519 research outputs found
Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model
We compute the expected number of cars that have at least one two-hop path to
a fixed roadside unit in a one-dimensional vehicular ad hoc network in which
other cars can be used as relays to reach a roadside unit when they do not have
a reliable direct link. The pairwise channels between cars experience Rayleigh
fading in the random connection model, and so exist, with probability function
of the mutual distance between the cars, or between the cars and the roadside
unit. We derive exact equivalents for this expected number of cars when the car
density tends to zero and to infinity, and determine its behaviour using
an infinite oscillating power series in , which is accurate for all
regimes. We also corroborate those findings to a realistic situation, using
snapshots of actual traffic data. Finally, a normal approximation is discussed
for the probability mass function of the number of cars with a two-hop
connection to the origin. The probability mass function appears to be well
fitted by a Gaussian approximation with mean equal to the expected number of
cars with two hops to the origin.Comment: 21 pages, 7 figure
Shortest Path Distance in Manhattan Poisson Line Cox Process
While the Euclidean distance characteristics of the Poisson line Cox process
(PLCP) have been investigated in the literature, the analytical
characterization of the path distances is still an open problem. In this paper,
we solve this problem for the stationary Manhattan Poisson line Cox process
(MPLCP), which is a variant of the PLCP. Specifically, we derive the exact
cumulative distribution function (CDF) for the length of the shortest path to
the nearest point of the MPLCP in the sense of path distance measured from two
reference points: (i) the typical intersection of the Manhattan Poisson line
process (MPLP), and (ii) the typical point of the MPLCP. We also discuss the
application of these results in infrastructure planning, wireless
communication, and transportation networks
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