On the Impact of Recharging Behavior on Mobility

We consider the behavior of mobile users that, upon depletion of their device's energy due to communication, can detour from their regular path, in order to reach a location where the device can be recharged. We develop abstractions of this recharging behavior and analytically derive a charging-aware mobility model. The device is viewed as a mobile node. Based on the Palm inversion formula, we derive the (integral-form) stationary probability density function of the node's location, subject to attraction exerted by one charger in a bounded convex area. The analytical and numerical results demonstrate the distortion effect the charger has on the spatial node distribution. We observe, and explain, a counter-intuitive effect whereby the node density exhibits peaks that are asymmetric, coupled with a relative decrease of the density around the charger area. In addition, we provide a method to approximate the probability density function when multiple chargers are deployed. We examine the accuracy of this approximation and comment on its limitations.