  We consider a hybrid wireless sensor network with regular and transmit-only
sensors. The transmit-only sensors do not have receiver circuit, hence are
cheaper and less energy consuming, but their transmissions cannot be
coordinated. Regular sensors, also called cluster-heads, are responsible for
receiving information from transmit-only sensors and forwarding it to sinks.
The main goal of such a hybrid network is to reduce the cost of deployment
while achieving some performance constraints (minimum coverage, sensing rate,
etc). In this paper we are interested in the communication between
transmit-only sensors and cluster-heads. We develop a detailed analytical model
of the physical and MAC layer using tools from queuing theory and stochastic
geometry. (The MAC model, that we call Erlang's loss model with interference,
might be of independent interest as adequate for any non-slotted; i.e.,
unsynchronized, wireless communication channel.) We give an explicit formula
for the frequency of successful packet reception by a cluster-head, given
sensors' locations. We further define packet admission policies at a
cluster-head, and we calculate the optimal policies for different performance
criteria. Finally we show that the proposed hybrid network, using the optimal
policies, can achieve substantial cost savings as compared to conventional
architectures.
