strategies for estimation of park-and-ride demand constrained by parking lot capacities luc...

Strategies for Estimation of Park-and-Ride Demand Constrained by Parking Lot Capacities

Luc Deneault, M.Sc.Service de la modélisation des systèmes de transportMinistère des transports du Québec

20th International EMME Users’ ConferenceOctober 19th 2006Montréal, Québec

http://www.emmeconference.org/en/index.html

Luc Deneault, M.Sc.Service de la modélisation des systèmes de transportMinistère des transports du Québec

Strategies for Estimation of Park-and-Ride Demand Constrained by Parking Lot Capacities

Experiment conducted with the regional travel model of the Central Transportation Planning Staff (CTPS) of the Boston MPO

http://www.emmeconference.org/en/index.html

1. Application1. Application

CTPS’ Commuter rail studyCommuter rail study request by Massachusetts Bay Transit Authority (MBTA) parking demand forecast for the 2025 AM pk period

CTPS regional travel model area : 2 700 square miles (164 cities) population : 4.3 M

base year model periods : AM, mid day, PM, night zones: 1205 (97 external zones, 122 P&R lots) coded network: 13,900 nodes, 58,500 links (17,300 walk-access)

Service de la modélisation des systèmes de transport

MBTA network :MBTA network :

Parking spaces : over 48,000


Mode Routes Stations / Stops

Line Miles

Rapid transit 3 53 38

Green line and Mattapan trolley

5 78 28

Commuter rail 12 119 410

Bus and trackless trolley

162 9,000 730

Water ferry 4 6 -

1999 1999 MBTA ridership dataMBTA ridership data 1,036,100 daily boardings 122,300 commuter rail boardings model estimate of 695,000 one-way daily passenger trips

PP&&R lotsR lots base year model of 122 lots, total capacity of 45,824 spaces very little on-street parking and most lots filled up early in the morning 2025 network of 136 lots, capacity of 51,171 spaces demographic trends indicate that the potential demand will likely exceed capacity

CTPS modelCTPS model parking choice model with no explicit P&R capacities uses auto and transit legs impedances through matrix convolutions


2. Model Formulation2. Model Formulation2.1) Parking Choice Model without Capacities (INRO) :


'

''' )exp(

)exp(

321

321

k

tr

qkk

au

pk

trkqk

aupkc

pqpkq uwu

uwugg

where

pkqg : number of trips from origin p to destination q

using park-and-lot k ; cpqg : demand of combined mode park-and-ride c

between origin p and destination q . aupku : auto mode time between p and k ; trkqu : transit impedances between k and q ;

kw : utility of parking lot k (cost, safety measure, capacity etc..).

« a little bit of greek! »

Resolution Resolution (INRO)(INRO)

auto demand (first leg of P&R trips)


where :

)exp( 21 kaupk

aupk wuU and )exp( 3

trkq

trkq uU

tr

qkk

au

pkpq UUd '

'

'

..solved by following convolution :

trqk

k pk

cpkau

pq

trqk

k

aupq

pk

cpkau

pq

Ud

gU

UUd

gg

using index k for destinations and q for parking lots

trkq

q

aupk

pq

cpq

qpkq

aupk UU

d

ggg

ResolutionResolution transit demand (second leg of P&R trips)


p pq

cpqau

pktrkq

p

aupk

pq

cpqtr

kq

trkq

p

aupk

pq

cpq

ppkq

trkq

d

gUU

Ud

gU

UUd

ggg

'

Model FormulationModel Formulation

2.2) Parking Choice Model with Capacities (Spiess [1996]) :


trkqk

aupkpkq

pkqpkq uwugg 3211log

subject to :

.,, QqPpGgk

pqpkq

and :

., KkCg kpq

pkq

where kC is the capacity of parking lot k .


