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

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

attraction

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

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

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 station’s

“shed”•Not database or GIS-

friendly

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

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

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

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

Example Result: Trip Records with Parking Choice (excerpt)

Orig Dest PeriodDep.Time Random

PARKZONE

496 769 1 636 0.92 243

234 767 1 636 0.99 243

1280 493 1 637 0.02 498

232 789 1 637 0.02 226

704 332 1 637 0.04 343

Example Result: Fill schedule

Order Time Park Zone1 0.21813 2432 0.31329 4983 0.34398 7184 0.36025 12475 0.36601 9136 0.42678 9247 0.52915 9278 0.55654 7039 0.67291 91210 0.76643 175

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…

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

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

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 destinationOrig

1Dest

1Period

1DepTime Rand

PARKZONE

Orig2

Dest2

Period2

496 769 1 636 0.92 243 769 496 3234 767 1 636 0.99 243 767 234 41280 493 1 637 0.02 498 493 1280 3232 789 1 637 0.02 226 789 232 3704 332 1 637 0.04 343 332 704 4

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

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

Questions?