The critical transmitting range for connectivity in mobile ad hoc networks

In this paper, we have investigated the critical transmitting range for connectivity in mobile ad hoc networks. We have proven that, in the presence of bounded and obstacle free mobility, the CTR in the mobile case is at least as large as the CTR in the case of uniformly distributed points (asymptotically). For the case of RWP mobility, we have proven a more accurate characterization of the CTR and shown that, if the pause time is 0, there is an asymptotic gap between the mobile and uniform scenario. We have verified the quality of our results through simulation. We have also presented a formula that, given the value of the CTR in the uniform case, provides a good approximation of the CTR in the most extreme case of RWP mobility, i.e., when the pause time is set to 0. We want to remark that the approach presented in this paper can be easily extended to other mobility models: If the expression of the pdf f_m that resembles the long-term node distribution is known and satisfies certain properties, it is sufficient to compute the minimum value of f_m on R to determine the value of the critical range for connectivity. We believe that the results presented in this paper provide a better understanding of the behavior of a fundamental network parameter in the presence of mobility and, in particular, of RWP mobility. From a practical point of view, our results can be used to improve the accuracy of RWP mobile ad hoc networks simulation, which is commonly used to evaluate the performance of ad hoc networking protocols.