John GibbDKS AssociatesTransportation 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 fillNo 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

Lot-Full Times

Thanks!

Questions, requests for reports welcomed at

jag@dksassociates.com

DKS AssociatesTRANSPORTATION SOLUTIONS

www.dksassociates.com