Abstract
This paper investigates connectivity in one-dimensional ad hoc networks by means of the distribution of the minimum hop count between source and destination nodes. We derive the exact probability distribution of the minimum hop count from the location density of relay nodes in the multihop path selected with the Most Forward within Radius (MFR) scheme. The probability that the source and destination nodes are connected (provided by Ghasemi and Nader-Esfahani [IEEE Commun. Lett. 10(4):251–253, 2006]) can be obtained by summing the probability masses for each possible value of the minimum hop count, which provides new insights to the connectivity probability. Numerical results show the effect of the number of nodes and the transmission range on the minimum hop count.
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References
Bettstetter, C. (2002). On the minimum node degree and connectivity of a wireless multihop network. In Proceedings of the ACM MobiHoc (pp. 80–91).
Camp, T., Boleng, J., & Davies, V. (2002). A survey of mobility models for ad hoc network research. Wireless Communications and Mobile Computing, 2(5), 483–502.
Desai, M., & Manjunath, D. (2002). On the connectivity in finite ad hoc networks. IEEE Communications Letters, 6(10), 437–439.
Domb, C. (1952). On the use of a random parameter in combinatorial problems. Proceedings Physical Society, Section A, 65(1), 305–309.
Foh, C. H., & Lee, B. S. (2004). A closed form network connectivity formula for one-dimensional MANETs. In Proceedings of the IEEE ICC 2004 (Vol. 6, pp. 3739–3742).
Foh, C. H., Liu, G., Lee, B. S., Seet, B.-C., Wong, K.-J., & Fu, C. P. (2005). Network connectivity of one-dimensional MANETs with random waypoint movement. IEEE Communications Letters, 9(1), 31–33.
Ghasemi, A., & Nader-Esfahani, S. (2006). Exact probability of connectivity in one-dimensional ad hoc wireless networks. IEEE Communications Letters, 10(4), 251–253.
Hyytia, E., Lassila, P., Penttinen, P., & Roszik, J. (2005). Traffic load in a dense wireless multihop network, In Proceedings of the 2nd ACM international workshop on performance evaluation of wireless ad hoc, sensor, and ubiquitous networks (pp. 9–17).
Jiang, S., & Rao, J. (2005). A prediction-based link availability estimation for routing metrics in MANETs. IEEE/ACM Transactions on Networking, 13(6), 1302–1312.
Kulkarni, V. G. (1995). Modeling and analysis of stochastic systems. New York: Chapman and Hall.
Li, J., Andrew, L. L. H., Foh, C. H., Zukerman, M., & Neuts, M. F. (2006). Meeting connectivity requirements in a wireless multihop network. IEEE Communications Letters, 10(1), 19–21.
Santi, P., & Blough, D. M. (2003). The critical transmitting range for connectivity in sparse wireless ad hoc networks. IEEE Transactions on Mobile Computing, 2(1), 25–39.
Takagi, H., & Kleinrock, L. (1984). Optimal transmission ranges for randomly distributed packet radio terminals. IEEE Transactions on Communications, 32(3), 246–257.
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Antunes, N., Jacinto, G. & Pacheco, A. On the minimum hop count and connectivity in one-dimensional ad hoc wireless networks. Telecommun Syst 39, 137–143 (2008). https://doi.org/10.1007/s11235-008-9118-9
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DOI: https://doi.org/10.1007/s11235-008-9118-9