42,324 research outputs found
Moving Walkways, Escalators, and Elevators
We study a simple geometric model of transportation facility that consists of
two points between which the travel speed is high. This elementary definition
can model shuttle services, tunnels, bridges, teleportation devices, escalators
or moving walkways. The travel time between a pair of points is defined as a
time distance, in such a way that a customer uses the transportation facility
only if it is helpful.
We give algorithms for finding the optimal location of such a transportation
facility, where optimality is defined with respect to the maximum travel time
between two points in a given set.Comment: 16 pages. Presented at XII Encuentros de Geometria Computacional,
Valladolid, Spai
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
We demonstrate applications of algebraic techniques that optimize and certify
polynomial inequalities to problems of interest in the operations research and
transportation engineering communities. Three problems are considered: (i)
wireless coverage of targeted geographical regions with guaranteed signal
quality and minimum transmission power, (ii) computing real-time certificates
of collision avoidance for a simple model of an unmanned vehicle (UV)
navigating through a cluttered environment, and (iii) designing a nonlinear
hovering controller for a quadrotor UV, which has recently been used for load
transportation. On our smaller-scale applications, we apply the sum of squares
(SOS) relaxation and solve the underlying problems with semidefinite
programming. On the larger-scale or real-time applications, we use our recently
introduced "SDSOS Optimization" techniques which result in second order cone
programs. To the best of our knowledge, this is the first study of real-time
applications of sum of squares techniques in optimization and control. No
knowledge in dynamics and control is assumed from the reader
Inter-plane satellite matching in dense LEO constellations
Dense constellations of Low Earth Orbit (LEO) small satellites are envisioned
to make extensive use of the inter-satellite link (ISL). Within the same
orbital plane, the inter-satellite distances are preserved and the links are
rather stable. In contrast, the relative motion between planes makes the
inter-plane ISL challenging. In a dense set-up, each spacecraft has several
satellites in its coverage volume, but the time duration of each of these links
is small and the maximum number of active connections is limited by the
hardware. We analyze the matching problem of connecting satellites using the
inter-plane ISL for unicast transmissions. We present and evaluate the
performance of two solutions to the matching problem with any number of orbital
planes and up to two transceivers: a heuristic solution with the aim of
minimizing the total cost; and a Markovian solution to maintain the on-going
connections as long as possible. The Markovian algorithm reduces the time
needed to solve the matching up to 1000x and 10x with respect to the optimal
solution and to the heuristic solution, respectively, without compromising the
total cost. Our model includes power adaptation and optimizes the network
energy consumption as the exemplary cost in the evaluations, but any other
QoS-oriented KPI can be used instead
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