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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?