John Gibb DKS Associates Transportation Solutions

The Park-and-Ride Problem for Transit Auto Access:  Which park-and-ride transit stop for a trip  Getting level of service “skim” values for auto and transit legs  Assigning auto and transit legs

Customary Solutions (Trip-Based)  Zone-Station links by auto access “shed”  Capacity restraint by art, trial and error  Drive legs not assigned  Intermediate zone  EMME triple-index (convolution)  Multinomial logit  Capacity restraint by shadow-price

Individual trip modeling - as in activity-based model  Heterogeneous choice sets & behavior  Time-specific  Sub-mode choice  Single outcome per choice  Determines auto & transit trips in both directions

“Real world”: Parking available to all until full  Time-dependent choice set  Arrival time determines individual’s priority (not drive distance or analyst’s judgment)  Commuter behavior:  Know when lots fill  No frustrated arrivals to full lots

Original Sacramento Application: Chronological Order  One-pass algorithm:  Sort trips by presumed departure time  Choose best-utility among available lots  Accumulate parking loads; make unavailable when full

Limitations of the one-pass method  Loss of choices  Departure & parking-arrival time varies among alternatives  One can leave earlier to beat a lot’s fill-time Improved method for Sacramento update and new Seattle ABM in progress…

Crawford-Knoer matching algorithm (1981)  Generalizes Gale-Shapely (1962)  Hospital-residents, college admissions, stable marriage problems  Iterative rounds of “proposals” until constraints satisfied.  In C-K, rejected proposals are adjusted & resubmitted

C-K algorithm for parking, briefly  Iterative rounds  Parking choice  Latecomer rejection  Rejectees adjust departure time to that lot a unit-step earlier  Departure-time adjustment counts against utility  Choice may repeat  Trip “accepted” may be “bumped” in a later round  Stop when no parking oversubscribed

Crawford-Knoer properties  User-optimal equilibrium  Escalation of early arrival times  Last-minute arrival rush  No denial of choice  Gradual adjustment avoids problems, can use efficient methods  Needs an early-departure utility parameter

System equilibration flow Skim Matrices Activity-Based Demand Model Trips P&R lot placement Network Assignment Lot-Full Times

Thanks! Questions, requests for reports welcomed at DKS Associates TRANSPORTATION SOLUTIONS