Abstract
In this chapter, we study the connectivity of one-dimensional small to medium sized networks with and without infrastructure support. Different from the connectivity of large static networks and dynamic networks where asymptotic analysis is a major tool used in the analysis, for small to medium sized networks, the number of nodes in the network is not necessarily large enough to warrant the use of asymptotic analysis. Therefore, for small to medium sized networks, our focus is on characterizing three related connectivity measures, collectively called the probabilities of k-hop connection or hop count statistics, viz., 1) the probability that a randomly selected node is k-hops apart from another randomly selected node, i.e., the length of the shortest path from the first node to the second node measured by the number of hops is k; 2) the probability that a node \(\boldsymbol{x}\) apart from another node is connected to that node in exactly k hops; and 3) the spatial distribution of the nodes k-hops apart from another designated node. In this chapter, we investigate the aforementioned three connectivity measures for one-dimensional small to medium sized networks with and without infrastructure support.
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Bibliography
Banerjee, N., Corner, M.D., Towsley, D., Levine, B.N.: Relays, base stations, and meshes: Enhancing mobile networks with infrastructure. In: ACM International Conference on Mobile Computing and Networking, pp. 81–91 (2008)
Benyamina, D., Hafid, A., Gendreau, M.: Wireless mesh networks design - a survey. IEEE Commun. Surv. Tutorials 14 (2), 299–310 (2012)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Conti, M., Giordano, S.: Multihop ad hoc networking: The reality. IEEE Commun. Mag. 45 (4), 88–95 (2007)
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the lambert w function. Adv. Comput. Math. 5 (1), 329–359 (1996)
David, H.A.: Order Statistics. Wiley, New York (1970)
De, S., Caruso, A., Chaira, T., Chessa, S.: Bounds on hop distance in greedy routing approach in wireless ad hoc networks. Int. J. Wirel. Mob. Comput. 1 (2), 131–140 (2006)
Desai, M., Manjunath, D.: On the connectivity in finite ad hoc networks. IEEE Commun. Lett. 6 (10), 437–439 (2002)
Dousse, O., Thiran, P., Hasler, M.: Connectivity in ad-hoc and hybrid networks. In: IEEE INFOCOM, pp. 1079–1088
Dulman, S., Havinga, P.: Statistically enhanced localization schemes for randomly deployed wireless sensor networks. In: Proceedings of the Intelligent Sensors, Sensor Networks and Information Processing Conference, pp. 403–410 (2004)
Foh, C.H., Lee, B.S.: A closed form network connectivity formula for one-dimensional MANETs. In: IEEE International Conference on Communications, vol. 6, pp. 3739–3742 (2004)
Gerla, M.: From battlefields to urban grids: New research challenges in ad hoc wireless networks. Pervasive Mob. Comput. 1 (1), 77–93 (2005)
Ghasemi, A., Nader-Esfahani, S.: Exact probability of connectivity in one-dimensional ad hoc wireless networks. IEEE Commun. Lett. 10 (4), 251–253 (2006)
Ghasemi, A., Sousa, E.S.: Asymptotic performance of collaborative spectrum sensing under correlated log-normal shadowing. IEEE Commun. Lett. 11 (1), 34–36 (2007)
Godehardt, E., Jaworski, J.: On the connectivity of a random interval graph. Random Struct. Algorithm 9 (1 and 2), 137–161 (1996)
Gudmundson, M.: Correlation model for shadow fading in mobile radio systems. Electron. Lett. 27 (23), 2145–2146 (1991)
Kashyap, A., Khuller, S., Shayman, M.: Relay placement for higher order connectivity in wireless sensor networks. In: IEEE INFOCOM, pp. 1–12 (2006)
Li, J.S., Kao, H.C., Ke, J.D.: Voronoi-based relay placement scheme for wireless sensor networks. IET Commun. 3 (4), 530–538 (2009)
Mainwaring, A., Culler, D., Polastre, J., Szewczyk, R., Anderson, J.: Wireless sensor networks for habitat monitoring. In: ACM international Workshop on Wireless Sensor Networks and Applications, pp. 88–97 (2002)
Miller, L.E.: Distribution of link distances in a wireless network. J. Res. Natl. Inst. Stand. Technol. 106 (2), 401–412 (2001)
Miorandi, D., Altman, E.: Connectivity in one-dimensional ad hoc networks: a queueing theoretical approach. Wirel. Netw. 12 (5), 573–587 (2006)
Rappaport, T.S.: Wireless Communications: Principles and Practice. Prentice Hall Communications Engineering and Emerging Technologies Series. Prentice Hall, Englewood Cliffs (2002)
Yamamoto, K., Kusuda, A., Yoshida, S.: Impact of shadowing correlation on coverage of multihop cellular systems. In: IEEE International Conference on Communications, pp. 4538–4542 (2006)
Yang, Y., Hu, H., Xu, J., Mao, G.: Relay technologies for wimax and lte-advanced mobile systems. IEEE Commun. Mag. 47 (10), 100–105 (2009)
Zhao, L., Liang, Q.: Hop-distance estimation in wireless sensor networks with applications to resource allocation. EURASIP J. Wirel. Commun. Netw. 2007, 1–8 (2007)
Zorzi, M., Rao, R.R.: Geographic random forwarding (geraf) for ad hoc and sensor networks: energy and latency performance. IEEE Trans. Mob. Comput. 2 (4), 349–365 (2003)
Zorzi, M., Rao, R.R.: Geographic random forwarding (geraf) for ad hoc and sensor networks: multihop performance. IEEE Trans. Mob. Comput. 2 (4), 337–348 (2003)
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Mao, G. (2017). Connectivity of One-Dimensional Small to Medium Sized Networks. In: Connectivity of Communication Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-52989-9_11
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DOI: https://doi.org/10.1007/978-3-319-52989-9_11
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