In this paper, we provide a spatial Poisson point pattern model of traffic in a code division multiple access (CDMA) wireless network. We show how the theory of Poisson processes can be applied to provide statistical information about interference levels in the network. In particular, we calculate approximations and a bound on the outage probability at a designated cell site in the network, utilizing high-order cumulants, which have very simple analytical forms and can easily be computed once the mean measure of the spatial Poisson point pattern is known. We consider a Poisson-Gaussian approximation and an Edgeworth approximation in which the Gaussian distribution is twisted to satisfy the required cumulants, and we provide a Chernoff bound on performance that also utilizes the cumulant information. We show that the theory can be applied to nonstationary, time nonhomogeneous systems. We provide a particular example of a M/M/∞ spatial queueing model of a CDMA wireless network.