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
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-todestination time estimates
Narrower search space than Dijkstra-to-destination
Exact best path
Network search spaces example
Dijkstra Tree
A-Star
12% of regional network
2.4% of regional network
(except other zone connectors)
(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
10
Average Gap (min)
1
0.1
0.01
AM
0.001
Mid-Day
0.0001
PM
Evening
0.00001
0.000001
0.0000001
0
50
100
150
Cumulative Run Time (min)
200
250
Vs. Trip-Based Assignment
10
Average Gap (min)
1
0.1
AM
Mid-Day
0.01
PM
Evening
0.001
0.0001
0
50
100
150
200
Cumulative Reapportioned Run Time (min)
250
Direct Comparison:
PM Average Gap
10
Disaggregate
Average Gap (min)
1
Disaggregate MovingAverage
Conventional Trip-Based
0.1
0.01
0.001
0.0001
0
50
100
150
200
Cumulative Run-Time (min, concurrent with all other periods)
250
Maximum Individual-Trip Gap (min)
Maximum Gap of Individual
Trips
100
10
1
AM
0.1
Mid-Day
PM
0.01
Evening
0.001
0.0001
0
50
100
150
Cumulative Run Time (min)
200
250
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?