Much work on wireless sensor networks deals with or considers the hot
spot problem, i.e., the problem that the sensor nodes closest to the
base station are critical for the lifetime of the sensor network
because these nodes need to relay more packet than nodes further away
from the base station. Since it is often assumed that sensor nodes
will become inexpensive, a simple solution to the hot spot problem is
to place additional sensor nodes around the base stations. Using a
simple mathematical model we discuss the possible performance gains of
adding these supplementary nodes. Our results show that for certain
networks only a limited number of additional nodes are required to
fourfold network lifetime. We also show that the possible gain depends
heavily on the fraction of nodes already present in the vicinity of
the base station