An improved partition merging algorithm to account for maximum waiting time in carpools

Abstract

Nowadays, traffic problems have become an issue that needs to be solved in every populous country. Especially in large urban areas, people face traffic problems such as road congestion and high exhaust emissions due to the rapid growth of vehicles on the roads. In this context, several researchers have shown that carpooling, i.e., vehicle sharing, is an attractive solution to effectively address the traffic stress that arises when a large number of cars are traveling at the same time. The goal of our carpool scheduling problem is to reduce the number of carpools required by all users while ensuring their waiting time. Previous studies on similar topics have introduced additional static capacity constraints to simplify the problem, which limits the number of carpooling users in a vehicle. However, this does not match most real-world situations. This is because when a passenger gets off the vehicle, their seat should also be vacated for the next user. In this paper, we eliminate the static capacity constraint to enable timely user turnover during the carpooling journey. A greedy algorithm based on iterative matching and summation is proposed. In addition, we introduce the concept of user waiting time, i.e., the amount of time a user is willing to wait to be picked up. We apply our algorithm to synthetic and real-world data sets, and our experimental results show that our algorithm has better performance than existing methods.