  The traffic in wireless networks has become diverse and fluctuating both
spatially and temporally due to the emergence of new wireless applications and
the complexity of scenarios. The purpose of this paper is to quantitatively
analyze the impact of the wireless traffic, which fluctuates both spatially and
temporally, on the performance of the wireless networks. Specially, we propose
to combine the tools from stochastic geometry and queueing theory to model the
spatial and temporal fluctuation of traffic, which to our best knowledge has
seldom been evaluated analytically. We derive the spatial and temporal
statistics, the total arrival rate, the stability of queues and the delay of
users by considering two different spatial properties of traffic, i.e., the
uniformly and non-uniformly distributed cases. The numerical results indicate
that although the fluctuation of traffic (reflected by the variance of total
arrival rate) when the users are clustered is much fiercer than that when the
users are uniformly distributed, the unstable probability is smaller. Our work
provides a useful reference for the design of wireless networks when the
complex spatio-temporal fluctuation of the traffic is considered.