Parking Choice Model with Capacities (Spiess)

Resolution (macro parkride):

successive coordinate descent algorithm

iteratively diverts P&R trips allocated to saturated P&R lots to alternative lots with available spaces

satisfaction of flow conservation constraints

P&R lots capacity constraints not necessarily satisfied



Parking Choice Model with Capacities (Spiess)

sum of utilities is expressed as follows :

Proposition by Hendricks, Outwater [1998]

computation of capacity-restrained impedances based on sum of utilities of the P&R mode

feedback of utilities in the mode choice step more accurate estimation of P&R demand


tr

qkk

kau

pkpq UUd '

'

'

Model FormulationModel Formulation2.3) Shifting P&R trips in excess of parking

capacities

Two operations :

1)

2)


removing the excess trips from the auto leg

(aupkg values) and transit leg (

trkqg values) demand

matrices computed in the parking choice step

removing the excess trips from the P&R trip demand

matrix (cpqg values)

then, submit trips back to mode choice or "arbitrarily" add trips to the demand of other modes.

straigthforward

Removing the excess P&R trips Removing the excess P&R trips from P&R trip matrixfrom P&R trip matrix

trips are removed from saturated P&R lots according to the proportion of trips allocated to the P&R lots by each O-D pair


For each O-D pair, find contribution of each parking lot k :

ratio of the sum of utilities over P&R lot k on the sum of utilities over all P&R lots

compute contribution of the excess P&R demand of

an O-D pair pq for P&R lot k , based on proportion of

pqg allocated to lot k

Steps of the procedureSteps of the procedure


(1) initialize shg , demand matrix of trips shifted

away from P&R mode;

then, for each park-and-ride lot k :

(2) let kC , the capacity of the park-and-ride lot k ;

compute kr , the ratio of trips allocated to a park-and-ride lot over its capacity:

k

pqpkq

k C

g

r

if 1kr , do the 3 following steps, else, go back to step (2).

Steps of the procedureSteps of the procedure


(3) adjust the auto-leg and transit-leg demand matrices, by applying firm capacity constraints:

k

aupk

au

pk r

gg and

k

trkq

tr

kq r

gg

(4) for each O-D pair pq , compute sum of utilities over P&R lot k :

trkq

aupkpq UUd

~

(5) compute trips to "shift away" from the combined mode park-and-ride c and cumulate those trips

in matrix shg :

cpq

pq

pq

k

kshpq

shpq g

d

d

r

rgg

~1

Approach with explicit P&R CapacitiesApproach with explicit P&R Capacities


Same procedure to shift trips away from the P&R matrix

only difference : computing sum of utilities

1) computation of pqd , matrix of the sum of utilities over all the P&R lots:

- computed in parkride at the beginning of each iteration of the algorithm

- final computation after completion of parkride (before proceeding with the shift of P&R trips that exceed P&R lots capacities)

Approach with explicit P&R CapacitiesApproach with explicit P&R Capacities


This matrix is computed applying the sum of utilities of the parking choice model with explicit capacities:

tr

qkk

kau

pkpq UUd '

'

'

where k is the multiplier of park-and-ride lot k (dual variable of P&R lot capacity constraint). 2) for each O-D pair pq , computation

of the sum of utilities over PNR lot k :

trkqk

aupkpq UUd ~

3. Implementation3. Implementation

Initialization step :

highway & walk-access (WA) skims

Park-and-ride demand step :

1) mode choice step (HBW, HBO, HBSC & NHB)

SOV, HOV, DA-transit, WA-transit tables

2) allocation of DA-transit (P&R) trips to PNR lots


Auto leg of DA-transit => SOV demandtransit leg of DA-transit => WA-transitParking choice step applied twice :

a) first, to compute skims for mode choice

b) then to allocate the DA-transit trips

3. Implementation3. Implementation

Initialization step :

highway & walk-access (WA) skims

Park-and-ride demand loop : for some strategies..

