The development of architectures and strategies that allow for rapid and cost-effective deployment of large scale geographically distributed sensor based systems that organize themselves in an ad hoc fashion in order to improve the monitoring and detection capabilities, is becoming more a requirement rather than a desire. In this paper, we first provide a model that characterizes the corresponding sensor connectivity distribution for a sensor networking system, and based on this model we gain some insight about the trade off among the node connectivity, power consumption, data rate, etc. The impact of node connectivity on system reliability is discussed. Furthermore in order to reduce the sensor power consumption we analyze the relationship between periodical sleeping strategies and the achieved power conservation. Several results and tradeoffs among various sleeping strategies, transmission scenarios and power gains, for given connectivity requirements, are also presented and evaluated.