Abstract
In this chapter, we continue to investigate connectivity of two-dimensional small to medium sized networks by analyzing the three connectivity related measures: 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, which are collectively called the probabilities of k-hop connection or hop count statistics. We start with networks assuming the unit disk connection model and then move to networks assuming the random connection model and the log-normal connection model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Agrawal, P., Patwari, N.: Correlated link shadow fading in multi-hop wireless networks. IEEE Trans. Wirel. Commun. 8 (8), 4024–4036 (2009). URL 10.1109/TWC.2009.071293
Bettstetter, C., Hartmann, C.: Connectivity of wireless multihop networks in a shadow fading environment. Wirel. Netw. 11 (5), 571–579 (2005)
Carvalho, M.M., Garcia-Luna-Aceves, J.J.: Delay analysis of ieee 802.11 in single-hop networks. In: IEEE International Conference on Network Protocols, pp. 146–155 (2003)
Chandler, S.A.G.: Calculation of number of relay hops required in randomly located radio network. Electron. Lett. 25 (24), 1669–1671 (1989)
Contla, P.A., Stojmenovic, M.: Estimating hop counts in position based routing schemes for ad hoc networks. Telecommun. Syst. 22 (1), 109–118 (2003)
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)
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)
Dulman, S., Rossi, M., Havinga, P., Zorzi, M.: On the hop count statistics for randomly deployed wireless sensor networks. Int. J. Sens. Netw. 1 (1/2), 89–102 (2006)
G.Xing, Lu, C., Pless, R., Huang, Q.: Impact of sensing coverage on greedy geographic routing algorithms. IEEE Trans. Parallel Distrib. Syst. 17 (4), 348–360 (2006)
Hekmat, R., Mieghem, P.V.: Connectivity in wireless ad-hoc networks with a log-normal radio model. Mob. Netw. Appl. 11 (3), 351–360 (2006)
Khalil, I., Bagchi, S., Shroff, N.: Liteworp: A lightweight countermeasure for the wormhole attack in multihop wireless networks. In: Proceedings of the 2005 International Conference on Dependable Systems and Networks, pp. 612–621 (2005)
Lo, N., Kuo, H.Y.: Two-hops neighbor-aware routing protocol in mobile ad hoc networks. In: Lecture Notes in Computer Science, vol. 4611/2007, pp. 340–349 (2008)
Mallery, C.J., Medidi, S., Medidi, M.: Relative localization with 2-hop neighborhood. In: International Symposium on a World of Wireless, Mobile and Multimedia Networks, pp. 1–4 (2008)
Miller, L.E.: Distribution of link distances in a wireless network. J. Res. Natl. Inst. Stand. Technol. 106 (2), 401–412 (2001)
Moin, P.: Fundamentals of Engineering Numerical Analysis. Cambridge University Press, Cambridge (2001)
Mukherjee, S., Avidor, D.: Connectivity and transmit-energy considerations between any pair of nodes in a wireless ad hoc network subject to fading. IEEE Trans. Veh. Technol. 57 (2), 1226–1242 (2008)
Nelson, R.: Probability, Stochastic Processes, and Qqueueing Theory: The Mathematics of Computer Performance Modelling. Springer, New York (1995)
Rajabi, S., Shahabadi, M., ArdebiliPoor, M.: Modeling of the correlation coefficients of a receive antenna array in a mimo multipath channel. In: The 2nd IEEE/IFIP International Conference in Central Asia on Internet, pp. 1–4 (2006). URL 10.1109/CANET.2006.279251
Rappaport, T.S.: Wireless Communications: Principles and Practice. Prentice Hall Communications Engineering and Emerging Technologies Series. Prentice Hall, Englewood Cliffs (2002)
Simon, M.K., Alouini, M.S.: Digital Communication Over Fading Channels. Wiley, New York (2000)
Wang, C.X., Patzold, M., Yao, Q.: Stochastic modeling and simulation of frequency-correlated wideband fading channels. IEEE Trans. Veh. Technol. 56 (3), 1050–1063 (2007). URL 10.1109/TVT.2007.895490
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)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Mao, G. (2017). Connectivity of Two-Dimensional Small to Medium Sized Networks. In: Connectivity of Communication Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-52989-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-52989-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52988-2
Online ISBN: 978-3-319-52989-9
eBook Packages: EngineeringEngineering (R0)