1. John Gibb DKS Associates Transportation Solutions

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 Solutions Problems Error-prone, subject to analysts 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 PNR NODE=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 stations 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 individuals priority (not drive distance or analysts 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) OrigDestPeriod Dep. TimeRandom PARK ZONE 49676916360.92243 23476716360.99243 128049316370.02498 23278916370.02226 70433216370.04343

11. Example Result: Fill schedule OrderTimePark Zone 10.21813243 20.31329498 30.34398718 40.360251247 50.36601913 60.42678924 70.52915927 80.55654703 90.67291912 100.76643175

12. What about the actual arrival time to parking? Departure order not exactly same as parking- arrival order Individuals 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 = mens preference-ranks of women Arrival time to parking = womens preference of men Iteration ratcheting: individuals best available utility stays same or gets worse, while any lots 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 Orig 1 Dest 1 Period 1 Dep TimeRand PARK ZONE Orig 2 Dest 2 Period 2 49676916360.922437694963 23476716360.992437672344 128049316370.0249849312803 23278916370.022267892323 70433216370.043433327044

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?