Abstract
The concept of small world phenomenon has been observed and applied in many types of networks. This paper presents a study of two small-world network models in clustering formation and routing in wireless network, the Watts and Stragtz’s (WS) and the Newman and Watts (NW) models and evaluates their properties in term of average node degree and path length. We tested the small world phenomenon in wireless networks by simulating a wireless mobile ad hoc network with distributed routing protocols. We present the research challenges of bridging the gap between theoretical models and practical wireless network implementation. This study provides insights on how wireless networks behave under small world network models with distributed routing protocols.
References
Middleton, J. 3UKoffloads network traffic ontoWiFi. [Online].Available
at: http://telecoms.com/268022/3-uk-offloads-network-traffic-onto-wifi/
Watts, D. J., and Strogatz, S. H. (1998). Collective dynamics of ‘smallworld’
networks. Nature, 393, 440–442.
Barab´asi, A.-L., and Albert, R. (1999). Emergence of scaling in random
networks. Science, 286, 509–512.
Watts, D. J. (1999). Small worlds: the dynamics of networks between
order and randomness. Princeton university press, Princeton.
Travers, J., and Milgram, S. (1969) An experimental study of the small
world problem. Sociometry, 32, 425–443.
Liu, C.-Y., Hu, X.-F., Si, G.-Y., and Luo. (2006). Public opinion
propagation model based on small world networks. J. Syst. Simul.
, 070.
Wang, B., Wang, W.-L., and Yang, X.-H., et al. (2009). Research of
modeling and simulation on WS and NWsmall-world network model. J.
Zhejiang Univ. Technol. 37, 179–189, 2009.
Humphries, M. D., and Gurney, K. (2008). Network smallworld-ness:
a quantitative method for determining canonical network equivalence.
PloS One, 3, p. e0002051
Small world exercises. [Online]. Available at: http://pages.physics.corn
ell.edu/∼myers/teaching/ComputationalMethods/ComputerExercises/S
mallWorld/SmallWorld.html
Helmy, A. (2003). Small worlds in wireless networks. Commun. Lett.
IEEE, 710, 490–492.
Mei, A., and Stefa, J. (2009). “Swim: A simple model to generate small
mobile worlds,” in INFOCOM 2009, IEEE 2009, 2106–2113.
Karp, B., and Kung, H.-T. (2000). “GPSR: Greedy perimeter stateless
routing for wireless networks,” in Proceedings of the 6th annual
international conference on Mobile computing and networking, ACM,
–254.
Yamazaki, K. (2002). Geographical routing protocol for the locationaware
services. IEICE, Japan.
N. working group. Optimized link state routing protocol (OLSR).
[Online]. Available at: https://tools.ietf.org/html/rfc3626
Dong, Z.,Wang, Z., Xie,W., Emelumadu, O., Lin, C., and Rojas-Cessa,
R. (2015). “An experimental study of small world network model for
wireless networks,” in Proceeding of the Sarnoff Symposium, 2015 36th
IEEE, 70–75, 20–22 September 2015, New York, NY.
Ping program. [Online]. Available at: http://linux.die.net/man/8/ping