3.25 Spatial Poisson
process Suppose that
response units are distributed throughout the city as a homogeneous
process, with an average of y response units per square
mile. Assume that the
travel time between
are travel speeds in the directions of the abscissa and ordinate,
Assume that an incident occurs somewhere in the
city, independent of
the locations of the response units.
a. Find the pdf for Tk,
Tk = 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.
E[Tk] and . and note
their functional dependence on k.