Soft Computing

, Volume 21, Issue 10, pp 2619–2629 | Cite as

Uncertain random spectra: a new metric for assessing the survivability of mobile wireless sensor networks

  • Li Xu
  • Jing Zhang
  • Pei-Wei Tsai
  • Wei Wu
  • Da-Jin Wang
Methodologies and Application


In this paper, a soft computing method, a probability theory, and a graph theoretic approach are utilized to describe this phenomenon. Uncertain random spectra, namely, natural tenacity, are established in this paper for assessing the survivability of MWSNs. We propose an elaborate mathematical formulation that relates the survivability to the natural tenacity. In addition, then the probability of link connectivity is proposed in order to connect the natural tenacity to the connectivity of the network, which reflects the most important indicators of network survivability. The natural tenacity of MWSNs is explored by both analytical and numerical ways. Moreover, we also compare it with other survivability measures. Under the smooth Gauss–semi-Markov mobility model, the effectiveness of the measure is verified through numerical analysis. The result indicates that the natural tenacity has a strong analytical ability to measure the survivability of MWSNs objectively.


Uncertainty theory Probability theory Natural tenacity Semi-Markov process Spectra 



The authors wish to thank National Natural Science Foundation of China (Grant no.: 61072080, U1405255). Fujian Normal University Innovative Research Team (no.: IRTL1207). The development project of Fujian provincial strategic emerging industries technologies: Key technologies in development of next generation Integrated High Performance Gateway, Fujian development and reform commission high-technical [2013]266. Key Project of Ministry of Education in Fujian Province (No.: JA15323, JA15329).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


  1. Akyildiz LF, Su W, Sankarasubramaniam Y, Cayirci E (2002) A survey on sensor networks. IEEE Commun Mag 40(8):102–114CrossRefGoogle Scholar
  2. Albert R, Jeong H, Barabasi AL (2000) Error and attack tolerance of complex networks. Nature 406:378–382CrossRefGoogle Scholar
  3. Aggarwal A, Garg B (2012) Survey on secure AODV for ad hoc networks routing mechanism. Int J Adv Res Comput Sci Softw Eng 2(3):203–206Google Scholar
  4. Bauer G, Bolch G (1990) Analytical approach to discrete optimization of queuing-networks. Comput Commun 13:494–502CrossRefGoogle Scholar
  5. Chen JIZ, Yeh LT (2012) Environments aware for prolonging the lifetime of sensor nodes deployed in WSNs. Sci Res Eng 4:100–106Google Scholar
  6. Dai L, Shen Z, Chen T (2014) Analysis and modeling of task scheduling in wireless sensor network based on divisible load theory. Int J Commun Syst 27(5):721–731CrossRefGoogle Scholar
  7. Fiedler M (1983) Conditional connectivity. Networks 13:346–357MathSciNetGoogle Scholar
  8. Hu F, Xiao Y, Hao Q (2009) Congestion-aware, loss-resilient bio-monitoring sensor networking for mobile health applications. IEEE J Select Areas Commun 27(4):450–465CrossRefGoogle Scholar
  9. Lima MN, Santos A, Pujolle G (2009) A survey of survivability in mobile ad hoc networks. IEEE Commun Surv Tutor 11(1):66–77CrossRefGoogle Scholar
  10. Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. List Fig. 85:13.4Google Scholar
  11. Liu Y (2013) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634CrossRefMATHGoogle Scholar
  12. Peng SC, Jia WJ, Wang GJ (2009) Survivability evaluation in large-scale mobile ad-hoc networks. J Comput Sci Technol 24(4):761–774CrossRefGoogle Scholar
  13. Peng SC, Wang G, Hu Z (2011) Survivability modeling and analysis on 3D mobile ad-hoc networks. Springer J Cent South Univ Technol 18:1144–1152CrossRefGoogle Scholar
  14. Shen S, Han R, Guo L (2012) Survivability evaluation towards attacked WSNs based on stochastic game and continuous-time Markov chain. Appl Soft Comput 12:1467–1476CrossRefGoogle Scholar
  15. Tseng CC, Chen HT, Chen KC (2007) Distribution of the node degree for wireless ad hoc networks in shadow fading environments. IEICET Trans Commun 90-B(8):2155–2158Google Scholar
  16. Wang YC, Wu FJ, Tseng YC (2012) Mobility management algorithms and applications for mobile sensor networks. Wirel Commun Mobile Comput 12(1):7–21CrossRefGoogle Scholar
  17. Wang W, Zhao MH (2008) joint effects of radio channels and node mobility on link dynamics in wireless networks. In: The 27th conference on computer communications, IEEE, INFOCOM. 146:933–941Google Scholar
  18. Whitney H (1932) Congruent graphs and the connectivity of graphs. Am J Math 54:150–168MathSciNetCrossRefMATHGoogle Scholar
  19. Wu J, Barahona M, Tan Y (2011) Robustness of regular ring lattices based on natural connectivity. Int J Syst Sci 42(7):1085–1092MathSciNetCrossRefMATHGoogle Scholar
  20. Wu J, Barahona M, Tan Y (2012) Robustness of random graphs based on graph spectra. Chaos 22:1–7MathSciNetMATHGoogle Scholar
  21. Yue Z, Jia Y (2013) An application of soft computing technique in group decision making under interval-valued intuitionistic fuzzy environment. Appl Soft Comput 13(5):2490–2503CrossRefGoogle Scholar
  22. Zhao M (2009) Design, modeling, and analysis of user mobility and its impact on multi-hop wireless networks. In: A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy, Computer Engineering, Raleigh, North CarolinaGoogle Scholar
  23. Zhao M, Wang W (2009) A unified mobility model for analysis and simulation of mobile wireless networks. Wirel Netw 15:365–389Google Scholar
  24. Zhao M, Li Y, Wang W (2012) Modeling and analytical study of link properties in multihop wireless networks. IEEE Trans Commun 60(2):445–455CrossRefGoogle Scholar
  25. Zhang HY, Xu D, Liu YH (2008) A smooth Gauss–semi-Markov mobility model for wireless sensor networks. J Softw 19(7):1707–1715CrossRefGoogle Scholar
  26. Zhang Z, Yi Y, Yang J (2014) Energy efficiency based on joint mobile node grouping and data packet fragmentation in short-range communication system. Int J Commun Syst 27(4):534–550CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Li Xu
    • 1
  • Jing Zhang
    • 2
  • Pei-Wei Tsai
    • 2
  • Wei Wu
    • 1
  • Da-Jin Wang
    • 3
  1. 1.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouPeople’s Republic of China
  2. 2.School of Information Science and EngineeringFujian University of TechnologyFuzhouPeople’s Republic of China
  3. 3.Department of Computer ScienceMontclair State UniversityUpper MontclairUSA

Personalised recommendations