## MOBILE AD HOC NETWORKS-ITS CONNECTIVITY AND ROUTING OVERHEAD

##### Abstract

This dissertation focuses on a study of network connectivity and routing overhead in mobile ad–hoc networks (MANETs). The first part examines the smallest communication range needed for bi–directional connectivity of a network, called the critical transmission range (CTR), under a class of group mobility models. In the second part, we study the smallest communication range of the nodes necessary for no node isolation when trust constraints are introduced for one–hop connectivity between nodes. In the third part, under the assumption that nodes employ the CTR for network connectivity in MANETs, we study the overhead required for location service under geographic routing.
We begin with an investigation of the communication range of the nodes necessary for network connectivity, which we call bi–directional connectivity, in one dimensional case. Unlike in most of existing studies, however, the locations or mobilities of the nodes are correlated through group mobility: Nodes are broken into groups, with each group comprising the same number of nodes, and lie on a unit circle. The locations of the nodes in the same group are not mutually independent, but are instead conditionally independent given the location of the group.
We examine the distribution of the CTR when both the number of groups and the number of nodes in a group are large. We first demonstrate that the CTR exhibits a parametric sensitivity with respect to the space each group occupies on the unit circle. Then, we offer an explanation for the observed sensitivity by identifying what is known as a very strong threshold and asymptotic bounds for CTR.
Related to the first part, we explore the communication range of the nodes necessary for no node isolation where the locations of nodes are mutually independent and uniformly distributed on a torus. However, unlike in our first study where the one–hop connectivity between two nodes depends only on their distance, one-hop connectivity of two nodes in this model is determined by both geometric and trust constraints. More specifically, in order to have a communication link between two nodes, they should be within a certain common communication range and satisfy trust requirements, i.e., the trust level of a node exceeds the required trust threshold of the other. Under this one–hop connectivity model, we find the smallest communication range needed so that no node will be isolated. While our analytical study focuses on the probability that no node will be isolated, our simulation results suggest that the probability of no node isolation and the probability of network connectivity behave very similarly.
In the third part of this dissertation, we study routing overhead due to location information collection and retrieval in MANETs employing geographic routing with no hierarchy. We first provide a new framework for quantifying overhead due to control messages generated to exchange location information. Second, we compute the minimum number of bits required on average to describe the locations of a node, borrowing tools from information theory. This result is then used to demonstrate that the expected overhead is Ω(n^{1.5} log(n)), where n is the number of nodes, under both proactive and reactive geographic routing, with the assumptions that (i) nodes' mobility is independent and (ii) nodes adjust their transmission range to maintain network connectivity. Finally, we prove that the minimum expected overhead under the same assumptions is Θ(n log(n)).

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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