Capacity allocation and tolling-rewarding schemes for the morning commute with carpooling

This study investigates the road capacity allocation scheme and step tolling-rewarding scheme for carpooling. Different from most studies that assume a single or a continuous carpooling ratio, this study models multiple scenarios explicitly considering two-person, three-person, and four-person carpooling, as well as shared vans or shuttle buses. The proposed capacity allocation schemes reserve road service capacity during designated time windows for specific carpooling vehicles. During these time windows, the road service capacity is exclusively allocated to carpooling vehicles with a designated number of commuters (or carpoolers), while other vehicles are only allowed to pass the roadway bottleneck outside these time windows. Multiple reserved time windows can be designed and allocated to carpooling vehicles with different numbers of carpoolers. We examine the commuting equilibrium profile under given temporal capacity allocation schemes. We also model the potential “braking or tactical waiting” behavior due to temporal changes of right-of-way under the capacity allocation schemes. On the one hand, the temporal capacity allocation scheme encourages more carpoolers to share one vehicle and thus the number of vehicles on the road is potentially reduced; on the other hand, the temporal capacity allocation scheme yields inconvenience costs due to carpooling and road capacity waste due to braking or tactical waiting behavior under the capacity allocation scheme. We model this trade-off and quantify the system performance under the temporal road capacity allocation scheme. We also extend the analysis to the cases with heterogeneous inconvenience costs due to carpooling and with both temporal and spatial road capacity allocation (i.e., a proportion of road capacity is used for carpooling during certain time windows). Furthermore, we integrate the step tolling-rewarding scheme with the capacity allocation scheme, which further manages the carpooling choices and reduces total system cost. Numerical studies are presented to illustrate the analytical results. We found that carpooling should not be rewarded in some occasions, and instead should be penalized to avoid overcrowded carpooling flows in order to improve system efficiency.