1. Capacity Constrained Park and Ride in trip-based and activity based models
Paul McMillan
May 2017

2. Issues with existing PnR techniques
Single “best” (closest?) lot for given OD pair
No benefit from choice of multiple lots
No capacity constraint
This is the 20% that we spend 80% of our effort on
Single “best” (closest?) lot for given OD pair

3. Capacity constrained theory
Each lot has a maximum capacity
“Shadow” penalty applied to keep lot use under maximum capacity
Reflects uncertainty and hassle of lot being full
Strict capacity constraint (very strict)

4. 
Downtown 
Comm. 1 
Comm. 2

5. 
Downtown 
Comm. 1
Lot A
Lot B 
Comm. 2

6.    Downtown Comm. 1 Lot A Demand exceeds capacity ∴ Add penalty
Lot B 
Comm. 2

7. 
Downtown 
Comm. 1
Lot A
Move to less appealing lot
Lot B 
Comm. 2

8.    Ultimately… mode choice shifts Downtown Comm. 1 Lot A Lot B

9. Multiple loops
“Inner loop” converges a fixed demand to respect supply at all park and ride locations
Similar to traffic assignment process
Resulting logsums fed into demand model for overall demand / supply loop
Congested park and ride results in reduced park and ride demand
So, how do we do this?

10. Constraint mechanism (inner loop)
Add penalty to lots that are overflowing
Similar function to that used in calibration:
ln⁡ 𝑙𝑜𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑙𝑜𝑡 𝑑𝑒𝑚𝑎𝑛𝑑
Reallocate demand to lots with new penalties
Repeat until converged
Within inner loop

11. Multiple time periods
Do PnR assignment of first period demand (early offpeak, <6:00AM)
Pass remaining capacity to next time period (6:00-7:00)
And so on…

12. Time-varying logsums Creates time-varying PnR logsums
If a lot fills up during the 7-8 AM period, the AM logsum will be relatively unconstrained but the 8 AM logsum will show PnR as very unappealing
Affects decisions further up the tree (time of day, mode choice, destination choice, generation)

13. Kiss and Ride Effectively park and ride at unconstrained lot
Generalised cost before lot penalized in any way (use first iteration)
Can include lots with capacity of as kiss and ride only lots
Only see the cost to get to the PnR lot and the cost to get to destination

14. Implementation Python script for Emme 4.2 Runtime <10 minutes
Produces:
Trips to and from lots
PnR usage by time period
PnR and KnR logsums
Implemented in two model systems

15. Model applications Brisbane Qld Calgary AB Metro population
2.4 million
1.5 million
Transit mode share:
All
PnR KnR
… overall
9.0%
2.2%
6.7%
1.3%
… home to work
16.3%
5.7%
16.5%
4.3%
… home to work in CBD
68.2%
26.1%
45.0%
15.0%
Number of lots
193 33
Total stalls
33,400
17,400
Lot capacity range
10 to 1,000
50 to 1,750

16. Brisbane: Aggregate nested logit model
Number of trips
Destination choice
Time of day AM
Mid PM
Off
Mode choice
Walk
Bike
Transit
SOV
PnR
HOV 2
HOV 3
KnR
Hour of peak
6-7
7-8
8-9

17. Calgary: Activity based model
PATLAS system model
Mode choice primarily by tours:
Park and ride natural fit
Peak spreading considers time- varying aspect

18. Conclusions Practical application:
Respects capacity
Time shifts
Kiss and ride
Same form works in multiple model contexts

19. Thank you! Thanks to my coauthors:
Ben Pool, State of Queensland, Transport and Main Roads
Alan Martin, City of Calgary, Forecasting
JD Hunt, Kevin Stefan and Alan Brownlee, HBA Specto Inc.