A Disaggregate Quasi-Dynamic Park-and-Ride Lot Choice Model Application with Parking Capacities

1. John Gibb DKS Associates Transportation Solutions A Disaggregate Quasi-Dynamic Park-and-Ride Lot Choice Model Application with Parking Capacities

2. 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 • Commuters, mostly • AM peak period (3+ hours) • Auto at home end, transit at work or attraction

3. Customary Drive-Access Solution • Zones placed into auto access “sheds” for each station • Observed drive-access legs tend to be short • One or few stations per zone • Parking location choice, if any, within transit path choice model

4. Customary Solution’s Problems • Error-prone, subject to analyst’s judgment, trial-and-error • Capacity restraint • Alternative forecast scenarios • Memory and computational limits may preclude multiple choices • Drive-access legs not included in auto assignment …except through unconventional tricks

5. Sample Transit Network Code ; 8003 Marconi/Arcade ; SUPPLINK N= 8003- 3046, DIST= 0, SPEED= 0, ONEWAY=F, MODE= 12 SUPPLINK N= 7099- 11285, DIST=10, SPEED=10.0, ONEWAY=F, MODE= 16 SUPPLINK N= 7026- 3046, DIST= 0, SPEED= 0, ONEWAY=F, MODE= 17 SUPPLINK N= 7026- 4492, DIST= 0, SPEED= 0, ONEWAY=F, MODE= 17 PNRNODE=7099-8003 MODE=11 LOTMODE=15 COST=2.26 TIME=2.00 ZONES=226-240, 295,299-303,310-312,347,350,351,355-358,360,372,375-381,881,882 • User must code list of zones comprising each park-and-ride station’s “shed” • Not database or GIS-friendly

6. Newer EMME solution • Matrix calculations with third intermediate-zone index • “Matrix convolution” = “triple-index operation” • Origin-to-intermediate, intermediate to destination • Special parking zones as intermediate zones • Multinomial logit choice (Blain 1994) • Drive utility weight ≈ 3 ∙ transit IVTT or more • Free choice favoring short drive distances • Capacity restraint (Spiess 1996) • Iteratively solve shadow-price where full

7. New opportunities • Activity-based travel model creates individual trips, not just zone-to-zone flows • TP+/Voyager record-processing • Calculations for each record in a file • TP+/Voyager generalized looping • Like Basic FOR…NEXT loop on arbitrary variable • Arbitrary-order matrix referencing

8. A “real world” model: Parking available to all until full • Maximum utility, subject to availability • Arrival time determines individual’s priority • (not drive distance or analyst’s judgment) • Assign each trip to one parking location • Commuter behavior assumed: • Know when lots fill, choose with knowledge • No frustrated arrivals to full lots

9. Chronological Method • Prioritize individuals by departure time from origin • Drive-times usually short, so departure order approximates parking-arrival order • Simple one-pass algorithm: • Sort trips by departure time • For each individual trip, choose best-utility available location • Accumulate parking loads; make unavailable when full

10. Example Result: Trip Records with Parking Choice (excerpt)

11. Example Result: Fill schedule

12. What about the actual arrival time to parking? • Departure order not exactly same as parking-arrival order • Individual’s parking-arrival time varies among alternatives • No single chronological order for choice • Exact reconciliation requires iteration • Fortunately, an algorithm has been invented…

13. Gale-Shapley pairing algorithm (1962) • Hospital-residents, college admissions, stable marriage problems • “Men” propose to favorite “woman” • “Women” provisionally accept favorite proposer • Unengaged “men” propose to next-favorites • Algorithm “ratchets”: rejected and jilted “men” must settle for lesser-favorites, while “women” trade up. • “Male” optimal

14. Gale-Shapley for park-and-ride • Trips = “men” • Parking lots = “women” • Individuals’ utilities of the parking locations = “men’s” preference-ranks of “women” • Arrival time to parking = “women’s” preference of “men” • Iteration “ratcheting”: individuals’ best available utility stays same or gets worse, while any lot’s fill-up time stays same or gets earlier. • Finished when no lot oversubscribed. • User-optimal

15. Further details • Return home via same parking location • Trip record with parking location transforms to drive trips and transit trips • Each with correct origin and destination

16. Further details • Return home via same parking location • Trip record with parking location transforms to drive trips and transit trips • Each with correct origin and destination • Full lots unavailable during midday period • Skimming all zone pairs • Average of each parking-state, weighted by loading-share of state • Fill-schedule indentifies parking states

17. Future study and development • Risk management behavior • Do commuters, avoiding the risk of a full parking location, prevent them from filling? • Time choice behavior • Do individuals leave home earlier for a “competitive” space? • Time-dependence in the activity-based model • Parking space turnover

18. Questions?