According to equation (1), the most energy-e?±cient
solution would require the average inter-epoch interval Tperiod to become very
large:
L
Tperiod
= Rdata ) (2)
lim
Rdata!0
(Tperiod) = lim
Rdata!0
(
L
Rdata
) = lim
Rdata!0
(
Lmin
Rdata
) = 1. (3)
A very large value of Tperiod essentially means that a node does not attempt
to communicate for a very long time and keeps its radio o?®. However, in most
practical applications there is a bound on how long a node can sleep at a time.
Another node should be able to contact it, for example to forward some critical
data within a particular maximum time span. This time span is essentially a
delay bound for data to move between nodes, and is directly related to the
responsiveness of the network. In the forest fire detection example, an end-toend
delay bound limits the maximum time between the detection of an event
and when this information has been forwarded to the user. Delay bounds of
individual node-pairs can be related to such an end-to-end delay bound.
Wakeup deals with this network state in which the tra?±c is so sporadic
that the node would sleep for prohibitively long time periods if only tra?±c
activity would be taken into account. Instead, a provision has to be made that
a node can be contacted within a certain time period, called the wakeup delay
Dwakeup, which is bounded by a certain maximum value:
Dwakeup ?· Dmax. (4)
198
Chapter 8 Wakeup Strategies in Wireless Sensor Networks
This maximum wakeup delay Dmax could be di?®erent for each node, and
might be optimized based on an overall network lifetime maximization [35].
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