Cost Bounds for Pickup and Delivery Problems with Application to Large-Scale Transportation Systems
Author(s)Treleaven, Kyle Ballantyne; Pavone, Marco; Frazzoli, Emilio
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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 spatially-distributed queueing systems.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the 2012 American Control Conference (ACC)
American Automatic Control Council
Treleaven, Kyle Ballantyne, Marco Pavone, and Emilio Frazzoli. "Cost bounds for Pickup and Delivery Problems with application to large-scale transportation systems." In 2012 American Control Conference, Fairmont Queen Elizabeth, Montréal, Canada, June 27-June 29, 2012. pp. 2120 - 2127.
Author's final manuscript
INSPEC Accession Number: 13036296