Wireless queues in Poisson interference fields: the continuum between zero and infinite mobility

This paper considers the time evolution of a queue that is placed in a Poisson point process of moving wireless interferers. The queue evolves according to an external arrival process and a time-varying service process that is a function of the SINR that it experiences. Static configurations of interferers result in infinite queue workload with positive probability. In contrast, a velocity-independent stability condition for the queue is established in the case where interferers possess any non-zero mobility that results in displacements that are both independent across interferers and with a distribution which is invariant to interferer positions. The proof leverages mixing properties of point processes under non-zero mobility. The effects of increasing mobility on statistical averages of queueing metrics are studied, and convex ordering tools are used to establish that faster moving interferers result in a queue workload that is dominated in the increasing convex sense by a queue workload resulting from slower interferers. As a corollary, it is shown that mean queue workload and mean delay improve as network mobility increases. It is shown that there is positive correlation between SINR level-crossing events at finitely separated time points. The notion of correlation between interference over time is made precise via an explicit correlation function. System behaviour is empirically analyzed using discrete-event simulation and the impact of the mobility model on system level performance is evaluated.