Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and 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 largescale 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 (i) scales to large numbers of passengers and trips and (ii) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff 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 ~3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 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 multivehicle, multitask assignment problems.@en

Vehicle sharing system consists of a fleet of vehicles (usually bikes or cars) that can be rented at one station and returned at another station. We study how to achieve guaranteed service availability in such systems. Specifically, we are interested in determining a) the fleet size and initial allocation of vehicles to stations and b) the minimum capacity of each station needed to guarantee that a) every customer will find an available vehicle at the origin station and b) the customer will find a free parking spot at the destination station. We model the evolution of number of vehicles at each station as a stochastic process and prove that the relevant probabilities in the system can be approximated from above using a computationally-tractable decoupled model. This property can be exploited to efficiently determine the size of fleet, initial distribution of vehicles to stations, and station capacities that are sufficient to achieve the desired service level. The applicability of the method is demonstrated by computing the initial vehicle stock and the capacity of each station that would be needed to avoid service failures in Boston's bike sharing system 'The Hubway'. Our simulation shows that the proposed method is able to find more efficient design parameters than the naive approach and consequently it can achieve the equivalent quality-of-service level with half of the vehicle fleet and half of the parking capacity.@en