Optimal spatial-temporal capacity allocation for morning commute with carpool considering parking supply constraint

Allocating urban highway capacity to prioritise carpooling traffic is a well-studied subject. However, one area of limited research so far is on the impact of parking constraint at workplace on its spatial-temporal design. This paper examines a multi-modal morning commute scenario, where commuters can freely choose solo driving, carpooling, or public transit to go to work. The highway bottleneck capacity is shared between a general-purpose lane for all drivers and a time-limited carpool lane for carpooling vehicles only. Analytical derivations of all possible commute patterns are provided, considering different parking supply levels and capacity allocation strategy. Results show that all bottleneck capacity should be allocated to carpool lane spatially, but the optimal temporal allocation of carpool lane may not be unique for minimizing total trip cost. This implies, the accurate estimation of extra carpool cost to optimize the temporal lane reservation may be no longer necessary for the traffic authority due to the limited parking supply, whilst it is really required when the parking supply is abundant. We also incorporate the traffic authority's social cost budget for both temporal and spatial allocations into the optimization problem, explaining why general-purpose lanes are still prevalent in reality. The research has implications on policy makers as well as workplace parking managers by providing them a framework to design optimized road-space allocation with workplace parking supply.