Temporal-spatial allocation of bottleneck capacity for managing morning commute with carpool

Carpooling as one of demand management measures is effective in reducing highway congestion. Recent studies have shown that an appropriate spatial allocation of bottleneck capacity between carpool lane and general-purpose lane can lead to peak-spread of the morning commuters' departure time and reduce the system's total trip cost. What is not clear however is whether temporal allocation of bottleneck capacity can also be effective and if so, what the impact would be, and furthermore what the combined effects of temporal-spatial allocation of bottleneck capacity would be. This paper investigates the impacts of a temporal allocation of bottleneck capacity, when carpool lane is available only within a reserved time window, and a joint temporal-spatial capacity allocation, on morning commute patterns. User equilibrium commute patterns are derived for both the temporal-only and the joint temporal-spatial capacity allocation schemes, along a highway corridor with two driving modes: solo driving and carpooling. The extra costs associated with carpooling are considered alongside of travel time and schedule delay costs. We identify three different cases representing the relative barriers and attractions of carpooling to commuters, and we show that the optimal capacity allocations are sensitive to the accurate estimation of the commuters' extra carpool cost. To assist in evaluating the difference between a non-optimal and the optimal temporal-spatial allocation schemes, we derive analytically the upper bounds on the efficiency loss and present numerical illustrations on how the upper bounds vary with the different operational and behavioral variables.