40,404 research outputs found
Euclidean versus hyperbolic congestion in idealized versus experimental networks
This paper proposes a mathematical justification of the phenomenon of extreme
congestion at a very limited number of nodes in very large networks. It is
argued that this phenomenon occurs as a combination of the negative curvature
property of the network together with minimum length routing. More
specifically, it is shown that, in a large n-dimensional hyperbolic ball B of
radius R viewed as a roughly similar model of a Gromov hyperbolic network, the
proportion of traffic paths transiting through a small ball near the center is
independent of the radius R whereas, in a Euclidean ball, the same proportion
scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at
the center of the hyperbolic ball scales as the square of the volume, whereas
the same traffic load scales as the volume to the power (n+1)/n in the
Euclidean ball. This provides a theoretical justification of the experimental
exponent discrepancy observed by Narayan and Saniee between traffic loads in
Gromov-hyperbolic networks from the Rocketfuel data base and synthetic
Euclidean lattice networks. It is further conjectured that for networks that do
not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of
maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure
Dynamic Vehicle Routing for Data Gathering in Wireless Networks
We consider a dynamic vehicle routing problem in wireless networks where
messages arriving randomly in time and space are collected by a mobile receiver
(vehicle or a collector). The collector is responsible for receiving these
messages via wireless communication by dynamically adjusting its position in
the network. Our goal is to utilize a combination of wireless transmission and
controlled mobility to improve the delay performance in such networks. We show
that the necessary and sufficient condition for the stability of such a system
(in the bounded average number of messages sense) is given by {\rho}<1 where
{\rho} is the average system load. We derive fundamental lower bounds for the
delay in the system and develop policies that are stable for all loads {\rho}<1
and that have asymptotically optimal delay scaling. Furthermore, we extend our
analysis to the case of multiple collectors in the network. We show that the
combination of mobility and wireless transmission results in a delay scaling of
{\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of
{\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding
system where the collector visits each message location.Comment: 19 pages, 7 figure
Dynamic Multi-Vehicle Routing with Multiple Classes of Demands
In this paper we study a dynamic vehicle routing problem in which there are
multiple vehicles and multiple classes of demands. Demands of each class arrive
in the environment randomly over time and require a random amount of on-site
service that is characteristic of the class. To service a demand, one of the
vehicles must travel to the demand location and remain there for the required
on-site service time. The quality of service provided to each class is given by
the expected delay between the arrival of a demand in the class, and that
demand's service completion. The goal is to design a routing policy for the
service vehicles which minimizes a convex combination of the delays for each
class. First, we provide a lower bound on the achievable values of the convex
combination of delays. Then, we propose a novel routing policy and analyze its
performance under heavy load conditions (i.e., when the fraction of time the
service vehicles spend performing on-site service approaches one). The policy
performs within a constant factor of the lower bound (and thus the optimal),
where the constant depends only on the number of classes, and is independent of
the number of vehicles, the arrival rates of demands, the on-site service
times, and the convex combination coefficients.Comment: Extended version of paper presented in American Control Conference
200
“Almost” subsidy-free spatial pricing in a multi-dimensional setting
Consider a population of citizens uniformly spread over the entire plane, that faces a problem of locating public facilities to be used by its members. The cost of every facility is financed by its users, who also face an idiosyncratic private access cost to the facility. We assume that the facilities' cost is independent of location and access costs are linear with respect to the Euclidean distance. We show that an external intervention that covers 0.19% of the facility cost is sufficient to guarantee secession-proofness or no cross-subsidization, where no group of individuals is charged more than its stand alone cost incurred if it had acted on its own. Moreover, we demonstrate that in this case the Rawlsian access pricing is the only secession-proof allocation.secession-proofness, optimal jurisdictions, Rawlsian allocation, hexagonal partition, cross-subsidization
Localization for Anchoritic Sensor Networks
We introduce a class of anchoritic sensor networks, where communications
between sensor nodes is undesirable or infeasible, e.g., due to harsh
environment, energy constraints, or security considerations
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