Abstract
We consider the behavior of mobile users that, upon depletion of their device's energy, 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.
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