An analytical model of many-to-one carpool system performance under cost-based detour limits

Carpooling has emerged as a highly efficient method for mitigating traffic congestion. By strategically consolidating multiple travelers into fewer vehicles, carpooling substantially cuts down the overall number of vehicles on the road. However, the effectiveness of a carpooling system highly depends on the proportion of interested users that can be successfully matched and the amount of benefits users gain from these matches. This paper develops analytical models to estimate these metrics for a carpooling system that serves a many-to-one demand pattern, in which travelers share the same basic destination but travel from different origins. Two distinct scenarios are incorporated in the models: one where users have a preferred role of a driver or rider and another in which they are ambivalent between the two roles. The models provide the system's expected match rate and average user surplus as a function of the network size, number of users, and travel costs. Different from previous studies, the proposed models developed here consider that users only participate in trips that are beneficial to them from a cost perspective, rather than assuming fixed detours. This allows for matching incorporating spatial and financial considerations, promising flexible and rational matches in carpool systems. Simulation tests are used to validate the effectiveness of the analytical models. Results also offer insights into how various factors impact the system's performance.