On Shared Rate Time Series for Mobile Users in Poisson Networks

Pranav Madadi, François Baccelli, Gustavo de Veciana

This paper focuses on modeling and analysis of the temporal performance variations 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 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 queueing theory the level crossings of the SNR process are shown to form an alternating renewal process whose distribution can be completely characterized. For large or small SNR levels, and associated rare events, we further derive simple distributional (exponential) models. We then characterize the second major contributor to variation, associated with changes in the number of other users sharing infrastructure. Combining these two effects, we study what are the dominant factors (infrastructure geometry or sharing number) given mobile experiences a very high or low shared rate. These results are then used to evaluate and optimize the system-level Quality of Service (QoS) and system-level capacity to support mobile users sharing 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 taken into account.

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