3.25 Spatial Poisson
process Suppose that
response units are distributed throughout the city as a homogeneous
spatial Poisson
process, with an average of y response units per square
mile. Assume that the
travel time between
(x_{1},
y_{1})
and (X_{2},
Y_{2})
is
where v_{x}.
and v_{y}
are travel speeds in the directions of the abscissa and ordinate,
respectively.
Assume that an incident occurs somewhere in the
city, independent of
the locations of the response units.
a. Find the pdf for T_{k},
where
T_{k} = travel time to
the kth nearest response
unit, kth = 1, 2, . . .
Hint: The set of points that are a given travel time
from the incident is
given by a diamond centered at the incident.
b. Find
E[T_{k}] and . and note
their functional dependence on k.
