We consider a small extent sensor network for event detection, in which nodes
take samples periodically and then contend over a {\em random access network}
to transmit their measurement packets to the fusion center. We consider two
procedures at the fusion center to process the measurements. The Bayesian
setting is assumed; i.e., the fusion center has a prior distribution on the
change time. In the first procedure, the decision algorithm at the fusion
center is \emph{network-oblivious} and makes a decision only when a complete
vector of measurements taken at a sampling instant is available. In the second
procedure, the decision algorithm at the fusion center is \emph{network-aware}
and processes measurements as they arrive, but in a time causal order. In this
case, the decision statistic depends on the network delays as well, whereas in
the network-oblivious case, the decision statistic does not depend on the
network delays. This yields a Bayesian change detection problem with a tradeoff
between the random network delay and the decision delay; a higher sampling rate
reduces the decision delay but increases the random access delay. Under
periodic sampling, in the network--oblivious case, the structure of the optimal
stopping rule is the same as that without the network, and the optimal change
detection delay decouples into the network delay and the optimal decision delay
without the network. In the network--aware case, the optimal stopping problem
is analysed as a partially observable Markov decision process, in which the
states of the queues and delays in the network need to be maintained. A
sufficient statistic for decision is found to be the network-state and the
posterior probability of change having occurred given the measurements received
and the state of the network. The optimal regimes are studied using simulation.Comment: To appear in ACM Transactions on Sensor Networks. A part of this work
was presented in IEEE SECON 2006, and Allerton 201
