One class of applications envisaged for the IEEE 802.15.4 LR-WPAN (low data rate—wireless personal area network) standard is wireless sensor networks for monitoring and control applications. In this paper we provide an analytical performance model for a network in which the sensors are at the tips of a star topology, and the sensors need to transmit their measurements to the hub node so that certain objectives for packet delay and packet discard are met. We first carry out a saturation throughput analysis of the system; i.e., it is assumed that each sensor has an infinite backlog of packets and the throughput of the system is sought. After a careful analysis of the CSMA/CA MAC that is employed in the standard, and after making a certain decoupling approximation, we identify an embedded Markov renewal process, whose analysis yields a fixed point equation, from whose solution the saturation throughput can be calculated. We validate our model against ns2 simulations (using an IEEE 802.15.4 module developed by Zheng ). We find that with the default back-off parameters the saturation throughput decreases sharply with increasing number of nodes. We use our analytical model to study the problem and we propose alternative back-off parameters that prevent the drop in throughput. We then show how the saturation analysis can be used to obtain an analytical model for the finite arrival rate case. This finite load model captures very well the qualitative behavior of the system, and also provides a good approximation to the packet discard probability, and the throughput. For the default parameters, the finite load throughput is found to first increase and then decrease with increasing load. We find that for typical performance objectives (mean delay and acket discard) the packet discard probability would constrain the system capacity. Finally, we show how to derive a node lifetime analysis using various rates and probabilities obtained from our performance analysis model.