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

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

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)

 Downtown  Comm. 1  Comm. 2

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

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

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

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

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?

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

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…

Time-varying logsums Creates time-varying PnR logsums If a lot fills up during the 7-8 AM period, the 6- 7 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)

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 0.01 as kiss and ride only lots Only see the cost to get to the PnR lot and the cost to get to destination

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

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

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

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

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

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.