Shared Rate Process for Mobile Users in Poisson Networks and Applications

Abstract

This paper focuses on the modeling and analysis of the temporal performance variation experienced by a mobile user in a wireless network and its impact on system-level design. We consider a simple stochastic geometry model: the infrastructure nodes are Poisson distributed while the user’s motion is the simplest possible, i.e., constant velocity on a straight line. We first characterize variations in the signal-to-noise ratio (SNR) process and associated downlink Shannon rate, resulting from variations in the infrastructure geometry seen by the mobile. Specifically, by making a connection between stochastic geometry and queuing theory, the level crossings of the SNR process are shown to form an alternating renewal process whose distribution is completely characterized. For large/small SNR levels, and associated rare events, we further derive simple distributional (exponential) models. We then characterize the second major contributor to such variations, namely, changes in the number of other users sharing the infrastructure. Combining these two phenomena, we study what are the dominant factors (infrastructure geometry or sharing number) when a mobile experiences a very high/low shared rate. These results are then used to evaluate and optimize the system-level quality of experience of the mobile users sharing such a wireless infrastructure, including mobile devices streaming video which proactively buffer content to prevent rebuffering and mobiles which are downloading large files. Finally, we use simulation to assess the fidelity of this model and its robustness to factors which are presently not taken into account.