547 research outputs found
Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective
In this paper we present and analyze a queueing-theoretical model for
autonomous mobility-on-demand (MOD) systems where robotic, self-driving
vehicles transport customers within an urban environment and rebalance
themselves to ensure acceptable quality of service throughout the entire
network. We cast an autonomous MOD system within a closed Jackson network model
with passenger loss. It is shown that an optimal rebalancing algorithm
minimizing the number of (autonomously) rebalancing vehicles and keeping
vehicles availabilities balanced throughout the network can be found by solving
a linear program. The theoretical insights are used to design a robust,
real-time rebalancing algorithm, which is applied to a case study of New York
City. The case study shows that the current taxi demand in Manhattan can be met
with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi
fleet). Finally, we extend our queueing-theoretical setup to include congestion
effects, and we study the impact of autonomously rebalancing vehicles on
overall congestion. Collectively, this paper provides a rigorous approach to
the problem of system-wide coordination of autonomously driving vehicles, and
provides one of the first characterizations of the sustainability benefits of
robotic transportation networks.Comment: 10 pages, To appear at RSS 201
Asymptotically Optimal Algorithms for Pickup and Delivery Problems with Application to Large-Scale Transportation Systems
The Stacker Crane Problem 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+\eps}), where is the number of pickup/delivery pairs
and \eps 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.Comment: 27 pages, plus Appendix, 7 figures, extended version of paper being
submitted to IEEE Transactions of Automatic Contro
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