Journal of Engineering Mathematics

, Volume 79, Issue 1, pp 183–199 | Cite as

Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling

  • Nathanial BurchEmail author
  • Edwin K. P. Chong
  • Don Estep
  • Jan Hannig


The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of large networks with continuum models. In this paper, we introduce nonlinear partial differential equations whose solutions approximate the expected behavior of large networks governed by probabilistic communication rules. The relative speed at which solutions can be obtained from the continuum models allows for the investigation of routing protocols and communication limitations due to interference—a feat that is not feasible via simulation methods. Specifically, we investigate the effects of a directed diffusion routing protocol and explore communication limitations in an interference-sensitive network. Network design studies using the approximating continuum models are then presented.


Continuum modeling Network design Stochastic network simulation Wireless ad hoc networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chiasserini CF, Gaeta R, Garetto M, Gribaudo M, Manini D, Sereno M (2007) Fluid models for large-scale wireless sensor networks. Perform Eval 64(7–8): 715–736CrossRefGoogle Scholar
  2. 2.
    Chong EKP, Estep D, Hannig J (2007) Continuum modeling of large networks. Int J Numer Model Electron Netw Devices Fields 21(3): 169–186CrossRefGoogle Scholar
  3. 3.
    Hart JK, Martinez K (2006) Environmental sensor networks: a revolution in the earth system science?. Earth-Sci Rev 78(3–4): 177–191ADSCrossRefGoogle Scholar
  4. 4.
    Estrin D, Govindan R, Heidemann J, Kumar S (1999) Next century challenges: scalable coordination in sensor networks. In: Proceedings of the 5th annual ACM/IEEE international conference on mobile computing and networking. ACM, New York, pp 263–270Google Scholar
  5. 5.
    Lees JM, Johnson JB, Ruiz M, Troncoso L, Welsh M (2008) Reventador volcano 2005: eruptive activity inferred from seismo-acoustic observation. J Volcanol Geotherm Res 176(1): 179–190ADSCrossRefGoogle Scholar
  6. 6.
    Werner-Allen G, Dawson-Haggerty S, Welsh M (2008) Lance: optimizing high-resolution signal collection in wireless sensor networks. In: Proceedings of the 6th ACM conference on embedded network sensor systems. ACM, New York, pp 169–182Google Scholar
  7. 7.
    Tolle G, Polastre J, Szewczyk R, Turner N, Tu K, Buonadonna P, Burgess S, Gay D, Hong W, Dawson T, Culler D (2005) A macroscope in the redwoods. In: Proceedings of the 3rd international conference on embedded networked sensor systems. ACM, New York, p 63Google Scholar
  8. 8.
    Akyildiz IF, Su W, Sankarasubramaniam Y, Cayirci E (2002) Wireless sensor networks: a survey. Comput Netw 38(4): 393–422CrossRefGoogle Scholar
  9. 9.
    Martinez K, Hart JK, Ong R (2004) Environmental sensor networks. Computer 37(8): 50–56CrossRefGoogle Scholar
  10. 10.
    Gamal HE (2005) On the scaling laws of dense wireless sensor networks: the data gathering channel. IEEE Trans Inf Theory 51(3): 1229–1234CrossRefGoogle Scholar
  11. 11.
    Toumpis S, Tassiulas L (2005) Packetostatics: deployment of massively dense sensor networks as an electrostatics problem. In: INFOCOM 2005. 24th Annual joint conference of the IEEE computer and communications societies. Proceedings IEEE, vol 4. IEEE, pp 2290–2301Google Scholar
  12. 12.
    Toumpis S, Tassiulas L (2006) Optimal deployment of large wireless sensor networks. IEEE Trans Inf Theory 52(7): 2935–2953MathSciNetCrossRefGoogle Scholar
  13. 13.
    Ganesan D, Krishnamachari B, Woo A, Culler D, Estrin D, Wicker S (2002) Complex behavior at scale: an experimental study of low-power wireless sensor networks. Technical report, CiteseerGoogle Scholar
  14. 14.
    Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Inf Theory 46(2): 388–404MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Herdtner JD, Chong EKP (2005) Throughput-storage tradeoff in ad hoc networks. In: Proceedings IEEE INFOCOM 2005. 24th Annual joint conference of the IEEE computer and communications societies, vol 4Google Scholar
  16. 16.
    Li J, Blake C, De Couto DSJ, Lee HI, Morris R (2001) Capacity of ad hoc wireless networks. In: Proceedings of the 7th annual international conference on mobile computing and networking. ACM, New York, p 69Google Scholar
  17. 17.
    Xie LL, Kumar PR (2004) A network information theory for wireless communication: scaling laws and optimal operation. IEEE Trans Inf Theory 50(5): 748–767MathSciNetCrossRefGoogle Scholar
  18. 18.
    Jain K, Padhye J, Padmanabhan VN, Qiu L (2005) Impact of interference on multi-hop wireless network performance. Wirel Netw 11(4): 471–487CrossRefGoogle Scholar
  19. 19.
    Klein DJ, Hespanha J, Madhow U (2010) A reaction-diffusion model for epidemic routing in sparsely connected MANETs. In: INFOCOM, 2010 proceedings IEEE. IEEE, pp 1–9Google Scholar
  20. 20.
    Kalantari M, Shayman M (2004) Energy efficient routing in wireless sensor networks. In: Proceedings of conference on information sciences and systems, CiteseerGoogle Scholar
  21. 21.
    Kalantari M, Shayman M (2004) Routing in wireless ad hoc networks by analogy to electrostatic theory. In: 2004 IEEE international conference on communications, vol 7. IEEE, pp 4028–4033Google Scholar
  22. 22.
    Kalantari M, Haghpanahi M, Shayman M (2008) A p-norm flow optimization problem in dense wireless sensor networks. In: INFOCOM 2008. The 27th conference on computer communications. IEEE, pp 341–345Google Scholar
  23. 23.
    Zhang Y, Chong EKP, Hannig J, Estep D (2010) On continuum limits of Markov chains and network modeling. In: 2010 49th IEEE conference on decision and control (CDC), pp 6779–6784. IEEEGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Nathanial Burch
    • 1
    Email author
  • Edwin K. P. Chong
    • 2
    • 4
  • Don Estep
    • 3
    • 4
  • Jan Hannig
    • 5
  1. 1.Statistical and Applied Mathematical Sciences InstituteResearch Triangle ParkUSA
  2. 2.Department of Electrical and Computer EngineeringColorado State UniversityFort CollinsUSA
  3. 3.Department of StatisticsColorado State UniversityFort CollinsUSA
  4. 4.Department of MathematicsColorado State UniversityFort CollinsUSA
  5. 5.Department of Statistics and Operations ResearchUniversity of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations