Estimations of Border Effect on Epoch Mobility Models in Mobile Ad Hoc Networks

Mobility models are often used to evaluate performances of mobile networks through either analysis or simulation. The epoch mobility model is one of important mobility models that can statistically describe mobile behavior in general. Here an epoch is a random length interval during which a node is supposed to move at a constant velocity. However, a border may force a node to change its motion during an epoch. This phenomenon is often called border effect in the literature. In this case, the original mobility model cannot reflect the real mobile behavior, and it is necessary to study border effect in depth. Epoch distribution is the key to epoch mobility models and may be severely impacted by border effect. Therefore, this paper discusses how to use geometric probability to estimate affected epoch distributions by proposing some methods to calculate border hitting probabilities and estimate epoch distributions that are affected by border effect. A simulation study is also conducted to verify the proposed methods and shows that they can provide good estimations.