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

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

3. 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?

4. 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

5. Single trip search space

6. Is there a better way?
A-star algorithm ( 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

7. 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)

8. 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

9. 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

10. Average Gap of Individual Trips

11. 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.

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

13. Maximum Gap of Individual Trips

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

15. Parcels: Elastic zone connectors

16. Parcels: Elastic zone connectors plus shortcuts

17. 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

18. 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

19. Questions?