Optimal Sleep-Wake Scheduling for Quickest Intrusion Detection Using Wireless Sensor Networks

We consider the problem of
quickest

detection

of

an

intrusion
using a sensor network, keeping only a minimal number of sensors
active
. By using a minimal number of sensor devices, we ensure that the energy expenditure for
sensin
g,
computation
and
communication
is minimized (and the lifetime of the network is maximized). We model the intrusion detection (or change detection) problem as a
Markov

decision

process
(MDP). Based on the theory of MDP, we develop the following closed loop
sleep/wake
scheduling algorithms: (1) optimal control of M
_k+1
, the number of sensors in the wake state in time slot k + 1, (2) optimal control of q
_k+1
, the probability of a sensor in the wake state in time slot k + 1, and an open loop
sleep/wake
scheduling algorithm which (3) computes q, the optimal probability of a sensor in the wake state (which does not vary with time), based on the sensor observations obtained until time slot k. Our results show that an optimum closed loop control on M
_k+1
significantly decreases the cost compared to keeping any number of sensors active all the time. Also, among the three algorithms described, we observe that the total cost is minimum for the optimum control on M
k+1
and is maximum for the optimum open loop control on q.