Effect of Spatial and Temporal Traffic Statistics on the Performance of Wireless Networks

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.