Network Assignment and Equilibrium for Disaggregate Models John Gibb DKS Associates Transportation Solutions

Disaggregate traffic assignment Solves pressing modeling problems Opens modeling opportunities Is practical

Activity-Based Demand Models: Disaggregate Synthesis Individual units of demand Process one at a time Heterogeneous choice behavior Single outcome of each choice Each choice linked to the person & itinerary Can you do this to assignment?

Assign each individual trip? You gotta be kidding! Millions of trees, instead of thousands No “bulk efficiency” Trees from origin to all destinations Can’t load whole matrix row at a time A row for each origin-class combination

Single trip search space

Is there a better way? A-star algorithm (1968 - Hart, Nilsson, Raphael) Vehicle-navigation systems, gaming programs, some dynamic assigners Very similar to Dijkstra’s “Informed” search helped by optimistic node-to-destination time estimates Narrower search space than Dijkstra-to-destination Exact best path

Network search spaces example Dijkstra Tree A-Star 12% of regional network (except other zone connectors) 2.4% of regional network (except other zone connectors)

Individual Trip Loading Single-outcome: One path per trip Save the path Deduct “old” path when assigning “new” path Iteration Step Size = fraction of the population assigned between link-delay updates Several iterations per pass Complete pass before starting new pass

Experimental Test Assignment ≈ 4,500,000 trips from an activity-based demand model Point-specific origin and destination 6 complete passes through all trips 900 iterations (link-delay updates) Gradually-declining step sizes from 300,000 trips in early iterations, to 7,100 trips in last iteration First pass ≈ 20 minutes, all others ≈ 40 minutes

Average Gap of Individual Trips

Vs. Trip-Based Assignment Reapportioned Run Time: Assignments were sequential, not concurrent. Total run time was 229 min. Same trips, same delay functions, but no centroid-shift feature.

Direct Comparison: PM Average Gap Disaggregate gaps are worst-case (oldest to newest paths); overall average is likely better.

Maximum Gap of Individual Trips

Disaggregate Assignment Solves Heterogeneous path choice Complex tolls, individual value of time Centroid aggregation error Origin, destination points (parcels, addresses…)

Parcels: Elastic zone connectors

Parcels: Elastic zone connectors plus shortcuts

Disaggregate Assignment Creates Opportunities Warm-starts Path queries Full information for dynamic simulation Activity-based model trip specified to the minute Any detail scale Lots of simulation runs, not once after-model Time-specific skims Stochastic path choice

Further development Loading schedule experiments Full Activity-Based Application Warm-starts Dynamic assignment Fast simulations preferred Individual skims to the activity-based model Destination choice samples Time-specific Transit

Questions?