Ride sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride sharing. Recently, a large-scale study highlighted some of the benefits of car pooling, but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride sharing that (1) scales to large numbers of passengers and trips, and (2) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it via a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. For the first time, we quantify experimentally the trade-off between fleet size, capacity, waiting time, travel delay, and operational costs for low to medium capacity vehicles, such as taxis and van shuttles. The algorithm is validated with approximately 3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride sharing with rider capacity of up to ten simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multi-vehicle, multi-task assignment problems.
A large-scale mathematical and empirical study on the number of cars and the optimality of waiting times was recently analyzed by Alonso-Mora et al. REF .
On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Engineering Medicine Computer Science