In this paper we use the Erlang theory to quantitatively analyse the trade offs between energy conservation and quality of service in an ad-hoc wireless sensor network. Nodes can be either sleeping, where no transmission or reception can occur, or awake where traffic is processed. Increasing the proportion of time spent in the sleeping state will decrease throughput and increase packet loss and delivery delay. However there is a complex relationship between sleeping time and energy consumption. Increasing the sleeping time does not always lead to an increase in the energy saved. We identify the energy consumption profile for various levels of sensor network activity and derive an optimum energy saving curve that provides a basis for the design of extended-life ad hoc wireless sensor networks.