  In this paper, we analyze the performance of cellular networks and study the
optimal base station (BS) density to reduce the network power consumption. In
contrast to previous works with similar purpose, we consider Poisson traffic
for users' traffic model. In such situation, each BS can be viewed as M/G/1
queuing model. Based on theory of stochastic geometry, we analyze users'
signal-to-interference-plus-noise-ratio (SINR) and obtain the average
transmission time of each packet. While most of the previous works on SINR
analysis in academia considered full buffer traffic, our analysis provides a
basic framework to estimate the performance of cellular networks with burst
traffic. We find that the users' SINR depends on the average transmission
probability of BSs, which is defined by a nonlinear equation. As it is
difficult to obtain the closed-form solution, we solve this nonlinear equation
by bisection method. Besides, we formulate the optimization problem to minimize
the area power consumption. An iteration algorithm is proposed to derive the
local optimal BS density, and the numerical result shows that the proposed
algorithm can converge to the global optimal BS density. At the end, the impact
of BS density on users' SINR and average packet delay will be discussed.
