The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of personal transportation in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer's location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.

Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world logistical operations. A widely-encountered type of PDP is the Stacker Crane Problem (SCP), where each commodity/customer is associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in consecutive order. The SCP is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. The objective of this paper is threefold. First, by embedding the problem within a stochastic framework, we present a novel algorithm for the SCP that: (i) is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; and (ii) has computational complexity O(n 2+ε ), where n is the number of pickup/delivery pairs and ε is an arbitrarily small positive constant. Second, we asymptotically characterize the length of the optimal SCP tour. Finally, we study a dynamic version of the SCP, whereby pickup and delivery requests arrive according to a Poisson process, and which serves as a model for large-scale demand-responsive transport (DRT)systems. For such a dynamic counterpart of the SCP, we derive a necessary and sufficient condition for the existence of stable vehicle routing policies, which depends only on the workspace geometry, the stochastic distributions of pickup and delivery points, the arrival rate of requests, and the number of vehicles. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional spatially-distributed queueing systems.

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Transportation-On-Demand (TOD) systems, where users generate requests for transportation from a pickup point to a delivery point, are already very popular and are expected to increase in usage dramatically as the inconvenience of privately-owned cars in metropolitan areas becomes excessive. Routing service vehicles through customers is usually accomplished with heuristic algorithms. In this paper we study TOD systems in a formal setting that allows us to characterize fundamental performance limits and devise dynamic routing policies with provable performance guarantees. Specifically, we study TOD systems in the form of a unit-capacity, multiple-vehicle dynamic pickup and delivery problem, whereby pickup requests arrive according to a Poisson process and are randomly located according to a general probability density. Corresponding delivery locations are also randomly distributed according to a general probability density, and a number of unit-capacity vehicles must transport demands from their pickup locations to their delivery locations. We derive insightful fundamental bounds on the steady-state waiting times for the demands, and we devise constant-factor optimal dynamic routing policies. Simulation results are presented and discussed.

Abstract-One of the most common combinatorial problems in logistics and transportation applications is the Stacker Crane problem (SCP), where commodities or customers are associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in consecutive order. While vastly many SCPs encountered in practice are embedded in road or road-like networks, very few studies explicitly consider such specific structure. In this paper, first we formulate an environment model that captures the essential features of a "small-neighborhood" road network, including a basic set of road rules. Then, we formulate a stochastic version of the SCP on such road network model, where pickup/delivery pairs are random points on network's edges and nodes. Finally, we provide an algorithm for such problem which: (i) is asymptotically optimal, i.e., it produces a solution approaching the optimal one as the number of pickups/deliveries goes to infinity, almost surely; and (ii) is efficient in the sense that it can be computed in time polynomial in n, where n is the number of pickup/delivery pairs. Simulation results show that with a number of pickup/delivery pairs as low as 50 the proposed algorithm delivers a solution whose cost is consistently within 10% of that of an optimal solution.

Abstract-Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world operations. One particular PDP is the Stacker Crane problem (SCP), where each commodity/customer is associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in consecutive order. The SCP is a route optimization problem behind several transportation systems, e.g., Transportation-On-Demand (TOD) systems. The SCP is NP-Hard and the best know approximation algorithm only provides a 9/5 approximation ratio. We present an algorithm for the stochastic SCP which: (i) is asymptotically optimal, i.e., it produces a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; and (ii) has computational complexity O(n 2+ ), where n is the number of pickup/delivery pairs and is an arbitrarily small positive constant. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations.

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Abstract-Demand-responsive transport (DRT) systems, where users generate requests for transportation from a pickup point to a delivery point, are expected to increase in usage dramatically as the inconvenience of privately-owned cars in metropolitan areas becomes excessive. However, despite the increasing role of DRT systems, there are very few rigorous results characterizing achievable performance (in terms, e.g., of stability conditions). In this paper, our aim is to bridge this gap for a rather general model of DRT systems, which takes the form of a generalized Dynamic Pickup and Delivery Problem. The key strategy is to develop analytical bounds for the optimal cost of the Euclidean Stacker Crane Problem (ESCP), which represents a general static model for DRT systems. By leveraging such bounds, we characterize a necessary and sufficient condition for the stability of DRT systems; the condition depends only on the workspace geometry, the stochastic distributions of pickup and delivery points, customers' arrival rate, and the number of vehicles. Our results exhibit some surprising features that are absent in traditional spatiallydistributed queueing systems.