A NUMERICAL STUDY OF LINK AND PATH DURATIONS IN MOBILE AD HOC NETWORKS by

Title of thesis: A NUMERICAL STUDY OF LINK AND PATH DURATIONS IN MOBILE AD HOC NETWORKS Hongqiang Zhang, Master of Science, 2006 Thesis directed by: Professor Richard La Department of Electrical and Computer Engineering A theoretical analysis has shown that under a set of assumptions, the distribution of path duration can be well approximated by an exponential distribution when the path hop count is sufficiently large. The goal of this thesis is two folds: Using NS-2 simulations to (i) Investigate how fast the path distributional convergence takes place, and how quickly the inverse of the expected duration of a path converges to the sum of the inverses of the expected durations of the links along the path, and (ii) Validate the conditions under which the distributional convergence is established. Simulations are run under four different mobility models and two different ondemand routing protocols. Simulation results show that the path duration distribution can be accurately approximated by an exponential distribution for path hop count larger than 5 or 6 with fitting error less than 0.05 using Kolmogorov-Smirnov test (K-S test) for all considered scenarios. However, the ratio of the inverse of the expected path duration to the sum of the inverses of the expected link durations along the path does not get close to one for path hop count less than 12 in the cases of all considered scenarios. We validate two mixing conditions for all considered scenarios. Specifically, a sufficient condition for one mixing condition is validated. Simulation results show that the probability of one link excess life less than a positive number conditioned on the excess life of another link in the same path less than the same number behaves similarly as the CDF of the link excess life as the number decreases to 0. Based on the observation that the correlation coefficients of link excess lives decrease with increasing hop distance, instead of directly validating the second mixing condition, we validate a condition that suggests that indeed the second mixing condition is likely to hold in a large scale network. Simulation results show that the difference between the joint CDF of two link excess lives and the product of their marginal CDFs decreases as the hop distance between the two links increases. A NUMERICAL STUDY OF LINK AND PATH DURATIONS IN MOBILE AD HOC NETWORKS