale-Shapely matching algorithm, but with the ability of "proposers" to adjust their "offers". It's not only a potential method of application, but shows that a stable user-equilibrium exists in many constrained matching problems, very similar to that of traffic assignment equilibrium.
Previous TRB Applications Conference paper http://trb-appcon.org/2009conf/TRB2009papers/1302_Gibb_session_13_appcon_PNR_lot_choice_paper.pdf
Presentation for Citilabs Futura 2016 user conference on both aggregate and disaggregate park-and-ride lot choice models.
Efficient disaggregate traffic assignment of individual trips, each retaining specific record of its path in the network.
TRB Applications Conference paper http://trb-appcon.org/2009conf/TRB2009papers/1909_Gibb_session_19_appcon_Disagg_assignment_paper.pdf
Land-use "smart-growth" effects upon mode choice and trip distribution, applied within the model stream, with system equilibration, instead of post-hoc adjustments to aggregate trips and VMTs:
ITE conference paper [View] [PDF]