Theoretical estimation of border effect on epoch length distributions in wireless networks

Mobility models are often used in simulation and analysis. An epoch mobility model can describe many mobile behaviors with epoch length distributions. Here an epoch is a random time interval, during which a node keeps moving at a constant velocity. Since wireless networks such as Mobile Ad Hoc Networks are often deployed or tested in a bordered space, borders may force a node to change its motion. This motion change may severely twist epoch length distributions by truncating the original epoch lengths. Many epoch length distribution models in the literature are originally established for an open space without taking into account this effect. Using this kind of models in a bordered environment inevitably causes a mismatch between the assumption and the actual situation. This mismatch may further lead to misinterpretations of the observed results, and it is necessary to study this effect on the epoch length distribution and to find a method to accurately describe the mobile behavior in bordered spaces. This paper just studies these methods for exponential and uniform epoch distributions in circles.

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