On the connectivity of a random interval graph
Proceedings of the seventh international conference on Random structures and algorithms
The number of neighbors needed for connectivity of wireless networks
Wireless Networks
Threshold Functions for Random Graphs on a Line Segment
Combinatorics, Probability and Computing
On k-coverage in a mostly sleeping sensor network
Proceedings of the 10th annual international conference on Mobile computing and networking
The bin-covering technique for thresholding random geometric graph properties
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Reliable density estimates for coverage and connectivity in thin strips of finite length
Proceedings of the 13th annual ACM international conference on Mobile computing and networking
The capacity of wireless networks
IEEE Transactions on Information Theory
Towards an information theory of large networks: an achievable rate region
IEEE Transactions on Information Theory
IEEE Journal on Selected Areas in Communications
Results on finite wireless sensor networks: Connectivity and coverage
ACM Transactions on Sensor Networks (TOSN)
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Analysis of finite wireless networks is a fundamental problem in the area of wireless networking. Today, due to the vast amount of literature on large-scale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. We refer to networks as being finite when the number of nodes is less than a few hundred. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the network's properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the Medium Access (MAC) layer capacity, i.e. the maximum number of possible concurrent transmissions. Towards this goal, we provide a linear time algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity.