This paper investigates wireless sensor network spatial resolution as a measurement of quality of service (QoS). We seek to control the network in such a way that sensors participate equally in the network while conserving energy and maintaining the desired spatial resolution. This work provides an analytic solution of a sensor network QoS control strategy demonstrated recently through simulation. General conclusions about the selection of parameters to control network performance, specifically the mean and variance of the QoS are presented. We show that there is a tradeoff between the static and dynamic QoS performance, as well as energy usage and conclude by presenting the several potential applications that are enabled by ability to control both the mean and variance of network QoS.