A Disaggregate QuasiDynamic ParkandRide Lot Choice Model Application with Parking Capacities

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

• John Gibb
• DKS Associates
• Transportation Solutions

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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

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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

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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

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Sample Transit Network Code

• 8003 Marconi/Arcade
• SUPPLINK N 8003- 3046, DIST 0, SPEED 0,
  ONEWAYF, MODE 12
• SUPPLINK N 7099- 11285, DIST10, SPEED10.0,
  ONEWAYF, MODE 16
• SUPPLINK N 7026- 3046, DIST 0, SPEED 0,
  ONEWAYF, MODE 17
• SUPPLINK N 7026- 4492, DIST 0, SPEED 0,
  ONEWAYF, MODE 17
• PNR NODE7099-8003 MODE11 LOTMODE15 COST2.26
  TIME2.00 ZONES226-240,
• 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

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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

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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 FORNEXT loop on arbitrary variable
• Arbitrary-order matrix referencing

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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

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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

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Example Result Trip Records with Parking Choice
(excerpt)
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Example Result Fill schedule
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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

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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

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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

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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

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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

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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

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Questions?