1) mode choice step (HBW, HBO, HBSC & NHB)

SOV, HOV, DA-transit, WA-transit tables

2) allocation of DA-transit (P&R) trips to PNR lots

Implementation within Implementation within CTPS modelCTPS model

Issues

Strategies of allocation of P&R trips

Characterization of P&R trips (mode choice step)

Calibration issues

Development of emme/2 macros


3.1 Strategies of Allocation of P&R 3.1 Strategies of Allocation of P&R TripsTripsImplementation of 6 different strategies ofskimming/allocation compared to each other

(AM peak period, year 2000)

1) logit without capacity constraints

2) option (1) with reallocation of exceeding trips;

3) logit with utilities relative to capacities (no constraint)

4) option (3) with reallocation of exceeding trips;

5) logit with explicit capacity constraint;

6) option (5) with reallocation of exceeding trips.Service de la modélisation des systèmes de transport

Computational effortsStrategies with P&R lots capacities are more computationally demanding


Requirements of Each PNR Allocation Strategy number of convolutions computed

Strategy P&R Skims Allocation Post-Allocation 1 1 convolution to

measure sum of utilities over P&R lots + 1 convolution per “skim measure”

2 convolutions, 1 for each leg of P&R trip.

none

2 see(1) see(1) one "quick" convolution/P&R lot

3 see(1) see(1) none


5 run macro parkride (3 convolutions/ iteration) + 1 convolution per “skim measure”

run macro parkride

none


Computational effortsStrategies 5 and 6 implemented as an iterative process

for each iteration:

i) new skims submitted to the mode choice step

ii) generation of a new P&R trip demand matrix

shifts of trips exceeding P&R lot capacities

convolutions successively applied to each P&R lot zone:

i) to determine the O-D pairs of the trips using each lot

ii) and remove the % of demand in excess of capacity


3.2 Characterization of P&R trips3.2 Characterization of P&R tripsGuidelines and assumptions to characterize P&R tripsand applied as constraints in the mode choice step ( the Greater Vancouver Regional District (GVRD) ; Edwin Hull Associates [1998])

Assumptions for the MBTA Commuter Rail Study:

DA-transit leg time < 4 X auto impedance (for O-D pairs where auto impedance (time) > 10 minutes)

[ in-vehicle time of DA-transit leg > 0 ] && [ out-of-vehicle time of DA-transit leg < 5 X in-vehicle time of DA-transit leg ]

transit leg weighted impedance < 1.5 X (WA-transit total

weighted transit impedance)

auto leg times < 1.5 X (total auto times)


3.3 Calibration issues3.3 Calibration issuesTwo objectives:1. Good fit of P&R lot counts (“reliable” P&R trips)2. quick convergence of solution of the problem


Coefficients of P&R allocation parameters

Experiments conducted with strategies 5 and 6

Parameter value

coefficient of auto time utility 0.25

coefficient of transit impedance utility

0.05

number of iterations of parkride (skims)

30

number of iterations of parkride (allocation)

10 (1995) 5 (2025)

number of iterations of the PNR feedback loop

3

Running the Running the parkrideparkride macromacro

Strategies adapted to a context of saturated P&R lots :

The number of iterations within parkride :

parkride decreases the attractivity of saturated P&R lots.. P&R trips diverted to P&R lots with available spaces.

Trip demand allocated to P&R lots may equal or violate P&R lot capacities.. a relatively high number of iterations within parkride will increase the probability of a "feasible" solution.


Running the Running the parkrideparkride macro macro

The number of iterations within parkride :

Computing skims for the mode choice procedure..

high number : will divert more and more trips to the "less" attractive P&R lots; implemented as such, parkride would generate relatively high skims values for the P&R mode and mode choice step would result in a lower number of P&R trips

low number : will generate a solution closer to that of “unconstrained” strategy, and therefore produces lower skims values for the P&R mode, which results in an higher number of P&R trips

high number of iterations of parkride in the skimming step to obtain the most “realistic” P&R skims


3.4 Development of 3.4 Development of emmeemme/2 macros/2 macros

pnr.mac : runs the logit intermediate destination choice model without explicit capacities computations of skims and allocations of P&R trips, essentially applies the implementation of Blain[1994] and INRO (emme/2 User's Manual) addition of convolution steps to remove trips that exceed the PNR lot capacities

Parking choice model with explicit capacities:

pnrskim.mac : computes P&R skims derived from the results of the parkride macro (using convolutions steps already presented by Spiess [1996])

postride.mac : implements the strategy that removes exceeding P&R trips


4. Results4. Results


reminder : 122 modeled P&R lots, for a total regional capacity of 45,824

in 1995, occupancy rate of 88,8% was observed for the 106 lots with counts (a total of 38,308 vehicles counted in AM peak period)

total target P&R demand for the calibration is of 40,685 trips (after estimation of occupancy of the 16 lots with no counts)

ResultsResults


Summary of Results - Calibration

Strategies P&R

demand

P&R demand

over capacity

Correlation with

counts

% of lots in excess of cap.

