18,678 research outputs found
Optimal routing in double loop networks
AbstractIn this paper, we study the problem of finding the shortest path in circulant graphs with an arbitrary number of jumps. We provide algorithms specifically tailored for weighted undirected and directed circulant graphs with two jumps which compute the shortest path. Our method only requires O(logN) arithmetic operations and the total bit complexity is O(log2NloglogNlogloglogN), where N is the number of the graph’s vertices. This elementary and efficient shortest path algorithm has been derived from the Closest Vector Problem (CVP) of lattices in dimension two and with an ℓ1 norm
Cayley digraphs of finite abelian groups and monomial ideals
In the study of double-loop computer networks, the diagrams known as L-shapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece of information, we can compute the graph’s diameter and average minimum distance. That monomial ideal is the initial ideal of a certain lattice with respect to a graded monomial ordering. This result permits the use of Gr¨obner bases for computing the ideal and finding an optimal routing. Finally, we present a family of Cayley digraphs parametrized by their diameter d, all of them associated to irreducible monomial ideals
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
Quantifying the benefits of vehicle pooling with shareability networks
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 towards 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.Comment: Main text: 6 pages, 3 figures, SI: 24 page
Relieving the Wireless Infrastructure: When Opportunistic Networks Meet Guaranteed Delays
Major wireless operators are nowadays facing network capacity issues in
striving to meet the growing demands of mobile users. At the same time,
3G-enabled devices increasingly benefit from ad hoc radio connectivity (e.g.,
Wi-Fi). In this context of hybrid connectivity, we propose Push-and-track, a
content dissemination framework that harnesses ad hoc communication
opportunities to minimize the load on the wireless infrastructure while
guaranteeing tight delivery delays. It achieves this through a control loop
that collects user-sent acknowledgements to determine if new copies need to be
reinjected into the network through the 3G interface. Push-and-Track includes
multiple strategies to determine how many copies of the content should be
injected, when, and to whom. The short delay-tolerance of common content, such
as news or road traffic updates, make them suitable for such a system. Based on
a realistic large-scale vehicular dataset from the city of Bologna composed of
more than 10,000 vehicles, we demonstrate that Push-and-Track consistently
meets its delivery objectives while reducing the use of the 3G network by over
90%.Comment: Accepted at IEEE WoWMoM 2011 conferenc
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