The culture of sharing instead of ownership is sharply increasing in individuals behaviors. Particularly in transportation, concepts of sharing a ride in either carpooling or ridesharing have been recently adopted. An efficient optimization approach to match passengers in real-time is the core of any ridesharing system. In this paper, we model ridesharing as an online matching problem on general graphs such that passengers do not drive private cars and use shared taxis. We propose an optimization algorithm to solve it. The outlined algorithm calculates the optimal waiting time when a passenger arrives. This leads to a matching with minimal overall overheads while maximizing the number of partnerships. To evaluate the behavior of our algorithm, we used NYC taxi real-life data set. Results represent a substantial reduction in overall overheads.
Some people may opt for the ride sharing merely for cost savings. Individuals not owning private cars have limited access to public transportation options can be other targets of ridesharing. People are likely to participate in ridesharing arrangements if they pay less fare in comparison with taking a taxi alone. Also, they have to accept a deviation from their shortest path too. There are different methods to share the travel-expenses among entities. The most straightforward intuitive way is to devide the costs evenly between passengers @cite_3 . This approach would not be fair as the portion of the shared path could be different. To overcome this, passengers may divide the related costs proportional to the distances they ride autonomously and the part they shared the car.
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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 societ al 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 ( 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. We proposed and developed a taxi-sharing system that accepts taxi passengers’ real-time ride requests sent from smartphones and schedules proper taxis to pick up them via ridesharing, subject to time, capacity, and monetary constraints. The monetary constraints provide incentives for both passengers and taxi drivers: passengers will not pay more compared with no ridesharing and get compensated if their travel time is lengthened due to ridesharing; taxi drivers will make money for all the detour distance due to ridesharing. While such a system is of significant social and environmental benefit, e.g., saving energy consumption and satisfying people's commute, real-time taxi-sharing has not been well studied yet. To this end, we devise a mobile-cloud architecture based taxi-sharing system. Taxi riders and taxi drivers use the taxi-sharing service provided by the system via a smart phone App. The Cloud first finds candidate taxis quickly for a taxi ride request using a taxi searching algorithm supported by a spatio-temporal index. A scheduling process is then performed in the cloud to select a taxi that satisfies the request with minimum increase in travel distance. We built an experimental platform using the GPS trajectories generated by over 33,000 taxis over a period of three months. A ride request generator is developed (available at http: cs.uic.edu ∼sma ridesharing) in terms of the stochastic process modelling real ride requests learned from the data set. Tested on this platform with extensive experiments, our proposed system demonstrated its efficiency, effectiveness and scalability. For example, when the ratio of the number of ride requests to the number of taxis is 6, our proposed system serves three times as many taxi riders as that when no ridesharing is performed while saving 11 percent in total travel distance and 7 percent taxi fare per rider. Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network, which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40 or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting toward a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low. Optimizing shared vehicle systems (bike-sharing car-sharing ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of complex network externalities. In particular, changes in the demand supply at any location (via dynamic pricing, rebalancing of empty vehicles, etc.) affect future supply throughout the system within short timescales. Such externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze and design shared vehicle systems. However, using such models to design pricing control policies is computationally difficult since the resulting optimization problems are high-dimensional and non-convex. To this end, we develop a general approximation framework for designing pricing policies in shared vehicle systems, based on a novel convex relaxation which we term elevated flow relaxation. Our approach provides the first efficient algorithms with rigorous approximation guarantees for a wide range of objective functions (throughput, revenue, welfare). For any shared vehicle system with @math stations and m vehicles, our framework provides a pricing policy with an approximation ratio of 1+(n-1) m. This guarantee is particularly meaningful when m n, the average number of vehicles per station is large, as is often the case in practice. Further, the simplicity of our approach allows us to extend it to more complex settings. Apart from pricing, shared vehicle systems enable other control levers for modulating demand and supply, e.g. rebalancing empty vehicles, redirecting riders to nearby vehicles, etc. Our approach yields efficient algorithms with the same approximation guarantees for all these problems, and in the process, obtains as special cases several existing heuristics and asymptotic guarantees. We also extend our approach to obtain bi-criterion guarantees in multi-objective settings; we illustrate this with the example of Ramsey pricing. From a technical perspective, our work develops a new approach for obtaining control policies with approximation guarantees in steady-state Markovian models. Our approach can be distilled into the following three-step program: (i) construct an upper bound via a relaxation to the original problem that encodes essential conservation laws of the system, (ii) identify a family of control policies inducing known steady-state distributions that achieve the value of the relaxed solution in an appropriate scaling limit (in our case, state-independent policies in the limit m++), and (iii) characterize the performance loss between the finite system (i.e. fixed m) and the scaling limit. This technique may be of independent interest for other settings.