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.
