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

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Abstract

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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Notes

  1. As mentioned earlier, the border can influence the node distribution and the probability where a node starts its motion [4, 5, 10]. The uniform assumption here is mainly used to simplify the H(l) derivation.

  2. Refer to http://mathworld.wolfram.com/IncompleteGammaFunction.html for more detail on \(\Upgamma[0,z]\).

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Acknowledgments

The author would like to take this opportunity to sincerely thank he anonymous Reviewers and the Editors for their valuable and constructive comments to the paper.

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  1. College of Information Engineering, Shanghai Maritime University, Shanghai, China

    Shengming Jiang

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  1. Shengming Jiang
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Correspondence to Shengming Jiang.

Additional information

Part of this work was published in the International Workshop on Performance Evaluation of Wireless Networks in conjunction with the Fifth International Conference on Mobile Ad-Hoc and Sensor Networks (MSN), December, 2009, China.

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Jiang, S. Theoretical estimation of border effect on epoch length distributions in wireless networks. Wireless Netw 20, 705–718 (2014). https://doi.org/10.1007/s11276-013-0633-6

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