1995 target demand (counts + estimates)

40,685

1 - (no capacities / no P&R utilities)

39,536 13,162 .533 57,5

2 - (1 with reallocation of trips)

26,374 0 .788 0

3 - (utilities relative to P&R capacities

44,666 9,365 .883 47,5

4 - (3 with reallocation of trips)

35,301 0 .898 0

5 - (with capacities) 41,673 1,761 .964 81,7 6 - (5 with reallocation of trips)

39,912 0 .968 0

ResultsResults


limitations of uncapacitated model: - strategy 1 estimates 39,536 P&R trips, but a third of those trips in excess of the capacity of their respective PNR lot! - strategy 2 is inadequate due to severe underestimation parking lot usage

better performance of approach with utilities tied to the capacities of P&R lots: - with strategy 3, 21% of the 44,666 estimated P&R trips are allocated to saturated lots - reasonable results with strategy 4

satisfactory results of capacitated approaches: - high correlations between counts and P&R demand with both strategies! - with strategy 5, only 4.2% of trips shifted to another mode - with strategy 6, the targeted regional P&R demand is underestimated by 1.9%

MTQ modeling activities (urban level)MTQ modeling activities (urban level)

MTQ involved in preparation and management of regional O-D surveys (avg. sample rate of 5%) periodic surveys : interval of 5 years for the Montréal region

Development and maintenance of transportation models for the Montréal, Québec City, Sherbrooke and Trois-Rivières regions: modeling strategy: expansion of O-D survey data, person and auto assignment models, trip forecasting model, mode transfer model, vehicle emissions model

Participation in the development and maintenance of the Ottawa-Gatineau region transportation model: classical four-step model developed and operated by the TRANS Committee


Park-and-ride StatisticsPark-and-ride StatisticsMTQ modelsMTQ models


Region P&R lots spaces counts occ. rate% lots >

90%

Montréal BUS P&R 18 10 464 7 595 73% 5 train - Blainville 5 2 178 2 107 97% 4 train - Delson 4 603 385 64% 1 train - Deux Montagnes 8 5 343 5 090 95% 6 train - Rigaud 15 2 897 1 893 65% 7 train - St-Hilaire 4 1 769 1 296 73% 0 Train P&R 36 12 790 10 771 84% 18

total 54 23 254 18 366 79% 23Outaouais Gatineau 15 1537 1405 91% 11 Ottawa 11 4806 4330 90% 7Québec City 27 1163 708 61% 8

MTQ’s P&R modelling opportunities MTQ’s P&R modelling opportunities

Montréal region - P&R lots of regional bus lines - extension of existing commuter rail lines and eventual new commuter rail lines (AMT) - eventual light rail studies (AMT)

Québec City region - light rail (“tramway”) study (RTC)

Ottawa-Gatineau region - Projet Rapibus (STO, Gatineau) - O-train (OC Transpo, Ottawa) - transitway (OC Transpo, Ottawa)


ConclusionConclusion

The proposed strategy:

combines the parking choice model implemented in the parkride macro with the strict satisfaction of parking lot capacities

forecasting tool : allows to incorporate the magnitude of planned expansions at P&R lots and capture their impacts at the neighboring stations and throughout the transit system

a by-product : several emme/2 macros


Merci !

Luc Deneault:

(514) [email protected]

Thank you !

Acknowledgements :

strategies for estimation of park-and-ride demand constrained by parking lot capacities luc...

Documents

parking lots

parking spaces

capacity of parking

street parking

saturated pr lots

parking lot capacities1

transit demand

alternative lots